List of top Quantitative Aptitude Questions asked in CAT

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

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

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

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?

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 $E$?

If $f_{1}(x) = \frac{2}{2+x}$ and $f_{n}(x) = \frac{1}{1+f_{n-1}(x)}$, where $n>1$, then find the approximate value of $f_{50}(1)$.

The sum of the squares of three consecutive integers is 110. What is the smallest integer?

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:

The numbers $1, 2, \dots, n$ are written in natural order. Numbers in odd places are struck off to form a new sequence. This process is continued until only one number is left. If $n = 1997$, find the last remaining number.

The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other number?

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 $2x + 3y = 15$ and $x - y = 1$, what is the value of $x + y$?

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 $(a + b)^2$?

If $3x = 4y = 12z$, what is the ratio $x:y:z$?

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 $2^{10}$?