Algebra — XAT Previous-Year Questions
190 previous-year questions on Algebra from XAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Algebra · XAT PYQs
In a small college, students are allowed to take only one specialization. Traditionally, only two specializations are offered: Science and Arts. Students enrolled to specialize in Science must take Physics and Mathematics subjects, while students enrolled to specialize in Arts must take Economics and Political Science subjects. Students enrolled in Science are not allowed to take either Economics or Political Science, while students enrolled in Arts are not allowed to take either Physics or Mathematics.
Recently, the college has started a third specialization called MatEco that requires students to take Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or Political Science. When the college opens this new specialization for enrolment, it allows students, originally enrolled in Science or Arts, to switch to MatEco. From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number of Science students twice the number of Arts students. After this, from among the students who originally enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the number of Science students.
In total, how many students, from among those originally enrolled in Science or Arts, are now taking Economics?
In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic progression. The total number of students from Class I to V is twice the total number of students from Class VI to X. If the total number of students from Class I to IV is 462, how many students are there in Class VI?
Consider the equation , where x is a real number log5(x - 2) = 2log25(2x - 4).
For how many different values of x does the given equation hold?
The least common multiple of a number and 990 is 6930. The greatest common divisor of that number and 550 is 110. What is the sum of the digits of the least possible value of that number?
Consider the system of two linear equations as follows: 3x + 21y + p = 0; and qx + ry – 7 = 0, where p, q, and r are real numbers.
Which of the following statements DEFINITELY CONTRADICTS the fact that the lines represented by the two equations are coinciding?
Consider a 4-digit number of the form abbb, i.e., the first digit is a (a > 0) and the last three digits are all b. Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4-digit number is divisible by a?
Read the following scenario and answer the TWO questions that follow.
Aman has come to the market with Rs. 100. If he buys 5 kilograms of cabbage and 4 kilograms of potato, he will have Rs. 20 left; or else, if he buys 4 kilograms of cabbage and 5 kilograms of onion, he will have Rs. 7 left. The per kilogram prices of cabbage, onion and potato are positive integers (in rupees), and any type of these vegetables can only be purchased in positive integer kilogram, or none at all.
Aman decides to buy only onion, in whatever maximum quantity possible (in positive integer kilogram), with the money he has come to the market with.
How much money will he be left with after the purchase?
Read the following scenario and answer the TWO questions that follow.
Aman has come to the market with Rs. 100. If he buys 5 kilograms of cabbage and 4 kilograms of potato, he will have Rs. 20 left; or else, if he buys 4 kilograms of cabbage and 5 kilograms of onion, he will have Rs. 7 left. The per kilogram prices of cabbage, onion and potato are positive integers (in rupees), and any type of these vegetables can only be purchased in positive integer kilogram, or none at all.
Aman decides to buy only onion and potato, both in positive integer kilogram, in such a way that the money left with him after the purchase will be insufficient to buy a full kilogram of either of the two vegetables.
If all such permissible combinations of purchases are equally likely, what is the probability that Aman buys more onion than potato?
Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?
Suppose Haruka has a special key â in her calculator called delta key:
Rule 1: If the display shows a one-digit number, pressing delta key â replaces the displayed number with twice its value.
Rule 2: If the display shows a two-digit number, pressing delta key â replaces the displayed number with the sum of the two digits.
Suppose Haruka enters the value 1 and then presses delta key â repeatedly.
After pressing the â key for 68 times, what will be the displayed number?
There are three sections in a question paper and each section has 10 questions. First section only has multiple-choice questions, and 2 marks will be awarded for each correct answer. For each wrong answer, 0.5 marks will be deducted. Any unattempted question in this section will be treated as a wrong answer. Each question in the second section carries 3 marks, whereas each question in the third section carries 5 marks. For any wrong answer or un-attempted question in the second and third sections, no marks will be deducted. A student’s score is the addition of marks obtained in all the three sections. What is the sixth highest possible score?
Let x and y be two positive integers and p be a prime number. If x(x – p) – y(y + p) = 7p, what will be the minimum value of x – y?
Consider an + 1 = for n = 1, 2, ...., 2008, 2009 where a1 = 1. Find the value of a1 a2 + a2 a3 + a3 a4 + ... + a2008 a2009
Given A = |x + 3| + |x - 2| - |2x - 8|. The maximum value of |A| is:
A supplier receives orders from 5 different buyers. Each buyer places their order only on a Monday. The first buyer places the order after every 2 weeks, the second buyer, after every 6 weeks, the third buyer, after every 8 weeks, the fourth buyer, every 4 weeks, and the fifth buyer, after every 3 weeks. It is known that on January 1st, which was a Monday, each of these five buyers placed an order with the supplier.
On how many occasions, in the same year, will these buyers place their orders together excluding the order placed on January 1st?
A marble is dropped from a height of 3 metres onto the ground. After the hitting theground, it bounces and reaches 80% of the height from which it was dropped. This repeats multiple times. Each time it bounces, the marble reaches 80% of the height previously reached. Eventually, the marble comes to rest on the ground.
What is the maximum distance that the marble travels from the time it was dropped until it comes to rest?
The sum of the cubes of two numbers is 128, while the sum of the reciprocals oftheir cubes is 2. What is the product of the squares of the numbers?
Nadeem’s age is a two-digit number X, squaring which yields a three-digit number,whose last digit is Y. Consider the statements below:
Statement I: Y is a prime number
Statement II: Y is one-third of X
To determine Nadeem’s age uniquely:
Read the following scenario and answer the THREE questions that follow.
An examination had ten multiple choice questions; labelled Q1 to Q10 respectively. Each question had four answer options — A, B, C and D — of which one and only one was the correct answer. For each correct answer, the candidate obtained 1 mark. There were no negative marks for wrong answers. The answers chosen by six candidates named Om, Pavan, Qadir, Rakesh, Simranjeet and Tracey to each of the ten questions and the total marks obtained by each of them are shown in the table.
âââââââ
Shireen draws a circle in her courtyard. She then measures the circle’s circumference and its diameter with her measuring tape and records them as two integers, A and B respectively. She finds that A and B are coprimes, that is, their greatest common divisor is 1. She also finds their ratio, A : B, to be: 3.141614161416… (repeating endlessly).
What is A - B?
Read the following scenario and answer the THREE questions that follow.
âââââââ
The given candlestick chart depicts the prices of a particular stock over 10 consecutive days. A candlestick comprises of a rectangular box pieced by a line. The top and bottom ends of the line respectively indicate the maximum and minimum prices of the stock on that day, while the horizontal edges of the rectangle correspond to the stock's opening and closing prices. If the rectangle is white, the opening price is lower than the closing price, but if the rectangle is black, then it is the other way around.
Using the above information, answer the questions that follow:
Wilma, Xavier, Yaska and Zakir are four young friends, who have a passion for integers. One day, each of them selects one integer and writes it on a wall. The writing on the wall shows that Xavier and Zakir picked positive integers, Yaska picked a negative one, while Wilma’s integer is either negative, zero or positive. If their integers are denoted by the first letters of their respective names, the following is true:
W4 + X3 + Y2 + Z ≤ 4
X3 + Z ≥ 2
W4 + Y2 ≤ 2
Y2 + Z ≥ 3
Given the above, which of these can W2 + X2 + Y2 + Z2 possibly evaluate to?
Read the following scenario and answer the THREE questions that follow.
âââââââ
The given candlestick chart depicts the prices of a particular stock over 10 consecutive days. A candlestick comprises of a rectangular box pieced by a line. The top and bottom ends of the line respectively indicate the maximum and minimum prices of the stock on that day, while the horizontal edges of the rectangle correspond to the stock's opening and closing prices. If the rectangle is white, the opening price is lower than the closing price, but if the rectangle is black, then it is the other way around.
Using the above information, answer the questions that follow:
If both the sequences x, a1, a2, y and x, b1, b2, z are in A.P. and it is given that y > x and z < x, then which of the following values can possibly take?
Read the following scenario and answer the THREE questions that follow.
âââââââ
The given candlestick chart depicts the prices of a particular stock over 10 consecutive days. A candlestick comprises of a rectangular box pieced by a line. The top and bottom ends of the line respectively indicate the maximum and minimum prices of the stock on that day, while the horizontal edges of the rectangle correspond to the stock's opening and closing prices. If the rectangle is white, the opening price is lower than the closing price, but if the rectangle is black, then it is the other way around.
Using the above information, answer the questions that follow:
Fatima found that the profit earned by the Bala dosa stall today is a three-digit number. She also noticed that the middle digit is half of the leftmost digit, while the rightmost digit is three times the middle digit. She then randomly interchanged the digits and obtained a different number. This number was more than the original number by 198.
What was the middle digit of the profit amount?
Read the following scenario and answer the THREE questions that follow.
âââââââ
The given candlestick chart depicts the prices of a particular stock over 10 consecutive days. A candlestick comprises of a rectangular box pieced by a line. The top and bottom ends of the line respectively indicate the maximum and minimum prices of the stock on that day, while the horizontal edges of the rectangle correspond to the stock's opening and closing prices. If the rectangle is white, the opening price is lower than the closing price, but if the rectangle is black, then it is the other way around.
Using the above information, answer the questions that follow:
The Madhura Fruits Company is packing four types of fruits into boxes. There are 126 oranges, 162 apples, 198 guavas and 306 pears. The fruits must be packed in such a way that a given box must have only one type of fruit and must contain thesame number of fruit units as any other box.
What is the minimum number of boxes that must be used?
Read the following scenario and answer the THREE questions that follow.
âââââââ
The given candlestick chart depicts the prices of a particular stock over 10 consecutive days. A candlestick comprises of a rectangular box pieced by a line. The top and bottom ends of the line respectively indicate the maximum and minimum prices of the stock on that day, while the horizontal edges of the rectangle correspond to the stock's opening and closing prices. If the rectangle is white, the opening price is lower than the closing price, but if the rectangle is black, then it is the other way around.
Using the above information, answer the questions that follow:
Consider the real-valued function f(x) = . Find the domain of f(x).
Read the following scenario and answer the three questions that follow.
A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:
1. Are you shopping at the website for the first time? (YES or NO)
2. Specify your gender: (MALE or FEMALE)
3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)
240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:
i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5
ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6
iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers
Which among the following cannot be determined uniquely?
Read the following scenario and answer the three questions that follow.
A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:
1. Are you shopping at the website for the first time? (YES or NO)
2. Specify your gender: (MALE or FEMALE)
3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)
240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:
i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5
ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6
iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers
Find z, if it is known that:
a: -y2 + x2 = 20
b: y3 - 2x2 - 4z ≥ -12 and
c: x, y and z are all positive integers
Read the following scenario and answer the three questions that follow.
A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:
1. Are you shopping at the website for the first time? (YES or NO)
2. Specify your gender: (MALE or FEMALE)
3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)
240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:
i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5
ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6
iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers
An encryption system operates as follows:
Step 1. Fix a number k (k ≤ 26).
Step 2. For each word, swap the first k letters from the front with the last k letters from the end in reverse order. If a word contains less than 2k letters, write the entire word in reverse order.
Step 3. Replace each letter by a letter k spaces ahead in the alphabet. If you cross Z in the process to move k steps ahead, start again from A.
Example: k = 2: zebra → arbez → ctdgb.
If the word “flight” becomes “znmorl” after encryption, then the value of k:
Read the following scenario and answer the three questions that follow.
The following plot describes the height (in cm), weight (in kg), age (in years) and gender (F for female, M for male) of 20 patients visiting a hospital.
âââââââ
A person’s body mass index (BMI) is calculated as weight (in kg) divided by squared height (measured in square metres). For example, a person weighing 100 kg and of height 100 cm (1m) will have a BMI of 100. A person with BMI less than or equal to 18.5 is considered as underweight, above 18.5 but less than or equal to 25 as normal weight, above 25 but less than or equal to 30 as overweight, and above 30 as obese.
