List of top Quantitative Aptitude Questions asked in CAT

A shopkeeper sells two types of items, A and B, at a profit of 20% and 30%, respectively. If the cost price of A is Rs. 100 and B is Rs. 200, and he sells 3 items of A and 2 items of B, what is the total profit?

A man sells an article at a loss of 10%. If he had sold it for Rs. 50 more, he would have gained 5%. What is the cost price?

The cost price of an article is Rs. 400. If it is sold at a profit of 25%, what is the selling price?

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less. What is the speed of the train?

Rohan and Sohan start from the same point on a circular track in the same direction. Speed of Rohan is nine times Sohan. How many times are they diametrically opposite by the time Sohan completes 3 rounds?

A car travels 240 km in 4 hours. What is its speed in km/h?

A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in 6.5 hours. What is the speed of the boat in still water?

The area of a rectangle is 48 cm$^2$, and its perimeter is 28 cm. What is the length of the rectangle?

The lengths of the sides of a right-angled triangle are in geometric progression. What is the ratio of the sines of its acute angles?

If the area of a circle is $154$ cm$^2$, what is its circumference?

Harry Potter bought a triangular piece of land of area $150\ \text{m}^2$. Harry measured two sides of the plot and found the largest side to be $50\ \text{m}$ and another side to be $10\ \text{m}$. Find the exact length of the third side.

Find the sum of the series: \[ 1 + \frac{2}{11} + \frac{5}{12} + \frac{10}{13} + \frac{17}{14} + \dots \]

If $a_1,a_2,\....,a_n$ $(n>3)$ are all unequal positive real numbers and \[ E = \frac{(1+a_1+a_1^2)(1+a_2+a_2^2)\dots(1+a_n+a_n^2)}{a_1 a_2 \dots a_n}, \] then which of the following best describes $E$?

The sum of a two-digit number and the number obtained by reversing its digits is 99. If the digits differ by 3, what is the number?

For an odd positive integer $n$ ($51 \le n \le 99$), the quantity $n^3 - n$ is always divisible by:

A series in which any term is equal to the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and determine the series. It is known that the difference of the squares of the ninth and eighth terms of a Fibonacci series is $840$. Find the 12th term of that series.

If $x + y = 10$ and $xy = 21$, what is the value of $x^2 + y^2$?

On a certain day, the sum of the date and the square root of the month gives the square of the month. Find the date.

The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and the second to the third is 5:8, what is the second number?

If $a^2 + b^2 = 25$ and $ab = 12$, what is $(a + b)^2$?

A rectangle MNOQ has $NO$ extended to point R. In $\triangle QPR$:
- $QP = \frac{2x}{3}QM$
- $\angle ORP = 45^\circ$
- $QR = 4\sqrt{17}$ cm
S and T are midpoints of sides QR and PR respectively. If $ST = 6$ units, find the area of rectangle MNOQ.

A bag contains 3 red and 5 black balls. Two balls are drawn at random. What is the probability that both are red?

The sum of the first $n$ terms of an arithmetic progression is $3n^2 + 2n$. What is the 10th term?

If $f(x) = x^2 + 2x + 1$, what is $f(3)$?

What is the value of $2^{10}$?