List of top Quantitative Aptitude Questions asked in CAT

In a survey of political preference, 78% of those asked were in favor of at least one of the proposals: I, II and III. 50% of those asked favored proposal I, 30% favored proposal II, and 20% favored proposal III. If 5% of those asked favored all three of the proposals, what percentage of those asked favored more than one of the 3 proposals.

If \( n = 1 + x \), where \( x \) is the product of four consecutive positive integers, then which of the following is/are true?
A. \( n \) is odd
B. \( n \) is prime
C. \( n \) is a perfect square

If \( |r - 6| = 11 \) and \( |2q - 12| = 8 \), what is the minimum possible value of \( q / r \)?

Forty percent of the employees of a certain company are men, and 75 percent of the men earn more than Rs. 25,000 per year. If 45 percent of the company's employees earn more than Rs. 25,000 per year, what fraction of the women employed by the company earn Rs. 25,000 year or less?

Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?

The speed of a railway engine is 42 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:

For a scholarship, at most n candidates out of 2n + 1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is:

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?

The remainder when \( 7^{84} \) is divided by \( 342 \) is :

Let a, b, c be distinct digits. Consider 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

The number of positive integer valued pairs \( (x, y) \), satisfying \( 4x - 17y = 1 \) and \( x < 1000 \) 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:

The following operations are defined for real numbers.
\(a \,\#\, b = a + b\), if \(a\) and \(b\) both are positive, else \(a \,\#\, b = 1\).
\(a \,\triangledown\, b = (a \times b)^{a+b}\) if \(a \times b\) is positive, else \(a \,\triangledown\, b = 1\).

\[ \dfrac{(2 \,\#\, 1)}{(1 \,\triangledown\, 2)} = \]

A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter \( \triangle ABC \). \( \angle BAC = 30^\circ \), \( AB = AC = 10 \) m. What is the area that can be grazed by the cow if the length of the rope is 12 m?

What is the digit in the unit's place of \( 2^{51} \)?

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.

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?
I. Amar wears blue and Akbar does not wear green
II. Amar does not wear blue and Akbar wears blue
III. Amar does not wear blue and Akbar does not wear blue
IV. Amar wears green, Akbar does not wear red, Anthony does not wear green

A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.

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, all these spots will simultaneously touch the ground again?

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?

Answer the questions based on the following information. Production pattern for number of units (in cubic feet) per day.

• Day 1: 150 units
• Day 2: 180 units
• Day 3: 120 units
• Day 4: 250 units
• Day 5: 160 units
• Day 6: 120 units
• Day 7: 150 units

The finished goods are to be transported to the market by a truck having a capacity of 2000 cubic feet. Any finished goods (ready at the end of the day) retained overnight at the factory will incur a storage cost of Rs 5 per cubic foot for each night of storage. The hiring cost for the truck is Rs 1000 per day.

If the storage cost is reduced to Re 0.80 per cubic feet per day, then on which day(s), should the truck be hired?

Answer the questions based on the following information. Production pattern for number of units (in cubic feet) per day.

• Day 1: 150 units
• Day 2: 180 units
• Day 3: 120 units
• Day 4: 250 units
• Day 5: 160 units
• Day 6: 120 units
• Day 7: 150 units

The finished goods are to be transported to the market by a truck having a capacity of 2000 cubic feet. Any finished goods (ready at the end of the day) retained overnight at the factory will incur a storage cost of Rs 5 per cubic foot for each night of storage. The hiring cost for the truck is Rs 1000 per day.

If all the units should be sent to the market, then on which days should the trucks be hired to minimize the cost?