The highest BMI among all patients is approximately
Read the following scenario and answer the three questions that follow.
The following plot describes the height (in cm), weight (in kg), age (in years) and gender (F for female, M for male) of 20 patients visiting a hospital.
âââââââ
A person’s body mass index (BMI) is calculated as weight (in kg) divided by squared height (measured in square metres). For example, a person weighing 100 kg and of height 100 cm (1m) will have a BMI of 100. A person with BMI less than or equal to 18.5 is considered as underweight, above 18.5 but less than or equal to 25 as normal weight, above 25 but less than or equal to 30 as overweight, and above 30 as obese.
The BMI of the oldest person considered as normal weight is approximately
If log4 m + log4 n = log2 (m + n) where m and n are positive real numbers, then which of the following must be true?
Let f(x) = if x ≠ 1, -1, and 1 if x = 1, -1. Let g(x) = if x ≠ 1, and 3 if x = 1. What is the minimum possible values of ?
Read the following scenario and answer the three questions that follow.
A company awards incentives to its employees for successful project performances. It rates successful project performance in categories A*, A, B, and C. Employees, in solo projects rated A*, A, B, and C, are awarded incentives â¹6 lakh, â¹5 lakh, â¹3 lakh, and â¹1 lakh respectively. When a project has multiple team members, the following scheme is used to award the incentives:
âââââââ
For example, for a project rated A, with three members, the team lead gets â¹4 lakh, and the other team members get â¹2.5 lakh each. A project always has a single team lead. Six employees: Altaf, Bose, Chakrabarthi, Dipa, Ernie, and Fatima receive a total of â¹45 lakh in incentives by participating in a total of eight different projects that does not involve any other person. Not all six employees are involved in all eight projects.
The following are additionally known about these eight projects:
1. One project involves all six employees. Four projects involve three each, and the rest, two each.
2. Exactly three projects are rated C, for which a total of â¹4.8 lakh is paid.
3. Only one project is rated A*
Total amount of money paid for projects rated A (in lakhs of Rupees) is:
Read the following scenario and answer the three questions that follow.
A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:
1. Are you shopping at the website for the first time? (YES or NO)
2. Specify your gender: (MALE or FEMALE)
3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)
240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:
i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5
ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6
iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers
What is the number of happy male shoppers?
Read the following scenario and answer the three questions that follow.
A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:
1. Are you shopping at the website for the first time? (YES or NO)
2. Specify your gender: (MALE or FEMALE)
3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)
240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:
i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5
ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6
iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers
Which among the following is the lowest?
Read the following paragraph carefully and answer the question that follows:
Vindhya, Shabnam and Amala are interning at a software organization as part of the requirement of their B-school curriculum.
The organization has allotted each of them a project based on their area of specialization. In the first meeting with the HR head, they are informed of a PPO possibility (pre-placement offer, i.e., an offer to join the company after their MBA), based on their performance. All of them are eager to convert their internship into a job offer.
Each of them is assigned a mentor who evaluates the intern's performance along with the HR head.
In the second week of her eight-week internship, Amala realizes that the project requires inputs from subjects she studied in her third trimester. However, during the third trimester, Amala was significantly distracted by an inter-college sports meet, affecting her grasp of the subjects.
Which of the following is the MOST appropriate way forward for Amala?
Read the following paragraph carefully and answer the question that follows:
Vindhya, Shabnam and Amala are interning at a software organization as part of the requirement of their B-school curriculum.
The organization has allotted each of them a project based on their area of specialization. In the first meeting with the HR head, they are informed of a PPO possibility (pre-placement offer, i.e., an offer to join the company after their MBA), based on their performance. All of them are eager to convert their internship into a job offer.
Each of them is assigned a mentor who evaluates the intern's performance along with the HR head.
Vindhya’s project is about understanding employee perception regarding the organization’s HR policies. Against her own instinct, she is suggested by her mentor to interview only the good performers identified by his office because poor performers, he believes, usually crib against the policies.
Which of the following courses of action will BEST enable Vindhya to provide the organization with a complete picture?
Read the following paragraph carefully and answer the question that follows:
Vindhya, Shabnam and Amala are interning at a software organization as part of the requirement of their B-school curriculum.
The organization has allotted each of them a project based on their area of specialization. In the first meeting with the HR head, they are informed of a PPO possibility (pre-placement offer, i.e., an offer to join the company after their MBA), based on their performance. All of them are eager to convert their internship into a job offer.
Each of them is assigned a mentor who evaluates the intern's performance along with the HR head.
Shabnam, who is working on sales executives’ work-life balance, has collected the following details about their frequent travels:
- Frequent meetings help strengthen relationships with key customers.
- Travelling has no effect on the personal lives of the sales executives as most of them are single.
- Travel enhances the financial health of the sales executives since their fixed salaries are low.
- Frequent travel has no significant impact on market budget, given the current high margins from sales.
- The sales executives have the autonomy to decide the frequency of their travel.
Shabnam thinks that the frequency of travel is higher than required.
Which of the following combinations of the above reasons can enable Shabnam BEST substantiate her thinking?
Read the following paragraph carefully and answer the question that follows:
Two industrial towns, Jayanagar and Ramnagar, about 15 kms. apart, are similar in land area, population, ethnic diversity and per capita incomes.
Jagdeep Singh owns a bakery named Le Baguette in Jayanagar. He specializes in croissants, masala bread and whole wheat bread; eggless cakes are also a favorite.
Among the four bakeries in Jayanagar, Jagdeep’s bakery with a market share of 30% is second only to the oldest Le Croissant bakery whose market share is 40%. Le Croissant commands a loyal customer base and does not offer eggless varieties.
Jagdeep has decided to open a branch in Ramnagar. Which of the following facts about Ramnagar will BEST support his decision?
Read the following paragraph carefully and answer the question that follows:
Two industrial towns, Jayanagar and Ramnagar, about 15 kms. apart, are similar in land area, population, ethnic diversity and per capita incomes.
Jagdeep Singh owns a bakery named Le Baguette in Jayanagar. He specializes in croissants, masala bread and whole wheat bread; eggless cakes are also a favorite.
Among the four bakeries in Jayanagar, Jagdeep’s bakery with a market share of 30% is second only to the oldest Le Croissant bakery whose market share is 40%. Le Croissant commands a loyal customer base and does not offer eggless varieties.
Jagdeep wishes to open a 100% eggless branch in Ramnagar. To explore feasibility, he collected the following facts:
- Eggless products account for 30% of Le Baguette’s sales.
- At least 20% of all bakery sales in Ramnagar is from eggless products.
- The eggless varieties of Le Baguette contain minute traces of egg.
- Le Baguette currently makes 3% of its revenue from Ramnagar customers and all of it comes from eggless products.
- Le Croissant’s Ramnagar branch struggles with a market share of 10%.
From the combinations below, in the DESCENDING order of effectiveness, choose the one that BEST supports Jagdeep’s decision.
Read the following paragraph carefully and answer the question that follows:
Two industrial towns, Jayanagar and Ramnagar, about 15 kms. apart, are similar in land area, population, ethnic diversity and per capita incomes.
Jagdeep Singh owns a bakery named Le Baguette in Jayanagar. He specializes in croissants, masala bread and whole wheat bread; eggless cakes are also a favorite.
Among the four bakeries in Jayanagar, Jagdeep’s bakery with a market share of 30% is second only to the oldest Le Croissant bakery whose market share is 40%. Le Croissant commands a loyal customer base and does not offer eggless varieties.
From a newspaper, Jagdeep has learnt that Americans use their own ovens to bake ready-to-bake products, sold by some bakeries. This idea is apparently catching up in Indian metros as well. Jagdeep wants to try this out in his bakery. He has gathered the following facts:
- US bakeries that also sell ready-to-bake products earned higher revenues compared to those that do not.
- Around 7% of Jagdeep’s regular customers own baking ovens in their homes.
- The sale of baking ovens in India is forecast to increase by 12% every year, for the next three years.
- 50% of Jagdeep’s regular customers are fulltime working couples.
- In Indian metros, ready-to-bake products give higher profit margins compared to finished products.
Select the BEST of the following sequences of the above facts, in DESCENDING order of effectiveness, to support Jagdeep.
Read the following paragraph carefully and answer the question that follows:
A Multinational Company (MNC) sources pristine natural spring water from Bori, a village in Satpura mountains. The unprocessed natural spring water is directly bottled by the MNC. The company brands it as “Natural Spring Water” and sells at 50% premium vis-a-vis other brands that sell processed water.
The local panchayat, under the Panchayati Raj Act, 1992 controls the spring water usage. Hence, the company signed a 30-year contract with the panchayat for exclusive access to the spring water for business purposes. This contract contributes 50% to the panchayat’s revenues besides providing 250 jobs in the panchayat. The spring also meets domestic and agricultural needs of the people of Bori and the surrounding villages
Chanchala owns a small parcel of farming land in Bori. She grows cannabis in some part of her land and earns a significant amount of money from it. Soon after the bottling plant was commissioned, Chanchala, instigated by a landlord with a vested interest, starts accusing the MNC of robbing her of water and impacting her livelihood.
She threatens to take the MNC to court.
Which of the following options will BEST solve the MNC’s problem?
Read the following paragraph carefully and answer the question that follows:
A Multinational Company (MNC) sources pristine natural spring water from Bori, a village in Satpura mountains. The unprocessed natural spring water is directly bottled by the MNC. The company brands it as “Natural Spring Water” and sells at 50% premium vis-a-vis other brands that sell processed water.
The local panchayat, under the Panchayati Raj Act, 1992 controls the spring water usage. Hence, the company signed a 30-year contract with the panchayat for exclusive access to the spring water for business purposes. This contract contributes 50% to the panchayat’s revenues besides providing 250 jobs in the panchayat. The spring also meets domestic and agricultural needs of the people of Bori and the surrounding villages
The MNC has spotted traces of chemicals in their fortnightly water quality analysis. The MNC realizes that this is due to the contaminated agricultural runoff, flowing into the spring from the nearby fields where farmers use pesticides and fertilizers. This requires an immediate solution. Which of the following options will BEST resolve the situation for the MNC?
Read the following paragraph carefully and answer the question that follows:
A Multinational Company (MNC) sources pristine natural spring water from Bori, a village in Satpura mountains. The unprocessed natural spring water is directly bottled by the MNC. The company brands it as “Natural Spring Water” and sells at 50% premium vis-a-vis other brands that sell processed water.
The local panchayat, under the Panchayati Raj Act, 1992 controls the spring water usage. Hence, the company signed a 30-year contract with the panchayat for exclusive access to the spring water for business purposes. This contract contributes 50% to the panchayat’s revenues besides providing 250 jobs in the panchayat. The spring also meets domestic and agricultural needs of the people of Bori and the surrounding villages
The MNC is concerned about chemical contamination of the natural spring water due to the agricultural runoff with pesticides and fertilizers. The MNC is looking for a sustainable solution to this contamination.
Which of the following courses of action will BEST solve the issue?
Read the following paragraph carefully and answer the question that follows:
When Deepti opened the package, she was aghast. She received cotton pillow covers instead of satin pillow covers, she had ordered. Deepti ordered them for her father from a popular ecommerce website that hosted products of many sellers.
Confused, Deepti contacted the seller’s office using the details given on the package. The seller’s representative profusely regretted and promised to send the satin pillow covers at no extra cost. He added that Deepti need not return the cotton covers she received. Deepti happily accepted the deal.
