List of top Questions asked in CAT

In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, the same number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years — 2001, 2002 and 2003. If floods are expected again in 2004, the number of huts expected to be destroyed is:

Let $a$, $b$, $c$, and $d$ be integers such that $a = 6b$, $a = 12c$, and $2b = 9d = 12e$. Then which of the following pairs contains a number that is not an integer?

A piece of paper is in the shape of a right-angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?

The number of roots common between the two equations $x^3 + 3x^2 + 4x + 5 = 0$ and $x^4 + 2x^3 + 7x + 3 = 0$ is:

If $13x + 2z = 5y^2$, then:

A real number $x$ satisfying $1 - \frac{1}{n}<x \leq 3 + \frac{1}{n}$, for every positive integer $n$, is best described by:

If $n$ is such that $36 \leq n \leq 72$, then $x = \frac{n^2 + 2\sqrt{n(n+4)} + 16}{n + 4\sqrt{n + 4}}$ satisfies:

Let ABCDEF be a regular hexagon. What is the ratio of the area of $\triangle ACE$ to that of the hexagon ABCDEF?

Let $n(>1)$ be a composite integer such that $\sqrt{n}$ is not an integer. Consider the following statements: A: $n$ has a perfect integer-valued divisor which is greater than 1 and less than $\sqrt{n}$ B: $n$ has a perfect integer-valued divisor which is greater than $\sqrt{n}$ but less than $n$ Then:

If three positive real numbers $x$, $y$ and $z$ satisfy $y - x = z - y$ and $x + y = 4$, then what is the minimum possible value of $y$?

Consider the sets $T_n = \{n, n+1, n+2, n+3, n+4\}$, where $n = 1, 2, 3, \dots, 96$. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?

In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If $\angle \angle ATC = 30^\circ$ and $\angle ACT = 50^\circ$, then the angle $\angle ABOA$ is:

Let $S_1$ be a square of side $a$. Another square $S_2$ is formed by joining the mid-points of the sides of $S_1$. The same process is applied to $S_1$ to form yet another square $S_3$, and so on. If $A_1$, $A_2$, $A_3$, \dots are the areas and $P_1$, $P_2$, $P_3$, \dots are the perimeters of $S_1$, $S_2$, $S_3$, \dots, respectively, then the ratio $\frac{P_1 + P_2 + P_3 + \dots}{A_1 + A_2 + A_3 + \dots}$ equals:

The infinite sum $1 + \frac{4}{7} + \frac{9}{72} + \frac{16}{73} + \frac{25}{74} + \dots$ equals:

What is the sum of $n$ terms in the series $\log m + \log \left( \frac{m^2}{n} \right) + \log \left( \frac{m^3}{n^2} \right) + \log \left( \frac{m^4}{n^3} \right) + \dots$?

What is the remainder when $4^8$ is divided by 6?

Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?

If $\frac{1}{3} \log N + 3 \log M = 1 + \log 1000$, then:

If $x$ and $y$ are integers, then the equation $5x + 19y = 64$ has:

In the figure below (not drawn to scale), rectangle ABCD is inscribed in the circle with center at O. The length of side AB is greater than side BC. The ratio of the area of the circle to the area of the rectangle ABCD is $\pi : \sqrt{3}$. The line segment DE intersects AB at E such that $\angle \text{DOC} = \angle \text{ADE}$. The ratio $AE : AD$ is:

The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are $c$, $t$, and $s$, respectively. Then,

What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?

If both a and b belong to the set $\{1, 2, 3, 4\}$, then the number of equations of the form $ax^2 + bx + 1 = 0$ having real roots is:

If $\log_x x - \log_10 \sqrt{x} = 2 \log_10 10$, then the possible value of $x$ is given by:

A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 min for the angle of elevation to change from $45^\circ$ to $60^\circ$. After how much more time will this car reach the base of the tower?