CAT 2006 — QA Questions with Solutions

QA

IndicesEasy

Q1.

If x = −0.5, then which of the following has the smallest value?

QA

Comparison of SurdsEasy

Q2.

Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ?

QA

RatioEasy

Q3.

If $\frac{a}{b} = \frac{1}{3}$ , $\frac{b}{c} = 2$ , $\frac{c}{d} = \frac{1}{2}$ , $\frac{d}{e} = 3$ and $\frac{e}{f} = \frac{1}{4}$ then what is the value of $\frac{a b c}{d e f}$ ?

QA

Basics of Mensuration/PrismEasy

Q4.

The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

QA

Miscellaneous ProgressionsEasy

Q5.

Consider a sequence where the n^th term, $t_{n} = \frac{n}{n + 2}, n = 1, 2, . . . .$

The value of $t_{3} \times t_{4} \times t_{5} \times . . . \times t_{53}$ equals:

QA

Arithmetic ProgressionEasy

Q6.

A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

QA

IndicesEasy

Q7.

What are the values of x and y that satisfy both the equations?

2^0.7x . 3^{−1. 25y} = $\frac{8 \sqrt{6}}{27}$

4^0.3x . 9^0.2y = 8 . (81)^1/5

QA

2 Variable EquationsEasy

Q8.

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:

QA

Venn DiagramEasy

Q9.

A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below:

Only September: 18; September but not August: 23; September and July: 8; September: 28; July: 48; July and August: 10; None of the three months: 24.

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?

QA

Even OddEasy

Q10.

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

QA

Domain & RangeEasy

Q11.

The graph of y – x against y + x is as shown below. (All graphs in this question are drawn to scale and the same scale has been used on each axis). Then, which of the options given shows the graph of y against x.

QA

Arithmetic ProgressionEasy

Q12.

Consider the set S = {1, 2, 3, …, 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

QA

Basics of Mensuration/PrismEasy

Passage / Data

Answer the next 2 questions based on the information given below:

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.

Q13.

The proportion of the sheet area that remains after punching is:

QA

Basics of Mensuration/PrismEasy

Passage / Data

Answer the next 2 questions based on the information given below:

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.

Q14.

Find the area of the part of the circle (round punch) falling outside the square sheet.

QA

Solving Quadratic EquationsEasy

Passage / Data

Answer the next 2 questions based on the information given below:

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.

Q15.

What values of x satisfy $x^{\frac{2}{3}} + x^{\frac{1}{3}} - 2 \leq 0$ ?

QA

Basics (Functions)Easy

Passage / Data

Answer the next 2 questions based on the information given below:

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.

Q16.

Let f(x) = max (2x + 1, 3 − 4x), where x is any real number. Then the minimum possible value of f(x) is:

QA

VariationEasy

Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

Q17.

What is the weight of Praja‘s luggage?

QA

VariationEasy

Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

Q18.

What is the free luggage allowance?

QA

Time, Speed & DistanceEasy

Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

Q19.

Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

QA

2 Variable EquationsEasy

Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

Q20.

When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

QA

Basics of CirclesEasy

Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

Q21.

A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semicircle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semicircle (in sq. cm.) will be:

QA

Forming a committeeEasy

Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

Q22.

There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

QA

Number TheoryEasy

Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

Q23.

The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:

QA

LogarithmsEasy

Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

Q24.

If log_yx = a × log_zy = b × log_xz = ab, then which of the following pairs of values for (a, b) is not possible?

QA

Basics of QuadrilateralsEasy

Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

Q25.

An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?

CAT 2006 — QA

CAT 2006 · QA