List of top Quantitative Aptitude Questions asked in CAT

In the figure (not drawn to scale) given below, if \(AD = CD = BC\) and \(\angle BCE = 96^\circ\), how much is the value of \(\angle DBC\)?

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

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

A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air conditioning, radio and power windows — were already installed. Following were the observation of the survey:
I. 15 had air conditioning
II. 2 had air conditioning and power windows but no radios
III. 12 had radio
IV. 6 had air conditioning and radio but no power windows
V. 11 had power windows
VI. 4 had radio and power windows
VII. 3 had all three options
What is the number of cars that had none of the options?

Let \(x\) and \(y\) be positive integers such that \(x\) is prime and \(y\) is composite. Then,

In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, twice the 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, d and e be integers such that a = 6b = 12c, and 2b = 9d = 12e. Then which of the following pairs contains a number that is not an integer?

A square tin sheet of side 12 inches is converted into a box with open top in the following steps. The sheet is placed horizontally. Then, equal-sized squares, each of side \(x\) inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If \(x\) is an integer, then what value of \(x\) maximizes the volume of the box?

Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/hr. They continue walking for 4 hr along their respective roads and reach points B and C on R1 and R2 respectively. There is a straight line path connecting B and C. Then Ram returns to point A after walking along line segments BC and CA. Shyam also returns to A after walking along line segments BC and CA. Their speeds remains unchanged. The time interval (in hours) between Ram's and Shyam's return to the point A is

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?

If \(|b| \ge 1\) and \(x = -|a|\,b\), then which one of the following is necessarily true?

If \(13x + 1 < 2z\) and \(z + 3 = 5y^2\), then

Let ABCDEF be a regular hexagon. What is the ratio of the area of the \(\Delta\)ACE to that of the hexagon ABCDEF?

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

The infinite sum \(1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + \cdots\) equals

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 \(\angle ATC = 30^\circ\) and \(\angle ACT = 50^\circ\), then the angle \(\angle BOA\) is

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

What is the remainder when \(4^{96}\) is divided by 6?

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,

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 \( \dfrac{1}{3}\log_3 M + 3\log_3 N = 1 + \log_{0.008} 5 \), then

In the figure below (not drawn to scale), rectangle ABCD is inscribed in the circle with centre 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 \( \angle \)ODC = \( \angle \)ADE. The ratio AE : AD is

Consider two different cloth-cutting processes. In the first one, \( n \) circular cloth pieces are cut from a square cloth piece of side \( a \) in the following steps: the original square of side \( a \) is divided into \( n \) smaller squares, not necessarily of the same size, then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side \( a \) and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is

An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, ..., 9 such that the first digit of the code is non-zero. The code, handwritten on a slip, can however potentially create confusion when read upside down — for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise?

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