List of top Quantitative Aptitude Questions asked in CAT

A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. The total area of the walkway is 516 m$^2$. How wide, in metres, is the walkway?

Let $b$ be a positive integer and $a = b^2 - b$. If $b \ge 4$, then $a^2 - 2a$ is divisible by:

In some code, letters $a, b, c, d, e$ represent 2, 4, 5, 6, and 10 in some order. Given:
I. $a + c = e$,
II. $b - d = d$,
III. $e + a = b$.
Which is true?

Ujakar and Keshab attempted to solve a quadratic equation.
- Ujakar made a mistake in writing down the constant term and got roots (4, 3).
- Keshab made a mistake in writing down the coefficient of $x$ and got roots (3, 2).
What will be the exact roots of the original quadratic equation?

A set of consecutive positive integers beginning with 1 is written on the blackboard. A student erased one number. The average of the remaining numbers is $35\frac{7}{17}$. What was the number erased?

Three runners A, B, C run a race, A finishes 12 m ahead of B and 18 m ahead of C, while B finishes 8 m ahead of C. All run entire distance at constant speed. What was the length of the race?

The owner of an art shop raises prices by X%, then later reduces all new prices by X%. After one such cycle, price decreased by Rs. 441. After a second such cycle, painting sold for Rs. 1,944.81. What was the original price?

Let $x$ and $y$ be positive numbers such that $x+y = 1$. Find the minimum value of $\left(x + \frac{1}{x}\right)^2 + \left(y + \frac{1}{y}\right)^2$.

Train X departs from station A at 11 a.m. for station B, 180 km away. Train Y departs from station B at 11 a.m. for station A. Train X speed = 70 km/h, no stops. Train Y speed = 50 km/h, stops for 15 min at station C, 60 km from B. Ignoring train lengths, find the distance from A to meeting point.

For a Fibonacci sequence, from the third term onwards, each term is the sum of the previous two. If the difference in squares of the 7th and 6th terms is 517, what is the 10th term?

Fresh grapes contain 90% water by weight while dried grapes contain 20% water. What is the weight of dry grapes available from 20 kg of fresh grapes?

Euclid has a triangle with longest side 20, another side 10, and area 80. What is the exact length of the third side?

If $a, b, c, d$ are four positive real numbers such that $abcd = 1$, what is the minimum value of $(1+a)(1+b)(1+c)(1+d)$?

Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom's steps. Shyama gets to the top after taking 25 steps, while Vyom takes 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?

At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?

Three friends — Asit, Arnold and Afzal — work together to get chores done. Time together is 6 hr less than Asit alone, 1 hr less than Arnold alone, and half the time Afzal alone would take. How long did it take them together?

Every 10 years the Indian Government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri:
- Chota Hazri has 4,522 fewer males than Mota Hazri.
- Mota Hazri has 4,020 more females than males.
- Chota Hazri has twice as many females as males.
- Chota Hazri has 2,910 fewer females than Mota Hazri.
What is the total number of males in Chota Hazri?

All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?

In a number system, the product of 44 and 11 is 3414. The number 3111 of this system, when converted to the decimal number system, becomes:

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. If he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour?

Three classes X, Y and Z take an algebra test. - Average score in X: 83.
- Average score in Y: 76.
- Average score in Z: 85.
- Average of X and Y together: 79.
- Average of Y and Z together: 81.
What is the average for all three classes?

$x$ and $y$ are real numbers satisfying the conditions $2<x<3$ and $-8<y<-7$. Which of the following expressions will have the least value?