A few days later, Deepti received another package from the seller. Unfortunately, this package also contained cotton pillow covers. Completely disillusioned with the seller’s professionalism, Deepti decided to put to use these cotton pillow covers also.
A few days later, Deepti received an email from the e-commerce website, requesting her to share feedback about the seller. Deeply frustrated with the overall online purchasing experience, she deliberately ignored it. Later that evening, over supper, her father opined that the balcony curtains needed to be changed. He suggested that they be bought from a local shop. “If something went wrong, we could at least yell at the seller,” he added.
Deepti stared at her laptop and began writing her feedback.
What would Deepti DEFINITELY achieve by giving feedback?
Read the following paragraph carefully and answer the question that follows:
When Deepti opened the package, she was aghast. She received cotton pillow covers instead of satin pillow covers, she had ordered. Deepti ordered them for her father from a popular ecommerce website that hosted products of many sellers.
Confused, Deepti contacted the seller’s office using the details given on the package. The seller’s representative profusely regretted and promised to send the satin pillow covers at no extra cost. He added that Deepti need not return the cotton covers she received. Deepti happily accepted the deal.
A few days later, Deepti received another package from the seller. Unfortunately, this package also contained cotton pillow covers. Completely disillusioned with the seller’s professionalism, Deepti decided to put to use these cotton pillow covers also.
In the feedback column, Deepti awarded 1-star out of the maximum 5 stars to the seller and described her negative experience.
Later that evening, the sales head called and pleaded with her to retract her feedback and upgrade them to 5-star, as they had already fired the employee concerned. He appealed that they were a young organization and that their sales were getting badly affected.
Given the circumstances, what should be the IDEAL response?
Read the following paragraph carefully and answer the question that follows:
When Deepti opened the package, she was aghast. She received cotton pillow covers instead of satin pillow covers, she had ordered. Deepti ordered them for her father from a popular ecommerce website that hosted products of many sellers.
Confused, Deepti contacted the seller’s office using the details given on the package. The seller’s representative profusely regretted and promised to send the satin pillow covers at no extra cost. He added that Deepti need not return the cotton covers she received. Deepti happily accepted the deal.
A few days later, Deepti received another package from the seller. Unfortunately, this package also contained cotton pillow covers. Completely disillusioned with the seller’s professionalism, Deepti decided to put to use these cotton pillow covers also.
After a few months, the sales head enquired, “In case you are using the cotton pillow covers and like them, kindly rate them on the e-commerce website. It will help us serve our customers better.”
Later that evening, her father remarked, “You know, I really love these pillow covers though I am not sure why you bought so many of them”.
Which of the following reasons gives Deepti the BEST rationale to ignore the sales head’s request?
Read the following paragraph carefully and answer the question that follows:
The Small Shop, selling computer peripherals, is the only one of its kind in the remote village of Turturunk. Because online purchases take two weeks or more to arrive, The Small Shop is a quick stop for buying items such as pen drives and USB cables. Besides selling computer peripherals, The Small Shop also undertakes repairs of out-of-warranty products.
The Small Shop which earlier recorded an annual increase of approximately 12% in revenues has been stagnating at 4% for the last three years, during which e-commerce sidelined brick and mortar outlets. The shop is struggling to increase profitability. In general, The Small Shop has been offering a discount on MRP to compete with ecommerce prices.
Which of the following is the BEST reason for The Small Shop NOT to reduce the current discount offered to the customers?
Read the following paragraph carefully and answer the question that follows:
The Small Shop, selling computer peripherals, is the only one of its kind in the remote village of Turturunk. Because online purchases take two weeks or more to arrive, The Small Shop is a quick stop for buying items such as pen drives and USB cables. Besides selling computer peripherals, The Small Shop also undertakes repairs of out-of-warranty products.
The Small Shop wants to increase the variety of products sold, including expensive ones. However, it is averse to accumulating unsold products, specifically of the expensive kind.
Which of the following is the BEST option if The Small Shop wants to increase the variety of the products it sells?
Read the following paragraph carefully and answer the question that follows:
The Small Shop, selling computer peripherals, is the only one of its kind in the remote village of Turturunk. Because online purchases take two weeks or more to arrive, The Small Shop is a quick stop for buying items such as pen drives and USB cables. Besides selling computer peripherals, The Small Shop also undertakes repairs of out-of-warranty products.
An emerging brand offers a franchise to The Small Shop for repairing its products, on a condition that other brands are not to be repaired. Repairs currently account for 15% of its revenues.
Which of the following, if true, will BEST help The Small Shop to decide on the franchise?
Read the following paragraph carefully and answer the question that follows:
A powerful, intelligent king Vanamali once ruled over an ancient kingdom, Vanarajya. The kingdom was known for its high mountains and sprawling plains, and ninety percent of its land was under forest cover. Trade in forest produce was the mainstay of its economy, supported by subsistence agriculture.
With the increase of population, over time the forest in the plains was cleared for agriculture. The forest in the mountains continued to supply nutrient-enriched water and abundant forest produce to the plains. As a result, agricultural yields were bountiful. The plains prospered as compared to the mountains.
The increasing prosperity of the plains people tempted those in the mountains to divert forest land for agriculture. Vanamali was afraid that expansion of agriculture would result in deforestation of the mountains.
Which of the following is the BEST course of action for Vanamali to conserve the mountain forest?
Read the following paragraph carefully and answer the question that follows:
A powerful, intelligent king Vanamali once ruled over an ancient kingdom, Vanarajya. The kingdom was known for its high mountains and sprawling plains, and ninety percent of its land was under forest cover. Trade in forest produce was the mainstay of its economy, supported by subsistence agriculture.
With the increase of population, over time the forest in the plains was cleared for agriculture. The forest in the mountains continued to supply nutrient-enriched water and abundant forest produce to the plains. As a result, agricultural yields were bountiful. The plains prospered as compared to the mountains.
Vanamali, afraid of further deforestation, issued a diktat against felling of trees in the mountains. In due course, thanks to the booming agriculture, the king along with plains people began to prosper. However, mountain people became relatively poor, thanks to Vanamali’s diktat.
Which of the following options should mountain people choose to BEST protect their long-term interests?
Read the following paragraph carefully and answer the question that follows:
A powerful, intelligent king Vanamali once ruled over an ancient kingdom, Vanarajya. The kingdom was known for its high mountains and sprawling plains, and ninety percent of its land was under forest cover. Trade in forest produce was the mainstay of its economy, supported by subsistence agriculture.
With the increase of population, over time the forest in the plains was cleared for agriculture. The forest in the mountains continued to supply nutrient-enriched water and abundant forest produce to the plains. As a result, agricultural yields were bountiful. The plains prospered as compared to the mountains.
The village elders of the mountains had informed Vanamali about the presence of a precious metal in abundance under a large part of the forest. They pleaded with him to repeal his diktat and permit felling of trees for mining.
Vanamali knew that the precious metal would make his kingdom prosper. However, he was worried that mining would reduce the flow of nutrients, water and forest produce to the plains.
Vanamali’s advisor Vanapandit presented the following action plans for his consideration:
- Repeal the forest diktat and charge hefty royalty for mining in the mountains
- Permit mining in the mountains and enforce rainwater harvesting in the plains
- Permit mining in the mountains and begin afforestation in the plains
- Continue with the forest diktat in the mountains
- Permit limited mining in rotation but maintain the forest diktat in the rest of the mountains
Which of the following sequences of action plans, in the DESCENDING order of their ability to contribute to Vanarajya’s sustainable prosperity, will be the MOST appropriate for Vanamali?
Read the following paragraph carefully and answer the question that follows:
Rakesh, who hailed from Dhanbad, worked in Jamshedpur with SPCIL, a government construction company. Although HR policies concerning job security & work-life balance attracted Rakesh to SPCIL, over time he found his work monotonous with no growth opportunities. However, the proximity to Dhanbad enabled him to visit his parents at his convenience.
Recently Rakesh applied to Grow and Prosper (G&P), a multinational company engaged in construction related operations, making inroads into many Indian states. G&P interviewed Rakesh and offered him three times his current salary at SPCIL.
While considering G&P’s offer, Rakesh pondered over the following facts:
- A recent government policy made poor performance punishable by salary reduction or dismissal.
- The first assignment at G&P is a bridge construction project in a village near Dhanbad.
- With his current savings, Rakesh need not depend on regular income for at least six months.
- Though an exemplary performer, Rakesh has hardly been recognized at SPCIL.
- Based on the annual performance review at G&P, Rakesh will either earn double the salary or get fired.
Which of the following combinations of the above facts will BEST help Rakesh decide on joining G&P?
Read the following paragraph carefully and answer the question that follows:
Rakesh, who hailed from Dhanbad, worked in Jamshedpur with SPCIL, a government construction company. Although HR policies concerning job security & work-life balance attracted Rakesh to SPCIL, over time he found his work monotonous with no growth opportunities. However, the proximity to Dhanbad enabled him to visit his parents at his convenience.
Recently Rakesh applied to Grow and Prosper (G&P), a multinational company engaged in construction related operations, making inroads into many Indian states. G&P interviewed Rakesh and offered him three times his current salary at SPCIL.
While mulling over the offer, Rakesh consulted Manikandan, his trusted senior at SPCIL. Manikandan, who had friends in G&P, disclosed that it preferred government employees for its projects in Jharkhand, Bihar and Chhattisgarh. “Once the project is completed, G&P may not need your skills,” observed Manikandan.
Which of the following, if true, will BEST enable Rakesh to decide on the offer?
Read the following paragraph carefully and answer the question that follows:
Rakesh, who hailed from Dhanbad, worked in Jamshedpur with SPCIL, a government construction company. Although HR policies concerning job security & work-life balance attracted Rakesh to SPCIL, over time he found his work monotonous with no growth opportunities. However, the proximity to Dhanbad enabled him to visit his parents at his convenience.
Recently Rakesh applied to Grow and Prosper (G&P), a multinational company engaged in construction related operations, making inroads into many Indian states. G&P interviewed Rakesh and offered him three times his current salary at SPCIL.
Rakesh, in his current job, came across incidences of bribing by private sector officials. He wondered if he might have to bribe government officials while at G&P. He reflected on his interview with G&P:
- The interviewers were puzzled how Rakesh could manage his EMIs with his current income.
- One interviewer was constantly probing how Rakesh managed to meet his project deadlines with little cooperation from his subordinates.
- “What would you do if your project has a fortnight’s deadline and it takes a month to obtain a permit?,” asked another interviewer.
- A question that intrigued Rakesh was, “Should a pack of dacoits share their loot with one of their gang, who had killed a bystander against their motto ‘Thou shalt not kill’?”
Which of the following sequences of the above statements is in the MOST appropriate DESCENDING order of bribing undertones?
A man is laying stones, from start to end, along the two sides of a 200-meter-walkway. The stones are to be laid 5 meters apart from each other. When he begins, all the stones are present at the start of the walkway. He places the first stone on each side at the walkway’s start. For all the other stones, the man lays the stones first along one of the walkway’s sides, then along the other side in an exactly similar fashion. However, he can carry only one stone at a time. To lay each stone, the man walks to the spot, lays the stone, and then walks back to pick another. After laying all the stones, the man walks back to the start, which marks the end of his work. What is the total distance that the man walks in executing this work? Assume that the width of the walkway is negligible.
What is the remainder if 1920 – 2019 is divided by 7?
When expressed in a decimal form, which of the following numbers will be nonterminating as well as non-repeating?
A shop sells bags in three sizes: small, medium and large. A large bag costs Rs.1000, a medium bag costs Rs.200, and a small bag costs Rs.50. Three buyers, Ashish, Banti and Chintu, independently buy some numbers of these types of bags. The respective amounts spent by Ashish, Banti and Chintu are equal. Put together, the shop sells 1 large bag, 15 small bags and some medium bags to these three buyers. What is the minimum number of medium bags that the shop sells to them?
