CAT 1995 — QA Questions with Solutions

QA

Basics of TrianglesEasy

Q1.

ABCD is a square of area 4, which is divided into four non-over lapping triangles as shown in figure. Then the sum of the perimeters of the triangles is

QA

FactorsEasy

Q2.

5⁶ - 1 is divisible by

QA

Successive Percentage ChangeEasy

Q3.

Ram purchased a flat at Rs.1 lakh and Prem purchased a plot of land worth Rs.1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then

QA

Simple EquationsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q4.

How many rupees did Suvarna start with?

QA

Simple EquationsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q5.

Who started with the lowest amount?

QA

Simple EquationsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q6.

Who started with the highest amount?

QA

Simple EquationsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q7.

What was the amount with Uma at the end of the second round?

QA

Number TheoryEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q8.

72 hens cost Rs.__ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand?

QA

PercentageEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q9.

A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is

QA

Number TheoryEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q10.

The value of $\frac{55^{3} + 45^{3}}{55^{2} - 55 \times 45 + 45^{2}}$ is

QA

Number TheoryEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q11.

For the product n(n + 1)(2n + 1), n ∈ N, which one of the following is not necessarily true?

QA

Number TheoryEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q12.

The remainder obtained when a prime number greater than 6 is divided by 6 is

QA

Fundamental Principles of P&CEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q13.

Boxes numbered 1, 2, 3, 4 and 5 are kept in a row, and they are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

QA

Basics of TrianglesEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q14.

AB ⊥ BC, BD ⊥ AC and CE bisects ∠C, ∠A = 30°. Then what is ∠CED?

QA

Simple InterestEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q15.

A man invests Rs.3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?

QA

PercentageEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q16.

$\frac{2}{5}$ of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then the total number of voters is

QA

Basics of QuadrilateralsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q17.

PQRS is a square. SR is a tangent (at point S) to the circle with centre O and TR = OS. Then the ratio of area of the circle to the area of the square is

QA

Linear RaceEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q18.

In a race of 200 m run, A beats S by 20 m and N by 40 m. If S and N are running a race of 100 m with exactly same speed as before, then by how many metres will S beat N?

QA

2 Variable EquationsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q19.

Three consecutive positive even numbers are such that thrice the first number exceeds double the third by 2, then the third number is

QA

Man Days (single group of people)Easy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q20.

A group of men decided to do a job in 8 days. But since 10 men dropped out every day, the job got completed at the end of the 12th day. How many men were there at the beginning?

QA

BasicsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q21.

If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability that the number is divisible by 25, if repetition of digits is not allowed?

QA

Working in ShiftsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q22.

Two typists undertake to do a job. The second typist begins working one hour after the first. Three hours after the first typist has begun working, there is still $\frac{9}{20}$ of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually ?

QA

EscalatorEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q23.

I live X floors above the ground floor of a high-rise building. It takes me 30 s per floor to walk down the steps and 2 s per floor to ride the lift. What is X, if the time taken to walk down the steps to the ground floor is the same as to wait for the lift for 7 min and then ride down?

QA

Basics of TrianglesEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q24.

The sides of a triangle are 5, 12 and 13 units. A rectangle is constructed, which is equal in area to the triangle, and has a width of 10 units. Then the perimeter of the rectangle is

QA

Basics of QuadrilateralsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q25.

In the adjoining figure, AC+ AB = 5AD and AC – AD = 8. Then the area of the rectangle ABCD is

QA

Forming a Quadratic Equation and Relation between roots and coefficientsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q26.

One root of x² + kx – 8 = 0 is square of the other. Then the value of k is

QA

Basics of CirclesEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q27.

In the given figure, AB is diameter of the circle and points C and D are on the circumference such that ∠CAD = 30° and ∠CBA = 70°. What is the measure of ∠ACD?

QA

Basics of TrianglesEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q28.

The length of a ladder is exactly equal to the height of the wall it is learning against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then the height of the wall is

QA

Dishonest MerchantEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q29.

A stockist wants to make some profit by selling sugar. He contemplates about various methods . Which of the following would maximise his profit?

I. Sell sugar at 10% profit.
II. Use 900 g of weight instead of 1 kg.
III. Mix 10% impurities in sugar and selling sugar at cost price.
IV. Increase the price by 5% and reduce weights by 5%.

