List of top Quantitative Aptitude Questions asked in CAT

The table below shows the age-wise distribution of the population of Reposia. The number of people aged below $35$ years is $400$ million.

Age Group Percentages

Age group	Percentages
Below 15 years	30.00
15 – 24	17.75
25 – 34	17.00
35 – 44	14.50
45 – 54	12.50
55 – 64	7.10
65 and above	1.15

If the ratio of females to males in the ‘below 15 years’ age group is $0.96$, find the number of females (in millions) in that age group.

Let $n$ be the number of different $5$-digit numbers, divisible by $4$, using the digits 1, 2, 3, 4, 5, 6 without repetition. Find $n$.

If a function $f(x)$ satisfies the equation \[ f\left(x + \frac{1}{x}\right) = x^2 + \frac{1}{x^2}, \quad x \neq 0 \] then $f(x)$ equals:

ABCDEFGH is a regular octagon. A and E are opposite vertices. A frog starts at A, may jump to adjacent vertices except E. When it reaches E, it stops. Let $a_n$ = number of distinct paths of exactly $n$ jumps ending at E. Find $a_{2n-1}$.

There are cities A, B, C. Each city is connected with the other two by at least one direct road. A traveller can go from one city to another directly or via the third city. There are 33 total routes from A to B, and 23 from B to C. Find the number of roads from A to C.

There are two disjoint sets $S_1$ and $S_2$: $S_1 = \{ f(1), f(2), f(3), \dots \}$, $S_2 = \{ g(1), g(2), g(3), \dots \}$ such that $S_1 \cup S_2$ = natural numbers. Also $f(1)<f(2)<f(3)<\dots$ and $g(1)<g(2)<g(3)<\dots$, and $f(n) = g(g(n)) + 1$. Find $g(1)$.

$x$ and $y$ are defined such that $x^2 + y^2 = 0.1$ and $|x-y| = 0.2$. Find $|x| + |y|$.

The expression $N = 55^3 + 17^3 - 72^3$ is exactly divisible by:

A circle of radius 1 has 7 sectors $S_1, S_2, \dots, S_7$, adjacent to each other. Total area of all 7 sectors = one eighth of area of circle. The $j$-th sector’s area is twice the $(j-1)$-th sector’s area. Find the angle subtended by $S_1$ at the center.

Find the area bounded by the curves $|x + y| = 1$, $|x| = 1$, $|y| = 1$.

The three sides of a triangle have lengths $a, b, c$. If $a^2 + b^2 + c^2 = ab + bc + ca$, then the triangle is:

If $x^3 - ax^2 + bx - a = 0$ has 3 real roots, then

1 red, 3 white, 2 blue flags in a line, no adjacent same colour, ends different. How many arrangements?

$D$ is a recurring decimal of type $0.\ a_1a_2a_1a_2a_1a_2 \dots$ Here $a_1$ and $a_2$ are single digit numbers between $0$ and $9$. This number $D$, when multiplied by which of the following numbers gives a product which is an integer?

$x=1,2,3,4,5,6$ give $y=4,8,14,22,32,44$. Find relation $y$ vs $x$.

ABCD is a rhombus with AC and BD intersecting at the origin. The equation of side AD is $x + y = 1$. What is the equation of BC?

$a_1=1,\ a_{n+1} = 2a_n + 5$, find $a_{100}$.

There are seven consecutive integers. The average of the first five is $n$. What is the average of all seven?

If $x>2$ and $y>-1$, which is true?

There are two positive integers – $x$ and $y$. A function of $x$ and $y$ is defined such that:
$f(0,y) = y + 1$,
$f(x + 1, 0) = f(x, 1)$,
$f(x + 1, y + 1) = f(x, f(x + 1, y))$
What is the value of $f(1, 2)$?

Evaluate:
$\frac{1}{2^2 - 1} + \frac{1}{4^2 - 1} + \frac{1}{6^2 - 1} + \dots + \frac{1}{20^2 - 1}$