Consider the four variables A, B, C and D and a function Z of these variables, Z = 15A2 − 3B4 + C + 0.5D. It is given that A, B, C and D must be non-negative integers and that all of the following relationships must hold:
i) 2A + B ≤ 2
ii) 4A + 2B + C ≤ 12
iii) 3A + 4B + D ≤ 15
If Z needs to be maximised, then what value must D take?
If is a whole number then which one of the statements below is consistent with it?
When opening his fruit shop for the day a shopkeeper found that his stock of apples could be perfectly arranged in a complete triangular array: that is, every row with one apple more than the row immediately above, going all the way up ending with a single apple at the top.
During any sales transaction, apples are always picked from the uppermost row, and going below only when that row is exhausted. When one customer walked in the middle of the day she found an incomplete array in display having 126 apples totally. How many rows of apples (complete and incomplete) were seen by this customer? (Assume that the initial stock did not exceed 150 apples.)
equals which of the following?
Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⯠(x + 98). The number of integers x for which f(x) < 0 is:
If x2 + x + 1 = 0, then x2018 + x2019 equals which of the following:
We have two unknown positive integers m and n, whose product is less than 100.
There are two additional statement of facts available:
- mn is divisible by six consecutive integers { j, j + 1,...,j + 5 }
- m + n is a perfect square.
Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?
Read the following poem and answer the questions that follow:
A spirit that lives in this world and does not wear the shirt of love, such an existence in a deep disgrace.
Be foolish in love, because love is all there is.
There is no way into presence except through love exchange.
If someone asks, But what is love? Answer, dissolving the will.
True freedom comes to those who have escaped the question of freewill and fate.
Love is an emperor. The two worlds play across him. He barely notices their tumbling game.
Love and lover live in eternity. Other desires are substitute for that way of being.
How long do you lay embracing a corpse? Love rather the soul, which cannot be held.
Anything born in spring dies in the fall, but love is not seasonal.
With wine pressed from grapes, expect a hangover.
But this love path has no expectations. You are uneasy riding the body?
Dismount, travel lighter. Wings will be given.
Be clear like mirror holding nothing.
Be clean of pictures and the worry that comes with images.
Gaze into what is not ashamed or afraid of any truth.
Contain all human faces in your own without any judgment of them.
Be pure emptiness. What is inside of that? You ask. Silence is all I can say.
Lovers have some secrets they keep.
"Music probably does something interesting," explains neuropsychologist Catherine Loveday of the University of Westminster. "It stimulates the brain in a very powerful way, because of our emotional connection with it." Unlike brain-games, playing an instrument is a rich and complex experience. This is because it's integrating information from senses like vision, hearing, and touch, along with fine movements. This can result in long-lasting changes in the brain. This can also be applicable in the business world.
Go through the following statements:
- Playing a musical instrument is a unique experience involving vision, hearing and touch.
- Instrumental musicians are far more creative than vocalists.
- Playing brain games does not integrate various senses and movements as much as playing a musical instrument.
- Integrating the five senses is critical in the business world.
Which of the above statements can definitely be interpreted based on the passage above?
Answer the following question based on the information given below.
Lal & Sons, a family business, comprises three different companies in three different industries. Sudarshan Lal was heading this entire business from the inception. Two years ago, he hired three managers, one for each company and Chhaganlal Jha as Chief Executive Officer (CEO) to look after the entire business. These three managers are reporting to the CEO. However, Sudarshan Lal and his family still own the entire business, though they are not involved in day to day operations. Two years after the handing over, Sudarshan was concerned that none of the companies, except one, is profitable.
Which of the following information, if true, will most likely reduce Sudarshan's concerns?
Find the value of the expression: 10 + 103 + 106 + 109
Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?
An antique store has a collection of eight clocks. At a particular moment, the displayed times on seven of the eight clocks were as follows: 1:55 pm, 2:03 pm, 2:11 pm, 2:24 pm, 2:45 pm, 3:19 pm and 4:14 pm. If the displayed times of all eight clocks form a mathematical series, then what was the displayed time on the remaining clock?
X and Y are the digits at the unit's place of the numbers (408X) and (789Y) where X ≠ Y. However, the digits at the unit's place of the numbers (408X)63 and (789Y)85 are the same. What will be the possible value(s) of (X + Y)?
Example: If M = 3 then the digit at unit's place of the number (2M) is 3 (as the number is 23) and the digit at unit's place of the number (2M)2 is 9 (as 232 is 529).
If 2 ≤ |x – 1|×|y + 3| ≤ 5 and both x and y are negative integers, find the number of possible combinations of x and y.
David has an interesting habit of spending money. He spends exactly £X on the Xth day of a month. For example, he spends exactly £5 on the 5th of any month. On a few days in a year, David noticed that his cumulative spending during the last 'four consecutive days' can be expressed as 2N where N is a natural number. What can be the possible value(s) of N?
Read the following stanza and answer the question that follows:
âââââââInvisible atoms coming together
Revealing themselves in visible forms
Seeds are hugged by the earth
Which renders them as gardens in bloom.
And yonder stars, are they not pearls
Floating on teeming seas?
Scattered, yet strung together in orderly constellations
Love binding them to one another
And each is perpetually seeking its like?
Which of the following options is grammatically correct and meaningful?
The sum of the series, (-100) + (-95) + (-90) + … + 110 + 115 + 120, is
If x and y are real numbers, the least possible value of the expression 4(x - 2)2 + 4(y - 3)2 – 2(x - 3)2 is:
If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:
Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.
An institute has 5 departments and each department has 50 students. If students are picked up randomly from all 5 departments to form a committee, what should be the minimum number of students in the committee so that at least one department should have representation of minimum 5 students?
If N = (11p+7)(7q-2)(5r+1)(3s) is a perfect cube, where p, q, r and s are positive integers, then the smallest value of p + q + r + s is:
Consider the set of numbers {1, 3, 32, 33,…...,3100}. The ratio of the last number and the sum of the remaining numbers is closest to:
f is a function for which f(1) = 1 and f(x) = 2x + f(x – 1Ø) for each natural number x ≥ 2. Find f(31).
Two number in the base system B are 2061B and 601B. The sum of these two numbers in decimal system is 432. Find the value of 1010B in decimal system.
For two positive integers a and b, if (a + b)(a+b) is divisible by 500, then the least possible value of a × b is:
a, b, c are integers, |a| ≠ |b| ≠ |c| and –10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a + b + c)]?
If a, b and c are 3 consecutive integers between –10 to +10 (both inclusive), how many integer values are possible for the expression ?
Analyse the passage given and provide an appropriate answer for the questions that follow.
The understanding that the brain has areas of specialization has brought with it the tendency to teach in ways that reflect these specialized functions. For example, research concerning the specialized functions of the left and right hemispheres has led to left and right hemisphere teaching. Recent research suggests that such an approach neither reflects how the brain learns, nor how it functions once learning has occurred. To the contrary, in most ‘higher vertebrates’ brain systems interact together as a whole brain with the external world. Learning is about making connections within the brain and between the brain and outside world.
What does this mean? Until recently, the idea that the neural basis for learning resided in connections between neurons remained a speculation. Now, there is direct evidence that when learning occurs, neuro – chemical communication between neurons is facilitated, and less input is required to activate established connections over time. This evidence also indicates that learning creates connections between not only adjacent neurons but also between distant neurons, and that connections are made from simple circuits to complex ones and from complex circuits to simple ones.
As connections are formed among adjacent neurons to form circuits, connections also begin to form with neurons in other regions of the brain that are associated with visual, tactile, and even olfactory information related to the sound of the word. Meaning is attributed to ‘sounds of words’ because of these connections. Some of the brain sites for these other neurons are far from the neural circuits that correspond to the component sounds of the words; they include sites in other areas of the left hemisphere and even sites in the right hemisphere. The whole complex of interconnected neurons that are activated by the word is called a neural network.
In early stages of learning, neural circuits are activated piecemeal, incompletely, and weakly. It is like getting a glimpse of a partially exposed and blurry picture. With more experience, practice, and exposure, the picture becomes clearer and more detailed. As the exposure is repeated, less input is needed to activate the entire network. With time, activation and recognition become relatively automatic, and the learner can direct her attention to other parts of the task. This also explains why learning takes time. Time is needed to establish new neutral networks and connections between networks. This suggests that the neutral mechanism for learning is essentially the same as the products of learning. Learning is a process that establishes new connections among networks. The newly acquired skills or knowledge are nothing but formation of neutral circuits and networks.
Read the following statements and answer the question that follows.
- âââââââThe two hemispheres of the brain are responsible for learning autonomously.
- Simultaneous activation of circuits can take place in different areas of the brain.
- There are specific regions of the brain associated with sight, touch and smell.
- The brain receives inputs from multiple external sources.
- Learning is not the result of connections between neurons.
Which of the above statements are consistent with ideas expressed in the passage?
What is the sum of the following series?
–64, –66, –68,……..….., –100
Find the equation of the graph shown below.
âââââââ
If f(x2 – 1) = x4 – 7x2 + k1 and f(x3 – 2) = x6 – 9x3 + k2 then the value of (k2 – k1) is
If a, b, c and d are four different positive integers selected from 1 to 25, then the highest possible value of ((a + b) + (c + d))/((a + b) + (c – d)) would be:
Devanand’s house is 50 km West of Pradeep’s house. On Sunday morning, at 10 a.m., they leave their respective houses.
Under which of the following scenarios, the minimum distance between the two would be 40 km?
Scenario I: Devanand walks East at a constant speed of 3 km per hour and Pradeep walks South at a constant speed of 4 km per hour.
Scenario II: Devanand walks South at a constant speed of 3 km per hour and Pradeep walks East at a constant speed of 4 km per hour.
Scenario III: Devanand walks West at a constant speed of 4 km per hour and Pradeep walks East at a constant speed of 3 km per hour.
For a positive integer x, define f(x) such that f(x + a) = f(a × x), where a is an integer and f(1) = 4. If the value of f(1003) = k, then the value of ‘k’ will be:
An ascending series of numbers satisfies the following conditions:
- When divided by 3, 4, 5 or 6, the numbers leave a remainder of 2.
- When divided by 11, the numbers leave no remainder.
The 6th number in this series will be:
In an examination, two types of questions are asked: one mark questions and two marks questions. For each wrong answer, of one mark question, the deduction is 1/4 of a mark and for each wrong answer, of two marks question, the deduction is 1/3 of a mark. Moreover, 1/2 of a mark is deducted for any unanswered question. The question paper has 10 one mark questions and 10 two marks questions. In the examination, students got all possible marks between 25 and 30 and every student had different marks. What would be the rank of a student, who scores a total of 27.5 marks?
If the last 6 digits of [(M)! – (N)!] are 999000, which of the following option is not possible for (M) × (M – N)?
Both (M) and (N) are positive integers and M > N. (M)! is factorial M.
A three-digit number has digits in strictly descending order and divisible by 10. By changing the places of the digits a new three-digit number is constructed in such a way that the new number is divisible by 10. The difference between the original number and the new number is divisible by 40. How many numbers will satisfy all these conditions?
Answer the questions on the basis of information given in the following case.
Bright Engineering College (BEC) has listed 20 elective courses for the next term and students have to choose any 7 of them. Simran, a student of BEC, notices that there are three categories of electives: Job-oriented (J), Quantitative-oriented (Q) and Grade-oriented (G). Among these 20 electives, some electives are both Job and Grade-oriented but are not Quantitative-oriented (JG type). QJ type electives are both job and Quantitative-oriented but are not Grade-oriented and QG type electives are both Quantitative and Grade-oriented but are not Job-oriented. Simran also notes that the total number of QJ type electives is 2 less than QG type electives. Similarly, the total number of QG type electives is 2 less than JG type and there is only 1 common elective (JQG) across three categories. Furthermore, the number of only Quantitative-oriented electives is same as only Job-oriented electives, but less than the number of only Grade-oriented electives. Each elective has at least one registration and there is at least one elective in each category, or combinations of categories.
