List of top Quantitative Aptitude Questions asked in CAT

Nayjivan Express starts from Ahmedabad towards Baroda at 6:30 am in the morning, moving at an average speed of 50 km/h. The distance between Baroda and Ahmedabad is 100 km. At 7:00 am in the morning the Howrah Ahmedabad express starts from Baroda and moves towards Ahmedabad at 40 km/h. At 7:30 am, Mr. Shah, the station controller, realizes that both the trains are running on the same track. How much time does he have to take action to prevent the collision?
The alphabets a, b, c represent integers forming a two-digit number 'ab' and a three digit number 'ccb'. Both defined under the usual decimal number system. If $(ab)^2 = ccb$ and $ccb>300$, then the value of b is:
In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals I, II and III. If 50% favoured the first proposal, 30% the second and 20% the third, 5% favoured all the three, what is the percentage of those asked favoured more than one of the three proposals?
Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?
There is a square field with each side 500 metres long. It has a compound wall along its perimeter. At one of its corners, a triangular area of the field is to be cordoned off by erecting a straight-line fence. The compound wall and the fence will form its borders. If the length of the fence is 100 metres, what is the maximum area in square metres that can be cordoned off?
40% of the employees of an organization are men. Of these 75% earn more than Rs. 25,000 per year. If 45% of the total employees of the company earn more than Rs. 25,000 per year, then what fraction of the women earn more than Rs. 25,000 per year?
There is a circle of radius 1 cm. Each member of a sequence of regular polygons S1(n), n = 4, 5, 6, ... where n = number of sides of the polygon, is circumscribing the circle and each member of the sequence of regular polygons S2(n), n = 4, 5, 6, ... where n is the number of sides of the polygon, is inscribed in the circle. Let L1(n) and L2(n) denote perimeters of the corresponding polygons of S1(n) and S2(n). Then $\angle L1(13) + 2\pi$ is L2(17) is:
Given $n^2 = 123456787654321$, find n.
The remainder when $7^{84}$ is divided by 342 is:
For two positive integers a and b define the function h(a, b) as the greatest common factor (gcf) of a, b. Let A be a set of n positive integers, G(A), the gcf of the elements of set A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is:
Three labeled boxes containing red and white cricket balls are all mislabeled. It is known that one of the boxes contains only white balls and one only red balls. The third contains a mixture of red and white balls. You are required to correctly label the boxes with the labels red, white and red and white by picking a sample of one ball from only one box. What is the label on the box you should sample?
A number is formed by writing first 54 natural numbers in front of each other as 12345678910111213... Find the remainder when this number is divided by 8.
What is the digit in the unit’s place of 251?
A, B, C, D, ..., X, Y, Z are the players who participated in a tournament. Everyone played with every other player exactly once. A win scores 2 points, a draw scores 1 point and a loss scores 0 point. None of the matches ended in a draw. No two players scored the same score. At the end of the tournament, a ranking list is published which is in accordance with the alphabetical order. Then
There are two containers: the first contains 500 ml of alcohol, while the second contains 500 ml of water. Three cups of alcohol from the first container is taken out and is mixed well in the second container. Then three cups of this mixture is taken out and is mixed in the first container. Let A denote the proportion of water in the first container and B denote the proportion of alcohol in the second container. Then
I started climbing up the hill at 6 a.m. and reached the top of the temple at 6 p.m. Next day I started coming down at 6 a.m. and reached the foothill at 6 p.m. I walked on the same road. The road is so short that only one person can walk on it. Although I varied my pace on my way, I never stopped on my way. Then which of the following must be true?
What is the maximum current gain possible?
If the USA dollar becomes cheap by 12% over its original cost and the cost of German mark increased by 20%, what will be the gain? (The selling price is not altered.)
You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg and each emerald weighs 0.4 kg. Your bag can carry at most 12 kg. What should you collect to get the maximum wealth?
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?
How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?

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?

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?

My son adores chocolates. He likes biscuits. But he hates apples. I told him that he can buy as many chocolates as he wishes. But then he must have biscuits twice the number of chocolates and should have apples more than biscuits and chocolates together. Each chocolate costs Rs. 1. The cost of an apple is twice the chocolate and four biscuits are worth one apple. Then which of the following can be the amount that I spent on that evening on my son if the number of chocolates, biscuits, and apples bought were all integers?
I have one-rupee coins, 50-paisa coins and 25-paisa coins. The number of coins are in the ratio 2.5 : 3 : 4. If the total amount with me is Rs. 210, find the number of one-rupee coins.