List of top Quantitative Aptitude Questions asked in CAT

How many three digit positive integers, with digits x, y and z in the hundred's, ten's and unit's place respectively, exist such that \(x < y\), \(z < y\) and \(x \neq 0\) ?

There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimeters then the area (in square centimeters) of the triangle ABC would be

Three horses are grazing within a semi-circular field. In the diagram given below, AB is the diameter of the semi-circular field with center at O. Horses are tied up at P, R and S such that PO and RO are the radii of semi-circles with centers at P and R respectively, and S is the center of the circle touching the two semi-circles with diameters AO and OB. The horses tied at P and R can graze within the respective semi-circles and the horse tied at S can graze within the circle centred at S. The percentage of the area of the semi-circle with diameter AB that cannot be grazed by the horses is nearest to

In the figure below, ABCDEF is a regular hexagon and \(\angle AOF = 90^{\circ}\). FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?

A vertical tower OP stands at the center O of a square ABCD. Let h and b denote the length OP and AB respectively. Suppose \(\angle APB = 60^{\circ}\) then the relationship between h and b can be expressed as

Let a, b, c, d be four integers such that a+b+c+d = 4m+1 where m is a positive integer. Given m, which one of the following is necessarily true?

Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is \(90^{\circ}\) or concave if the internal angle is \(270^{\circ}\). If the number of convex corners in such a polygon is 25, the number of concave corners must be

The 288th term of the series a,b,b,c,c,c,d,d,d,d,e,e,e,e,e,f,f,f,f,f,f... is

Let p and q be the roots of the quadratic equation \(x^2 - (\alpha - 2) x - \alpha -1= 0\) . What is the minimum possible value of \(p^2 + q^2\)?

At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added \(p\%\) of the goats at the beginning of the year and sold \(q\%\) of the goats at the end of the year where \(p > 0\) and \(q > 0\). If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

The function \( f(x) = |x - 2| + |2.5 - x| + |3.6 - x| \), where \( x \) is a real number, attains a minimum at

A positive whole number \( M \) less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then \( M \) equals

How many even integers \( n \), where \( 100 \leq n \leq 200 \), are divisible neither by seven nor by nine?

In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

Twenty-seven persons attend a party. Which one of the following statements can never be true?

A test has 50 questions. A student scores 1 mark for a correct answer, \(-1/3\) for a wrong answer, and \(-1/6\) for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than

Let \( g(x) = \max(5 - x,\ x + 2) \). The smallest possible value of \( g(x) \) is

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that \( p + q + r \neq 0 \)?
\( x + 2y - 3z = p \)
\( 2x + 6y - 11z = q \)
\( x - 2y + 7z = r \)

The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero?

When the curves \( y = \log_{10} x \) and \( y = x^{-1} \) are drawn in the x-y plane, how many times do they intersect for values \( x \geq 1 \) ?

The number of non-negative real roots of \( 2^x - x - 1 = 0 \) equals

Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be

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 \(S_2\) to form yet another square \(S_3\), and so on. If \(A_1, A_2, A_3, \ldots\) be the areas and \(P_1, P_2, P_3, \ldots\) be the perimeters of \(S_1, S_2, S_3, \ldots\), respectively, then the ratio \(\dfrac{P_1 + P_2 + P_3 + \cdots}{A_1 + A_2 + A_3 + \cdots}\) equals