On her way back Simran met her friend Raj and shared the above information. Raj is preparing for XAT and is only interested in Grade-oriented (G) electives. He wanted to know the number of G-type electives being offered. Simran replied, “You have all the information. Calculate the number of G-type electives yourself. It would help your XAT preparation”. Raj calculates correctly and says that there can be _______ possible answers.
Which of the following options would best fit the blank above?
Answer the questions on the basis of information given in the following case.
Bright Engineering College (BEC) has listed 20 elective courses for the next term and students have to choose any 7 of them. Simran, a student of BEC, notices that there are three categories of electives: Job-oriented (J), Quantitative-oriented (Q) and Grade-oriented (G). Among these 20 electives, some electives are both Job and Grade-oriented but are not Quantitative-oriented (JG type). QJ type electives are both job and Quantitative-oriented but are not Grade-oriented and QG type electives are both Quantitative and Grade-oriented but are not Job-oriented. Simran also notes that the total number of QJ type electives is 2 less than QG type electives. Similarly, the total number of QG type electives is 2 less than JG type and there is only 1 common elective (JQG) across three categories. Furthermore, the number of only Quantitative-oriented electives is same as only Job-oriented electives, but less than the number of only Grade-oriented electives. Each elective has at least one registration and there is at least one elective in each category, or combinations of categories.
Simran prefers J-type electives and wants to avoid Q-type electives. She noted that the number of only J-type electives is 3. Raj’s preference is G-type electives followed by Q-type electives. However, they want to take as many common electives as possible. What is the maximum number of electives that can be common between them, without compromising their preferences?
Answer the questions on the basis of information given in the following case.
Bright Engineering College (BEC) has listed 20 elective courses for the next term and students have to choose any 7 of them. Simran, a student of BEC, notices that there are three categories of electives: Job-oriented (J), Quantitative-oriented (Q) and Grade-oriented (G). Among these 20 electives, some electives are both Job and Grade-oriented but are not Quantitative-oriented (JG type). QJ type electives are both job and Quantitative-oriented but are not Grade-oriented and QG type electives are both Quantitative and Grade-oriented but are not Job-oriented. Simran also notes that the total number of QJ type electives is 2 less than QG type electives. Similarly, the total number of QG type electives is 2 less than JG type and there is only 1 common elective (JQG) across three categories. Furthermore, the number of only Quantitative-oriented electives is same as only Job-oriented electives, but less than the number of only Grade-oriented electives. Each elective has at least one registration and there is at least one elective in each category, or combinations of categories.
Vijay and Raj want to avoid each other. Vijay is interested in J-type electives and wants to avoid Q-type electives. Raj’s preference is G-type electives followed by Q-type electives. Raj noted that the number of only G-type electives is 2. Is there a possibility that they would not share any common electives(s)?
Answer the questions on the basis of information given in the following case.
Mr. Dipangshu Barua, a young IT professional, came early to office to assist his boss in the preparation for an important client presentation. When be switched on his computer, he saw an email from Mr. Patel. The email was as follows:
January 2, 2015
Dear Mr. Barua,
This email serves as a follow-up of my conversation with you on December 1, 2014. I have already conveyed need for improvement in your behaviour as desired as desired by your project leader and colleagues. They are yet to notice any visible improvements. I am apprehensive that your failure to act may warrant further action leading to dismissal. I will continue to monitor and assess your performance over the next three months to determine whether improvements meet the expectations. At the same time, I would like to re-affirm that you are very valuable for our organization.
Best Wishes,
Mr. A. Patel
HR Director
Initially, the e-mail distracted Dipangshu but he decided to focus on the job. Which of the following options might best explain his decision to do so?
Answer the questions on the basis of information given in the following case.
Mr. Dipangshu Barua, a young IT professional, came early to office to assist his boss in the preparation for an important client presentation. When be switched on his computer, he saw an email from Mr. Patel. The email was as follows:
January 2, 2015
Dear Mr. Barua,
This email serves as a follow-up of my conversation with you on December 1, 2014. I have already conveyed need for improvement in your behaviour as desired as desired by your project leader and colleagues. They are yet to notice any visible improvements. I am apprehensive that your failure to act may warrant further action leading to dismissal. I will continue to monitor and assess your performance over the next three months to determine whether improvements meet the expectations. At the same time, I would like to re-affirm that you are very valuable for our organization.
Best Wishes,
Mr. A. Patel
HR Director
The scheduled presentation went off smoothly. Back in his cabin, Dipangshu read
Mr. Patel’s e-mail once more and pondered over it. During the last meeting he tried hard to put forward his explanation but Mr. Patel had not allowed him to speak. Dipangshu was thinking of meeting Mr. Patel once again but was doubtful that would help. Incidentally, he had a job offer from a start-up with a comparable salary. If Dipangshu was to join the new job, he had to accept the offer within the next two weeks. However, he cannot think of a life without a job. Dipangshu was confused!
Which of the following options would be the best move for Dipangshu?
Answer the questions on the basis of information given in the following case.
Mr. Dipangshu Barua, a young IT professional, came early to office to assist his boss in the preparation for an important client presentation. When be switched on his computer, he saw an email from Mr. Patel. The email was as follows:
January 2, 2015
Dear Mr. Barua,
This email serves as a follow-up of my conversation with you on December 1, 2014. I have already conveyed need for improvement in your behaviour as desired as desired by your project leader and colleagues. They are yet to notice any visible improvements. I am apprehensive that your failure to act may warrant further action leading to dismissal. I will continue to monitor and assess your performance over the next three months to determine whether improvements meet the expectations. At the same time, I would like to re-affirm that you are very valuable for our organization.
Best Wishes,
Mr. A. Patel
HR Director
After a couple of weeks, Mr. Patel came to know that Dipangshu’s project leader Mr. John, a very competent senior executive, may have wilfully influenced his team members to file a wrong complaint against Dipangshu. Mr. John may have done it because Dipangshu has refused to tow John’s line. Mr. Patel also came to know that Dipangshu was thinking of quitting this job. He felt regretful about his letter to Dipangshu. He wanted to resolve the complicated situation. He was contemplating following five actions in his mind.
- Talk to Mr. John about Dipangshu and convey to him that losing a bright employee would cost the organization dearly.
- Catch up with Mr. John during coffee break and convey that Dipangshu has a very good track record.
- Chat with Dipangshu during coffee break.
- Catch up with Dipangshu during coffee break and convey that the organization values him.
- Arrange a meeting among Mr. John, Dipangshu and himself to sort out the difference.
Which of the following is the best sequence of actions for resolving the problem?
Answer the questions on the basis of information given in the following case.
A few years back Mr. Arbit and Mr. Boring started an oil refinery business. Their annual earing is currently just 50,000 million rupees. They are now exploring various options to improve the business. Mr. Xanadu, a salesperson from Innovative Technology Solutions (ITS), is trying to sell a new oil refinery technology to Mr. Arbit and Mr. Boring. This technology could potentially enhance their annual earning to 150,000 million rupees within a year. But they have to make one-time investment of 100,000 million rupees to implement the technology. If the technology is not successful, the investment would be lost. Mr. Arbit and Mr. Boring are discussing about possible risks of the investment.
Mr. Arbit is enthusiastic about this investment idea but Mr. Boring is a little sceptical. This impasse makes them approach a consultant. The consultant makes some observations. Which of the following observations, made by the consultant, might reduce Mr. Arbit’s enthusiasm for the new investment idea?
Answer the questions on the basis of information given in the following case.
A few years back Mr. Arbit and Mr. Boring started an oil refinery business. Their annual earing is currently just 50,000 million rupees. They are now exploring various options to improve the business. Mr. Xanadu, a salesperson from Innovative Technology Solutions (ITS), is trying to sell a new oil refinery technology to Mr. Arbit and Mr. Boring. This technology could potentially enhance their annual earning to 150,000 million rupees within a year. But they have to make one-time investment of 100,000 million rupees to implement the technology. If the technology is not successful, the investment would be lost. Mr. Arbit and Mr. Boring are discussing about possible risks of the investment.
In order to sell the technology to Mr. Arbit and Mr. Boring, Mr. Xanadu is thinking of five possible sales pitches. Which of the following sales pitches would reduce uncertainties the most for Mr. Arbit and Mr. Boring?
Answer the questions on the basis of information given in the following case.
A few years back Mr. Arbit and Mr. Boring started an oil refinery business. Their annual earing is currently just 50,000 million rupees. They are now exploring various options to improve the business. Mr. Xanadu, a salesperson from Innovative Technology Solutions (ITS), is trying to sell a new oil refinery technology to Mr. Arbit and Mr. Boring. This technology could potentially enhance their annual earning to 150,000 million rupees within a year. But they have to make one-time investment of 100,000 million rupees to implement the technology. If the technology is not successful, the investment would be lost. Mr. Arbit and Mr. Boring are discussing about possible risks of the investment.
Mr. Arbit and Mr. Boring did not invest in the new technology, but the new technology is a big success. Repentant, they are now estimating the additional amount they would have earned (i.e. forgone earnings) had they invested in the new technology. However, the two owners differed on expected lifespan of the new technology. Mr. Arbit expected lifespan to be 5 years, whereas, Mr. Boring expected it to be 2 years. After the technology gets out-dated, the earnings from the business would drop back to 50,000 million rupees.
What would be the difference between two expected foregone earnings after 5 years of the technology investment, if yearly earnings are deposited in a bank @10%, compounded annually?
Note: Forgone Earnings = (Earnings from business with new technology) – (Earnings from business without new technology)
Answer the questions on the basis of information given in the following case.
Life saving Pharmaceuticals (LSP) is India-based Pharmaceuticals Company. Their business mostly revolves around a couple of generic drugs and a few patented drugs. LSP operates in 30 odd countries and more than 50% of their sales volume is from outside India.
If more than 50% of their sales volume is from generic drugs, which of the following options is definitely correct? (Note : All percentages figures are with respect to total sales volume)
Answer the questions on the basis of information given in the following case.
Life saving Pharmaceuticals (LSP) is India-based Pharmaceuticals Company. Their business mostly revolves around a couple of generic drugs and a few patented drugs. LSP operates in 30 odd countries and more than 50% of their sales volume is from outside India.
Mr. Sinha, a senior executive of LSP, observes that their business in India is not vibrant. LSP faces stiff competition from Indian and global players, except in rural areas. Interestingly, most of their sales in the rural area are from cough syrup, used as sedatives by teenagers. Mr. Sinha is planning the following actions to improve business in the long run.
- Invest in development of new drugs.
- Increase sales of cough syrup in the rural markets.
- Try and cut costs.
- Recruit more medical representatives in the rural areas.
Which of the following sequences is best arranged in the descending order of appropriateness?
Answer the questions on the basis of information given in the following case.
Life saving Pharmaceuticals (LSP) is India-based Pharmaceuticals Company. Their business mostly revolves around a couple of generic drugs and a few patented drugs. LSP operates in 30 odd countries and more than 50% of their sales volume is from outside India.
Mr. Rastogi, HR head of LSP, is contemplating of transferring MR. Jose, from India to their Luxembourg office. Mr. Jose’s wife is also with the HR department of LSP. The couple is expecting their first child within next four months and hence they want to be together. Mr. Rastogi is wondering whether Mr.Jose would accept the transfer. If he doesn’t, Mr. Rastogi would have to send a less competent person for this job as early as possible. The office in Luxembourg is very important for the company’s future. It is at its nascent stage and does not yet have an HR department. Hence, it is not possible to transfer Mrs. Jose to Luxembourg.
