List of top Questions asked in CAT

Number of students who have opted for subjects A, B and C are 60, 84 and 108 respectively. The examination is to be conducted for these students such that only the students of the same subject are allowed in one room. Also the number of students in each room must be same. What is the minimum number of rooms that should be arranged to meet all these conditions?

Amar, Akbar and Anthony are three friends. Only three colours are available for their shirts, viz. red, green and blue. Amar does not wear red shirt. Akbar does not wear green shirt. Anthony does not wear blue shirt.
If Akbar and Anthony wear the same colour of shirts, then which of the following is not true?

Amar, Akbar and Anthony are three friends. Only three colours are available for their shirts, viz. red, green and blue. Amar does not wear red shirt. Akbar does not wear green shirt. Anthony does not wear blue shirt.
If two of them wear the same colour, then how many of the following must be false?

Answer the questions based on the following information.
A, B, C and D collected one-rupee coins following the given pattern.
Together they collected 100 coins. Each one of them collected even number of coins.
Each one of them collected at least 10 coins. No two of them collected the same number of coins.
The maximum number of coins collected by any one of them cannot exceed

Answer the questions based on the following information.
A, B, C and D collected one-rupee coins following the given pattern.
Together they collected 100 coins. Each one of them collected even number of coins.
Each one of them collected at least 10 coins. No two of them collected the same number of coins.
If A collected 54 coins, then the difference in the number of coins between the one who collected maximum number of coins and the one who collected the second highest number of coins must be at least

Answer the questions based on the following information.
A, B, C and D collected one-rupee coins following the given pattern.
Together they collected 100 coins. Each one of them collected even number of coins.
Each one of them collected at least 10 coins. No two of them collected the same number of coins.
If A collected 54 coins and B collected two more coins than twice the number of coins collected by C, then the number of coins collected by B could be

Three wheels can complete 60, 36, and 24 revolutions per minute. There is a red spot on each wheel that touches the ground at time zero. After how much time will all these spots will simultaneously touch the ground again?
A is the set of positive integers such that when divided by 2, 3, 4, 5, 6 leaves the remainders 1, 2, 3, 4, 5 respectively. How many integers between 0 and 100 belong to set A?
A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.

Four identical coins are placed in a square. For each coin the ratio of area to circumference is the same as the ratio of circumference to area. Then find the area of the square that is not covered by the coins.

A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter ∆ ABC.
∠ BAC = 30°
| (AB) = | (AC) = 10 m

What is the area that can be grazed by the cow if the length of the rope is 8 m?

A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter ∆ ABC.
∠ BAC = 30°
| (AB) = | (AC) = 10 m

What is the area that can be grazed by the cow if the length of the rope is 12 m?

A, B, C and D are to be seated in a row. But C and D cannot be together. Also B cannot be at the third place.
Which of the following must be false?

A, B, C and D are to be seated in a row. But C and D cannot be together. Also B cannot be at the third place.
If A is not at the third place, then which of the following options does C have?

A, B, C and D are to be seated in a row. But C and D cannot be together. Also B cannot be at the third place.
If A and B are together, then which of the following must be necessarily true?

A yearly payment to the servant is Rs. 90 plus one turban. The servant leaves the job after 9 months and receives Rs. 65 and a turban. Then find the price of the turban.
How many numbers can be formed from 1, 2, 3, 4, 5, without repetition, when the digit at the unit’s place must be greater than that in the ten’s place?

(BE)2 = MPB, where B, E, M and P are distinct integers. Then M =

Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed of 4 km/hr. While the other man travelled with varying speed as follows: in the first hour his speed was 2 km/hr, in the second hour it was 2.5 km/hr, in the third hour it was 3 km/hr, and so on. When will they meet each other?
Evaluate the following expression: \[ \left( \frac{X \ Y}{- X \times Y} \right) = \frac{3}{8}, \] \text{then which of the following must be true?}
Five-digit numbers are formed using only 0, 1, 2, 3, 4 exactly once. What is the difference between the maximum and minimum number that can be formed?
P, Q, R and S are four statements. Relation between these statements is as follows. I. If P is true, then Q must be true.
II. If Q is true, then R must be true.
III. If S is true, then either Q is false or R is false.
Which of the following must be true?

Three circles, each of radius 20, have centres at P, Q, and R. Further, AB = 5, CD = 10 and EF = 12. What is the perimeter of \( \triangle PQR \)?

Evaluate the following expression: \[ \left( (|1| \ 2) - \left( 10^{1.3} \vee \log_{10} 0.1 \right) \right) \div (1 \vee 2) \]
One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and the remaining 50% dies after producing the next generation. If the seventh generation number is 4,096 million, what is the number in the first generation?