List of top Questions asked in CAT

What are the ages of X and Y?
Statement A
A. The difference in their ages is $6$.
Statement B
B. The product of their ages is divisible by $6$.

$x$ is a real number. Is $|x|<3$?
Statement A
A. $x(x+3)<0$
Statement B
B. $x(x-3)>0$

$a \oplus b = 1$ if $a,b>0$ or $a,b<0$; \quad $a \oplus b = -1$ otherwise.
What is $(2 \oplus 0) \oplus (-5 \oplus -6)$?
Statement A
A. $a \oplus b = 0$ if $a=0$
Statement B
B. $a \oplus b = b \oplus a$

Harshad bought shares of a certain company on one day and sold them the next day. He paid a brokerage of $1%$. What was Harshad’s profit per rupee?
Statement A
A. His selling price was $1.05$ times his purchase price.
Statement B
B. The number of shares he purchased was $100$.

How many people watch program P?
Statement A
A. The number watching Q is $1000$; the number watching both P and Q is $100$.
Statement B
B. The number of people watching either P or Q or both is $1500$.

Each of the numbers $x_1, x_2, \dots, x_n, \ n \ge 4$, is equal to $1$ or $-1$. Suppose, \[ x_1 x_2 x_3 x_4 + x_2 x_3 x_4 x_5 + x_3 x_4 x_5 x_6 + \dots + x_{n-3} x_{n-2} x_{n-1} x_n + x_{n-2} x_{n-1} x_n x_1 + x_{n-1} x_n x_1 x_2 + x_n x_1 x_2 x_3 = 0, \] then which of the following is true?

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.

There is a vertical stack of books marked 1, 2 and 3 on Table-A, with 1 at the bottom and 3 on the top. These are to be placed vertically on Table-B with 1 at the bottom and 2 on the top, by making a series of moves from one table to another. During a move, the topmost book, or the topmost two books, or all the three, can be moved from one of the tables to the other. If there are any books on the other table, the stack being transferred should be placed on the top of the existing books, without changing the order of the books in the stack that is being moved in that move. If there are no books on the other table, the stack is simply placed on the other table without disturbing the order of books in it. What is the minimum number of moves in which the above task can be accomplished?

In a triangle PQR, $\angle PRQ = 90^\circ$. What is $PR + RQ$?
Statement A
A. The diameter of the incircle is $10$.

Statement B
B. The diameter of the circumcircle is $18$.

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:

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 $g(1)$.

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.

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

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

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

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.

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