Which of the following options would be most appropriate, from the organization’s perspective, to resolve the issue?
Answer the questions on the basis of information given in the following case.
Life saving Pharmaceuticals (LSP) is India-based Pharmaceuticals Company. Their business mostly revolves around a couple of generic drugs and a few patented drugs. LSP operates in 30 odd countries and more than 50% of their sales volume is from outside India.
Mr. Khan used to work as the Vice President of LSP India. However, he had resigned from LSP India for a better job in New York. In the meantime, his wife was promoted to head the HR of LSP India. Mrs. Khan had struggled hard to reach this position and was quite popular and respected within the organization. Mrs. Khan was contemplating whether she should give up her career and join him in New York. Mrs. Khan is considering the following actions:
- Take a break for the time being and focus on personal life. Given her reputation, she can always get back to the same job, if required.
- Go to New York, on leave without pay for two months to help Mr. Khan settle down. After that she can come back and resume her responsibility in LSP India.
- Request Mr. Khan to look for an equivalent job in India.
- Resign form LSP India, join Mr. Khan in New York, and look for a similar job there.
- Request LSP India for a similar position in LSP USA and follow Mr. Khan to New York.
Which of the following sequence of actions can be immediately taken by Mrs. Khan to maintain her work-life balance?
Answer the questions on the basis of information given in the following case.
Mohan’s was a popular fast-food joint at Connaught Place, Delhi. Initially Mohan handled his business alone. His sons, Ram and Kishan, joined the business after graduation from college. Ram was entrepreneurial in nature. Subsequently, another branch of Mohan’s was opened in Panipat. Mohan had chosen Ram to head the Panipat branch. Though Ram increased sales in short time, he had stopped using premium quality organic vegetables, the speciality of Mohan’s. Mohan and Kishan were not happy with his way of doing business.
Now, the foremost challenge for Mohan was to sort out this issue with Ram. Mohan knew that replacing Ram with Kishan was difficult as Kishan did not want to leave Delhi. However, giving a freehand to Ram might have long term negative consequences. Mohan was confused about the future of course of actions.
Mohan sought the help of five consultants, who give the following opinions:
- Organic vegetables might be a big success at Connaught place but awareness about organic vegetables is low among Panipat customers.
- The Connaught place model can be implemented in Panipat provided the business is prepared to face the consequences.
- Many high end restaurants in Panipat use organic vegetables. So, using organic vegetables will not be a differentiating factor.
- Selling prices of their dishes in Panipat are significantly lower. Using organic vegetables will bring down profits.
- Premium quality organic vegetables are not easily available in Panipat.
Which of the following set of options would support Ram’s argument of not using organic vegetables?
Answer the questions on the basis of information given in the following case.
Mohan’s was a popular fast-food joint at Connaught Place, Delhi. Initially Mohan handled his business alone. His sons, Ram and Kishan, joined the business after graduation from college. Ram was entrepreneurial in nature. Subsequently, another branch of Mohan’s was opened in Panipat. Mohan had chosen Ram to head the Panipat branch. Though Ram increased sales in short time, he had stopped using premium quality organic vegetables, the speciality of Mohan’s. Mohan and Kishan were not happy with his way of doing business.
Now, the foremost challenge for Mohan was to sort out this issue with Ram. Mohan knew that replacing Ram with Kishan was difficult as Kishan did not want to leave Delhi. However, giving a freehand to Ram might have long term negative consequences. Mohan was confused about the future of course of actions.
Mohan sought feedback from a few of his businessmen friends, who were familiar with both the branches. Here is what they said:
- Businessman 1 : Customers of Connaught place and Panipat are very different.
- Businessman 2 : Customers in Panipat are extremely happy with Ram’s behaviour.
- Businessman 3 : Panipat branch does not use the same quality of ingredients but maintains good hygiene and taste.
- Businessman 4 : Who knows, tomorrow the customers of Panipat might also appreciate what Connaught place customers appreciate today!
If Mohan thinks all these are valid concerns, which of the following actions would be best for the business?
Answer the questions on the basis of information given in the following case.
Mohan’s was a popular fast-food joint at Connaught Place, Delhi. Initially Mohan handled his business alone. His sons, Ram and Kishan, joined the business after graduation from college. Ram was entrepreneurial in nature. Subsequently, another branch of Mohan’s was opened in Panipat. Mohan had chosen Ram to head the Panipat branch. Though Ram increased sales in short time, he had stopped using premium quality organic vegetables, the speciality of Mohan’s. Mohan and Kishan were not happy with his way of doing business.
Now, the foremost challenge for Mohan was to sort out this issue with Ram. Mohan knew that replacing Ram with Kishan was difficult as Kishan did not want to leave Delhi. However, giving a freehand to Ram might have long term negative consequences. Mohan was confused about the future of course of actions.
After discussing with a few customers, Mohan realised that compromising on the quality of ingredients at Panipat branch may not be good idea but at the same time he also realised that Panipat branch had grown fast. He was contemplating following five actions. Which of the following actions would be the best for the future of his business?
Answer the following question based on the information given below.
MBA entrance examination comprises two types of problems: formula-based problems and application-based problem. From the analysis of past data, Interesting School of Management (ISM) observes that students good at solving application-based problems are entrepreneurial in nature. Coaching institutes for MBA entrance exams train them to spot formula-based problems and answer them correctly, so as to obtain the required overall cut-off percentile. Thus students, in general, shy away from application-based problem and even those with entrepreneurial mind-set target formula-based problems.
Half of a mark is deducted for every wrong answer.
ISM wants more students with entrepreneurial mind-set in the next batch. To achieve this, ISM is considering following proposals:
- Preparing a question paper of two parts, Parts A and Part B of duration of one hour each. Part A and Part B would consist of formula-based problems and application-based problems, respectively. After taking away Part A, Part B would be distributed. The qualifying cut-off percentile would be calculated on the combined scores of two parts.
- Preparing a question paper comprising Part A and Part B. While Part A would comprise formula-based problems, Part B would comprise application-based problems, each having a separate qualifying cut-off percentile.
- Assigning one mark for formula-based problems and two marks for application based problems as an incentive for attempting application-based problems.
- Allotting one mark for formula-based problems and three marks for application-based problem, without mentioning this is the question paper.
Which of the following proposal (or combination of proposals) is likely to identify students with best entrepreneurial mind-set?
Answer the following question based on the information given below.
MBA entrance examination comprises two types of problems: formula-based problems and application-based problem. From the analysis of past data, Interesting School of Management (ISM) observes that students good at solving application-based problems are entrepreneurial in nature. Coaching institutes for MBA entrance exams train them to spot formula-based problems and answer them correctly, so as to obtain the required overall cut-off percentile. Thus students, in general, shy away from application-based problem and even those with entrepreneurial mind-set target formula-based problems.
Half of a mark is deducted for every wrong answer.
ISM conducts a common entrance examination every year. This year, the question paper would comprise 60 questions with an equal mix of formula-based problems and application-based problems. All questions would carry equal marks. Balaji is appearing for the examination. Before, appearing for the examination he gets the following information from coaching institutes:
- Application-oriented problems take more time to solve in an examination hall.
- Chances of silly mistakes would be low in application-based problems.
- ISM would assist the students with bank loans to start a new venture.
- Options are generally confusing for formula-based problems.
- ‘Practice makes a man perfect’ can apply only to formula-based problems.
- Students get very good campus jobs.
Based on above information, which of the following options would help him to be better prepared for the examination?
Answer the questions on the basis of information given in the following case.
The Disciplinary Committee of Nation Political Party (NPP) is meeting today to decide on the future of two of their party members, Mr. Loyal and his son Mr. Prodigal. Mr. Prodigal is the prime accused in the brutal murder of Mr. Victim, an opposition party leader. Mr. Prodigal is in police custody and his appeal for bail has got rejected. Mr. Loyal claims that his son is innocent and Mr. Victim’s death was the result of internal rivalry in the opposition party. Though Mr. Loyal is not accused in this case, his weakness for his son is well known. The media is blaming him for influencing key witnesses to protect his son. Severe criticism of his father-son duo, both by the media and some social activists, is damaging the image of the party. However, Mr. Loyal has significant followers within the party and is considered an asset to the party. Any harsh decision against Mr. Loyal would adversely affect the future of NPP and could even lead to a split in the party. This would benefit the opposition.
Which of the following actions would adversely affect both NPP and Mr. Loyal, the most?
Answer the questions on the basis of information given in the following case.
The Disciplinary Committee of Nation Political Party (NPP) is meeting today to decide on the future of two of their party members, Mr. Loyal and his son Mr. Prodigal. Mr. Prodigal is the prime accused in the brutal murder of Mr. Victim, an opposition party leader. Mr. Prodigal is in police custody and his appeal for bail has got rejected. Mr. Loyal claims that his son is innocent and Mr. Victim’s death was the result of internal rivalry in the opposition party. Though Mr. Loyal is not accused in this case, his weakness for his son is well known. The media is blaming him for influencing key witnesses to protect his son. Severe criticism of his father-son duo, both by the media and some social activists, is damaging the image of the party. However, Mr. Loyal has significant followers within the party and is considered an asset to the party. Any harsh decision against Mr. Loyal would adversely affect the future of NPP and could even lead to a split in the party. This would benefit the opposition.
At the Disciplinary Committee meeting, members came up with the following suggestions. Which of the following suggestions would harm the party, the least?
Answer the questions on the basis of information given in the following case.
The Disciplinary Committee of Nation Political Party (NPP) is meeting today to decide on the future of two of their party members, Mr. Loyal and his son Mr. Prodigal. Mr. Prodigal is the prime accused in the brutal murder of Mr. Victim, an opposition party leader. Mr. Prodigal is in police custody and his appeal for bail has got rejected. Mr. Loyal claims that his son is innocent and Mr. Victim’s death was the result of internal rivalry in the opposition party. Though Mr. Loyal is not accused in this case, his weakness for his son is well known. The media is blaming him for influencing key witnesses to protect his son. Severe criticism of his father-son duo, both by the media and some social activists, is damaging the image of the party. However, Mr. Loyal has significant followers within the party and is considered an asset to the party. Any harsh decision against Mr. Loyal would adversely affect the future of NPP and could even lead to a split in the party. This would benefit the opposition.
Mr. Opportunist, a veteran member of NPP, stakes his claims to be nominated as an NPP candidate in the upcoming election. Mr. Opportunist presented the following arguments in favour of his candidature to the NPP Executive Committee.
- Mr. Loyal’s candidature in the upcoming election will adversely impact NPP’s chances. Hence, the party should not nominate him.
- The party should call a press conference to disown Mr. Loyal. This would enhance the party’s image.
- The party would not be able to take any strong disciplinary action against Mr. Loyal, if he gets re-elected.
- I have a lot of goodwill and significant followers in the constituency,
- None of my close relatives are into active politics.
Which of the following combinations would best strengthen the claim of Mr. Opportunist?
Answer the questions on the basis of information given in the following case.
The Disciplinary Committee of Nation Political Party (NPP) is meeting today to decide on the future of two of their party members, Mr. Loyal and his son Mr. Prodigal. Mr. Prodigal is the prime accused in the brutal murder of Mr. Victim, an opposition party leader. Mr. Prodigal is in police custody and his appeal for bail has got rejected. Mr. Loyal claims that his son is innocent and Mr. Victim’s death was the result of internal rivalry in the opposition party. Though Mr. Loyal is not accused in this case, his weakness for his son is well known. The media is blaming him for influencing key witnesses to protect his son. Severe criticism of his father-son duo, both by the media and some social activists, is damaging the image of the party. However, Mr. Loyal has significant followers within the party and is considered an asset to the party. Any harsh decision against Mr. Loyal would adversely affect the future of NPP and could even lead to a split in the party. This would benefit the opposition.