QA

EscalatorEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q30.

A man can walk up a moving ‘up’ escalator in 30 s. The same man can walk down this moving ‘up’ escalator in 90 s. Assume that his walking speed is same upwards and downwards. How much time will he take to walk up the escalator, when it is not moving?

QA

Solving Quadratic EquationsEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q31.

Two positive integers differ by 4 and sum of their reciprocals is $\frac{10}{21}$ . Then one of the numbers is

QA

Number TheoryEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q32.

Three bells chime at an interval of 18 min, 24 min and 32 min. At a certain time they begin to chime together. What length of time will elapse before they chime together again?

QA

Solving InequalitiesEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q33.

What is the value of m which satisfies 3m² – 21m + 30 < 0?

QA

Successive Percentage ChangeEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q34.

The rate of inflation was 1000%. Then what will be the cost of an article, which costs 6 units of currency now, 2 years from now?

QA

Basics (Functions)Easy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q35.

Largest value of min(2 + x², 6 – 3x), when x > 0, is

QA

MiscellaneousEasy

Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Q36.

A, B, C and D are four towns, any three of which are non-collinear. Then the number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is

QA

Basics (Functions)Easy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q37.

Find the value of me(a + mo(le(a, b)); mo(a + me(mo(a), mo(b))), at a = –2 and b = –3.

QA

Basics (Functions)Easy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q38.

Which of the following must always be correct for a, b > 0?

QA

Basics (Functions)Easy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q39.

For what values of ‘a’ is me(a² – 3a, a – 3) < 0?

QA

Basics (Functions)Easy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q40.

For what values of ‘a’ is le(a² – 3a, a – 3) < 0?

QA

Data SufficiencyEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q41.

Direction: Each of these questions is followed by two statements, I and II. Mark the answer as

1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.

If x, y and z are real numbers, is z – x even or odd?

I. xyz is odd.
II. xy + yz + zx is even.

QA

Data SufficiencyEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q42.

Direction: Each of these questions is followed by two statements, I and II. Mark the answer as

1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.

What is the value of x, if x and y are consecutive positive even integers?

I. (x – y)² = 4
II. (x + y)² < 100

QA

Data SufficiencyEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q43.

Direction: Each of these questions is followed by two statements, I and II. Mark the answer as

1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.

What is the profit percentage?

I. The cost price is 80% of the selling price.
II. The profit is Rs.50.

QA

Data SufficiencyEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q44.

Direction: Each of these questions is followed by two statements, I and II. Mark the answer as

1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.

What is the area of the triangle?

I. Two sides are 41 cm each.
II. The altitude to the third side is 9 cm long.

QA

Data SufficiencyEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q45.

Direction: Each of these questions is followed by two statements, I and II. Mark the answer as

1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.

What is the price of bananas?

I. With Rs.84, I can buy 14 bananas and 35 oranges.
II. If price of bananas is reduced by 50%, then we can buy 48 bananas in Rs.12.

QA

Data SufficiencyEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q46.

Direction: Each of these questions is followed by two statements, I and II. Mark the answer as

1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.

What is the first term of an arithmetic progression of positive integers?

I. Sum of the squares of the first and the second term is 116.
II. The fifth term is divisible by 7.

QA

Data SufficiencyEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q47.

Direction: Each of these questions is followed by two statements, I and II. Mark the answer as

1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.

What is the length of rectangle ABCD?

I. Area of the rectangle is 48 square units.
II. Length of the diagonal is 10 units.

QA

Data SufficiencyEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q48.

Direction: Each of these questions is followed by two statements, I and II. Mark the answer as

1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.

What is the number x?

I. The LCM of x and 18 is 36.
II. The HCF of x and 18 is 2.

QA

Data SufficiencyEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q49.

Direction: Each of these questions is followed by two statements, I and II. Mark the answer as

1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.

Is x + y – z + t even?

I. x + y + t is even.
II. t and z are odd.

QA

Basics of TrianglesEasy

Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Q50.

Which one of the following cannot be the ratio of angles in a right-angled triangle?

CAT 1995 — QA

CAT 1995 · QA