The Disciplinary Committee has decided to suspend Mr. Loyal from the party because they felt he was influencing the judicial process. However, Mr. Loyal feels that the committee is biased and he is being framed. Now, election has been announced. The last time. Mr. Loyal had won with a majority on account of his good work. Which of the following options is most likely to resurrect Mr. Loyal’s immediate political career?
Innovative Institute of Business (IIB) has decided to be the first green campus in India. IIB Administration has advised all campus residents to reduce carbon footprints. IIB faculty members did a brainstorming and came up with the following suggestions:
- Replacing electricity source for street lights with solar panels.
- Replacing the existing buildings with environment friendly buildings.
- Organizing a seminar on ‘Towards a Sustainable Future’ involving all students, staff, and experts from around the country.
- Introducing a compulsory course on sustainability to increase awareness among students.
- Conducting an initial energy audit to explore where IIB can reduce carbon footprints.
Which of the following options would be the most preferred sequence of actions to reduce carbon footprints on campus?
x, 17, 3x – y2 – 2, and 3x + y2 – 30, are four consecutive terms of an increasing arithmetic sequence. The sum of the four number is divisible by:
In quadrilateral PQRS, PQ = 5 units, QR = 17 units, RS = 5 units, and PS = 9 units. The length of the diagonal QS can be:
Consider the formula,
Prof. Suman takes a number of quizzes for a course. All the quizzes are out of 100. A student can get an A grade in the course if the average of her scores is more than or equal to 90.Grade B is awarded to a student if the average of her scores is between 87 and 89 (both included). If the average is below 87, the student gets a C grade. Ramesh is preparing for the last quiz and he realizes that he will score a minimum of 97 to get an A grade. After the quiz, he realizes that he will score 70, and he will just manage a B. How many quizzes did Prof. Suman take?
A polynomial “ax3 + bx2 + cx + d” intersects x-axis at 1 and –1, and y-axis at 2. The value of b is:
The sum of the possible values of X in the equation |X + 7| + |X – 8| = 16 is:
There are two windows on the wall of a building that need repairs. A ladder 30 m long is placed against a wall such that it just reaches the first window which is 26 m high. The foot of the ladder is at point A. After the first window is fixed, the foot of the ladder is pushed backwards to point B so that the ladder can reach the second window. The angle made by the ladder with the ground is reduced by half, as a result of pushing the ladder. The distance between points A and B is
Amitabh picks a random integer between 1 and 999, doubles it and gives the result to Sashi. Each time Sashi gets a number from Amitabh, he adds 50 to the number, and gives the result back to Amitabh, who doubles the number again. The first person, whose result is more than 1000, loses the game. Let ‘x’ be the smallest initial number that results in a win for Amitabh. The sum of the digits of ‘x’ is:
Consider four natural numbers: x, y, x + y, and x – y. Two statements are provided below:
- All four numbers are prime numbers.
- The arithmetic mean of the numbers is greater than 4.
Which of the following statements would be sufficient to determine the sum of the four numbers?
Triangle ABC is a right angled triangle. D and E are mid points of AB and BC respectively. Read the following statements.
- AE = 19
- CD = 22
- Angle B is a right angle.
Which of the following statements would be sufficient to determine the length of AC?
There are two circles C1 and C2 of radii 3 and 8 units respectively. The common internal tangent, T, touches the circles at points P1 and P2 respectively. The line joining the centers of the circles intersects T at X. The distance of X from the center of the smaller circle is 5 units. What is the length of the line segment P1P2?
The probability that a randomly chosen positive divisor of 1029 is an integer multiple of 1023 is: a2/b2, then ‘b – a’ would be:
Circle C1 has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X axis. P and Q are points on curves given by the equations y = ax and y = 2ax respectively, where a < 1. The value of a is:
There are two squares S1 and S2 with areas 8 and 9 units, respectively. S1 is inscribed within S2, with one corner of S1 on each side of S2. The corners of the smaller square divides the sides of the bigger square into two segments, one of length ‘a’ and the other of length ‘b’, where, b > a. A possible value of ‘b/a’, is:
Diameter of the base of a water – filled inverted right circular cone is 26 cm. A cylindrical pipe, 5 mm in radius, is attached to the surface of the cone at a point. The perpendicular distance between the point and the base (the top) is 15 cm. The distance from the edge of the base to the point is 17 cm, along the surface. If water flows at the rate of 10 meters per minute through the pipe, how much time would elapse before water stops coming out of the pipe?
Aditya has a total of 18 red and blue marbles in two bags (each bag has marbles of both colors). A marble is randomly drawn from the first bag followed by another randomly drawn from the second bag, the probability of both being red is 5/16. What is the probability of both marbles being blue?
Consider a rectangle ABCD of area 90 units. The points P and Q trisect AB, and R bisects CD. The diagonal AC intersects the line segments PR and QR at M and N respectively. What is the area of the quadrilateral PQMN?
Two numbers, 297B and 792B, belong to base B number system. If the first number is a factor of the second number then the value of B is:
A teacher noticed a strange distribution of marks in the exam. There were only three distinct scores: 6, 8 and 20. The mode of the distribution was 8. The sum of the scores of all the students was 504. The number of students in the in most populated category was equal to the sum of the number of students with lowest score and twice the number of students with the highest score. The total number of students in the class was:
Read the following instruction carefully and answer the question that follows:
Expression
can also be written as
What would be the remainder if x is divided by 11?
A rectangular swimming pool is 48 m long and 20 m wide. The shallow edge of the pool is 1 m deep. For every 2.6 m that one walks up the inclined base of the swimming pool, one gains an elevation of 1 m. What is the volume of water (in cubic meters), in the swimming pool? Assume that the pool is filled up to the brim.
The value of the expression:
Answer the questions based on the trends lines from the following graphs.
Note: Left side of X axis represents countries that are “poor” and right side of X axis represents countries that are “rich”, for each region. GDP is based on purchasing power parity (PPP).
These are World Bank (WB) estimates.
âââââââ
Which of the following could be the correct ascending order of democratic regions for poor?
Answer the questions based on the trends lines from the following graphs.
Note: Left side of X axis represents countries that are “poor” and right side of X axis represents countries that are “rich”, for each region. GDP is based on purchasing power parity (PPP).
These are World Bank (WB) estimates.
âââââââ
Which region has the highest disparity, of democratic participation, between rich and poor?
Answer the questions based on the trends lines from the following graphs.
Note: Left side of X axis represents countries that are “poor” and right side of X axis represents countries that are “rich”, for each region. GDP is based on purchasing power parity (PPP).
These are World Bank (WB) estimates.
âââââââ
The maximum GDP of African region is higher than the maximum GDP of South American region by factor of:
Answer the questions based on the given data on the tourism sector in India.
âââââââ
In which of the following years the percentage increase in the number of Indians going abroad was greater than the percentage increase in the number of domestic tourists?
Answer the questions based on the given data on the tourism sector in India.
âââââââ
In which of the following years was the rupee cheapest with respect to the dollar?
Answer the questions based on the given data on the tourism sector in India.
âââââââ
Let ‘R’ be the ratio of Foreign Exchange Earnings from Tourism in India (in US $ million) to Foreign Tourist Arrivals in India (in million). Assume that R increases linearly over the years. If we draw a pie chart of R for all the years, the angle subtended by the biggest sector in the pie chart would be approximately:
Answer the questions based on the following information:
The exhibit given below compares the countries (first column) on different economic indicators (first row), from 2000-2010. A bar represents data for one year and a missing bar indicates missing data. Within an indicator, all countries have same scale.
âââââââ
Which of the following countries, after United States, has the highest spending on military as % of GDP, in the period 2000-2010?
Answer the questions based on the following information:
The exhibit given below compares the countries (first column) on different economic indicators (first row), from 2000-2010. A bar represents data for one year and a missing bar indicates missing data. Within an indicator, all countries have same scale.
âââââââ
Which country (and which year) has witnessed maximum year-to-year decline in “industry as percentage of GDP”? Given that the maximum value of industry as percentage of GDP is 49.7% and the minimum value of industry as percentage of GDP is 20.02%, in the chart above.
Answer the questions based on the following information:
The exhibit given below compares the countries (first column) on different economic indicators (first row), from 2000-2010. A bar represents data for one year and a missing bar indicates missing data. Within an indicator, all countries have same scale.
âââââââ
Which of the following countries has shown maximum increase in the “services, value added as % of GDP” from year 2000 to year 2010?
Three Vice Presidents (VP) regularly visit the plant on different days. Due to labour unrest, VP (HR) regularly visits the plant after a gap of 2 days. VP (Operations) regularly visits the plant after a gap of 3 days. VP (Sales) regularly visits the plant after a gap of 5 days. The VPs do not deviate from their individual schedules. CEO of the company meets the VPs when all the three VPs come to the plant together. CEO is one leave from January 5th to January 28th, 2012. Last time CEO met the VPs on January 3, 2012. When is the next time CEO will meet all the VPs?
Answer the following question based on the information given below.
The following graphs shows the revenue (in $ million) of three companies in their initial six years of operations, in an economy which is characterized by a persistent inflation.
âââââââ
Nikhil’s mother asks him to buy 100 pieces of sweets worth Rs. 100/-. The sweet shop has 3 kinds of sweets, kajubarfi, gulabjamun and sandesh. Kajubarfi costs Rs. 10/- per piece, gulabjamun costs Rs. 3/- per piece and sandesh costs 50 paise per piece. If Nikhil decides to buy at least one sweet of each type, how many gulabjamuns should he buy?
Answer the following question based on the information given below.
The following graphs shows the revenue (in $ million) of three companies in their initial six years of operations, in an economy which is characterized by a persistent inflation.
âââââââ
A potter asked his two sons to sell some pots in the market. The amount received for each pot was same as the number of pots sold. The two brothers spent the entire amount on some packets of potato chips and one packet of banana chips. One brother had the packet of banana chips along with some packets of potato chips, while the other brother just had potato chips. Each packet of potato chips costs Rs. 10/- and the packet of banana chips costs less than Rs. 10/-. The packets of chips were divided between the two brothers so each brother received equal number of packets. How much money should one brother give to the other to make the division financially equitable?
Answer the following question based on the information given below.
Ramya, based in Shanpur, took her car for a 400 km trip to Rampur. She maintained a log of the odometer readings and the amount of petrol she purchased at different petrol pumps at different prices (given below). Her car already had 10 litres of petrol at the start of the journey, and she first purchased petrol at the start of the journey, as given in table below, and she had 5 litres remaining at the end of the journey.
âââââââ
Three truck drivers, Amar, Akbar and Anthony stop at a road side eating joint. Amar orders 10 rotis, 4 plates of tadka, and a cup of tea. Akbar orders 7 rotis, 3 plates of tadka, and a cup of tea. Amar pays Rs. 80 for the meal and Akbar pays Rs. 60. Meanwhile, Anthony orders 5 rotis, 5 plates of tadka and 5 cups of tea. How much (in Rs.) will Anthony pay?
Answer the following question based on the information given below.
Ramya, based in Shanpur, took her car for a 400 km trip to Rampur. She maintained a log of the odometer readings and the amount of petrol she purchased at different petrol pumps at different prices (given below). Her car already had 10 litres of petrol at the start of the journey, and she first purchased petrol at the start of the journey, as given in table below, and she had 5 litres remaining at the end of the journey.
âââââââ
A computer program was tested 300 times before its release. The testing was done in three stages of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6 times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times the software failed in a single stage only?
Answer the following question based on the information given below.
The following graphs give annual data of Assets, Sales (as percentage of Assets) and Spending on Corporate Social Responsibility (CSR) (as percentage of Sales), of a company for the period 2004 – 2009.
âââââââ
In which year was the increase in spending on CSR, vis-à-vis the previous year, the maximum?
Answer the following question based on the information given below.
The following graphs give annual data of Assets, Sales (as percentage of Assets) and Spending on Corporate Social Responsibility (CSR) (as percentage of Sales), of a company for the period 2004 – 2009.
âââââââ
Of the years indicated below, in which year was the ratio of CSR/Assets the maximum?
Answer the following question based on the information given below.
The following graphs give annual data of Assets, Sales (as percentage of Assets) and Spending on Corporate Social Responsibility (CSR) (as percentage of Sales), of a company for the period 2004 – 2009.
âââââââ
What was the maximum value of spending on CSR activities in the period 2004-2009?
Answer the following question based on the information given below.
The following graphs give annual data of Assets, Sales (as percentage of Assets) and Spending on Corporate Social Responsibility (CSR) (as percentage of Sales), of a company for the period 2004 – 2009.
âââââââ
In which year, did the spending on CSR (measured in Rs) decline, as compared to previous year?
Answer the following question based on the information given below.
Five years ago Maxam Glass Co. had estimated its staff requirements in the five levels in their organization as: Level-1: 55; Level-2: 65; Level-3: 225; Level-4: 255 & Level-5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defence service men and ex-policemen. The following graph shows actual staff strength at various levels as on date.
âââââââ
The level in which the Ex-Defence Servicemen are highest in percentage terms is:
Answer the following question based on the information given below.
Five years ago Maxam Glass Co. had estimated its staff requirements in the five levels in their organization as: Level-1: 55; Level-2: 65; Level-3: 225; Level-4: 255 & Level-5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defence service men and ex-policemen. The following graph shows actual staff strength at various levels as on date.
âââââââ
If the company decides to abolish all vacant posts at all levels, which level would incur the highest reduction in percentage terms?
Answer the following question based on the information given below.
Five years ago Maxam Glass Co. had estimated its staff requirements in the five levels in their organization as: Level-1: 55; Level-2: 65; Level-3: 225; Level-4: 255 & Level-5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defence service men and ex-policemen. The following graph shows actual staff strength at various levels as on date.
âââââââ
Among all levels, which level has the lowest representation of Ex-policemen?
Answer the following question based on the information given below.
Five years ago Maxam Glass Co. had estimated its staff requirements in the five levels in their organization as: Level-1: 55; Level-2: 65; Level-3: 225; Level-4: 255 & Level-5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defence service men and ex-policemen. The following graph shows actual staff strength at various levels as on date.
âââââââ
In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?
Answer the following question based on the information given below.
Five years ago Maxam Glass Co. had estimated its staff requirements in the five levels in their organization as: Level-1: 55; Level-2: 65; Level-3: 225; Level-4: 255 & Level-5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defence service men and ex-policemen. The following graph shows actual staff strength at various levels as on date.
âââââââ
If x = (9 + 4√5)48 = [x] + f
where [x] is defined as integral part of x and f is a faction, then x(1 – f) equals
Answer the following question based on the information given below.
Five years ago Maxam Glass Co. had estimated its staff requirements in the five levels in their organization as: Level-1: 55; Level-2: 65; Level-3: 225; Level-4: 255 & Level-5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defence service men and ex-policemen. The following graph shows actual staff strength at various levels as on date.
âââââââ
Let an = 1 1 1 1 1 1 1….. 1, where 1 occurs n number of times. Then,
i. a741 is not a prime.
ii. a534 is not a prime.
iii. a123 is not a prime.
iv. a77 is not a prime.
Answer the following question based on the information given below.
âââââââ
Total income tax payable is obtained by adding two additional surcharges on calculated income tax.
- Education Cess: An additional surcharge called ‘Education Cess’ is levied at the late of 2% on the amount of income tax.
- Secondary and Higher Education Cess: An additional surcharge called ‘Secondary and Higher Education Cess` is levied at the rate of 1% on the amount of income tax.
Sangeeta is a young working lady. Towards the end of the financial year 2009-10, she found her total annual income to be Rs. 3, 37, 425/-. What % of her income is payable as income tax?
Answer the following question based on the information given below.
âââââââ
Total income tax payable is obtained by adding two additional surcharges on calculated income tax.
- Education Cess: An additional surcharge called ‘Education Cess’ is levied at the late of 2% on the amount of income tax.
- Secondary and Higher Education Cess: An additional surcharge called ‘Secondary and Higher Education Cess` is levied at the rate of 1% on the amount of income tax.
Mr. Madan observed his tax deduction at source, done by his employer, as Rs. 3,17,910/-. What was his total income (in Rs.) if he neither has to pay any additional tax nor is eligible for any refund?
Answer the following question based on the information given below.
âââââââ
Total income tax payable is obtained by adding two additional surcharges on calculated income tax.
- Education Cess: An additional surcharge called ‘Education Cess’ is levied at the late of 2% on the amount of income tax.
- Secondary and Higher Education Cess: An additional surcharge called ‘Secondary and Higher Education Cess` is levied at the rate of 1% on the amount of income tax.
A straight line through point P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. lf S is not the centre of the circumcircle, then which of the following is true?
Answer the following question based on the information given below.
âââââââ
Total income tax payable is obtained by adding two additional surcharges on calculated income tax.
- Education Cess: An additional surcharge called ‘Education Cess’ is levied at the late of 2% on the amount of income tax.
- Secondary and Higher Education Cess: An additional surcharge called ‘Secondary and Higher Education Cess` is levied at the rate of 1% on the amount of income tax.
What is the maximum possible value of (21 Sin X + 72 Cos X)?
Answer the following question based on the information given below.
âââââââ
Total income tax payable is obtained by adding two additional surcharges on calculated income tax.
- Education Cess: An additional surcharge called ‘Education Cess’ is levied at the late of 2% on the amount of income tax.
- Secondary and Higher Education Cess: An additional surcharge called ‘Secondary and Higher Education Cess` is levied at the rate of 1% on the amount of income tax.
The scheduling officer for a local police department is trying to schedule additional patrol units in each of two neighbourhoods – southern and northern. She knows that on any given day, the probabilities of major crimes and minor crimes being committed in the northern neighbourhood were 0.418 and 0.612, respectively, and that the corresponding probabilities in the southern neighbourhood were 0.355 and 0.520. Assuming that all crime occur independent of each other and likewise that crime in the two neighbourhoods are independent of each other, what is the probability that no crime of either type is committed in either neighbourhood on any given day?
Answer the following question based on the information given below.
A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.
The height of the light house above the sea level is:
Answer the following question based on the information given below.
A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.
What is the horizontal distance of the man from the lighthouse in the second position?
Answer the following question based on the information given below.
A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.
A 25 ft long ladder is placed against the wall with its base 7 ft from the wall. The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range:
Answer the following question based on the information given below.
A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.
The domain of the function
f(x) = log7{ log3(log5(20x – x2 – 91 ))} is:
Answer the following question based on the information given below.
A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.
There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?
Answer the following question based on the information given below.
A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.
The football league of a certain country is played according to the following rules:
- Each team plays exactly one game against each of the other teams.
- The winning team of each game is awarded l point and the losing team gets 0 point.
- If a-match ends in a draw, both the teams get 1/2 point.
After the league was over, the teams were ranked according to the points that they earned at the end of the tournament. Analysis of the points table revealed the following:
- Exactly half of the points earned by each team were earned in games against the ten teams which finished at the bottom of the table.
- Each of the bottom ten teams earned half of their total points against the other nine teams in the bottom ten.
- How many teams participated in the league?
Answer the following question based on the information given below.
A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.
In a city, there is a circular park. There are four points of entry into the park, namely - P, Q, R and S. Three paths were constructed which connected the points PQ, RS, and PS. The length of the path PQ is 10 units, and the length of the path RS is 7 units. Later, the municipal corporation extended the paths PQ and RS past Q and R respectively, and they meet at a point T on the main road outside the park. The path from Q to T measures 8 units, and it was found that the angle PTS is 60 . Find the area (in square units) enclosed by the paths PT, TS, and PS.
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
Which position should a contender choose if he has to be the leader?
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
One of the contending politicians, Mr. Chanaya, was quite proficient in calculations and could correctly figure out the exact position. He was the last person remaining in the circle. Sensing foul play the politicians decided to repeat the game. However, this time, instead of removing every alternate person, they agreed on removing every 300th person from the circle. All other rules were kept intact. Mr. Chanaya did some quick calculations and found that for a group of 542 people the right position to become a leader would be 437. What is the right position for the whole group of 545 as per the modified rule?
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
Little Pika who is five and half years old has just learnt addition. However, he does not know how to carry. For example, he can add 14 and 5, but he does not know how to add 14 and 7. How many pairs of consecutive integers between 1000 and 2000 (both 1000 and 2000 included) can Little Pika add?
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
In the country of Twenty, there are exactly twenty cities, and there is exactly one direct road between any two cities. No two direct roads have an overlapping road segment. After the election dates are announced, candidates from their respective cities start visiting the other cities. Following are the rules that the election commission has laid down for the candidates:
- Each candidate must visit each of the other cities exactly once.
- Each candidate must use only the direct roads between two cities for going from one city to another.
- The candidate must return to his own city at the end of the campaign.
- No direct road between two cities would be used by more than one candidate.
The maximum possible number of candidates is
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 0030l6?
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
Consider a square ABCD of side 60 cm. lt contains arcs BD and AC drawn with centres at A and D respectively. A circle is drawn such that it is tangent to side AB, and the arcs BD and AC. What is the radius of the circle?
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
There are 240 second year students in a B-School. The Finance area offers 3 electives in the second year. These are Financial Derivatives, Behavioural Finance, and Security Analysis. Four students have taken all the three electives, and 48 students have taken Financial Derivatives. There are twice as many students who study Financial Derivatives and Security Analysis but not Behavioural Finance, as those who study both Financial Derivatives and Behavioural Finance but not Security Analysis, and 4 times as many who study all the three. 124 students study Security Analysis. There are 59 students who could not muster courage to take up any of these subjects. The group of students who study both Financial Derivatives and Security Analysis but not Behavioural Finance, is exactly the same as the group made up of students who study both Behavioural Finance and Security Analysis. How many students study Behavioural Finance only?
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
ln a plane rectangular coordinate system, points L, M, N and O are represented by the coordinates (–5, 0), (1, –1), (0, 5), and (–1, 5) respectively. Consider a variable point P in the same plane. The minimum value of PL + PM + PN + PO is
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
ln a bank the account numbers are all 8 digit numbers, and they all start with the digit 2. So, an account number can be represented as 2x1x2x3x4x5x6x7. An account number is considered to be a ‘magic’ number if x1x2x3 is exactly the same as x4x5x6, or x5x6x7 or both. xi can take values from 0 to 9, but 2 followed by seven 0s is not a valid account number. What is the maximum possible number of customers having a ‘magic’ account number?
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
In a list of 7 integers, one integer, denoted as x is unknown. The other six integers are 20, 4, 10, 4, 8, and 4. If the mean, median, and mode of these seven integers are arranged in increasing order, they form an arithmetic progression. The sum of all possible values of x is
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
Prof. Bee noticed something peculiar while entering the quiz marks of his five students into a spreadsheet. The spreadsheet was programmed to calculate the average after each score was entered. Prof. Bee entered the marks in a random order and noticed that after each mark was entered, the average was always an integer. In ascending order, the marks of the students were 71, 76, 80, 82 and 91. What were the fourth and fifth marks that Prof. Bee entered?