List of top Quantitative Aptitude Questions asked in CAT

Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

Leaving home at the same time, Amal reaches office at 10: 15 am if he travels at 8 km/hr, and at 9: 40 am if he travels at 15 km/hr. Leaving home at 9: 10 am, at what speed, in km/hr, must he travel so as to reach office exactly at 10 am?

In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is

A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

A solid right circular cone of height 27 cm is cut into two pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is [This Question was asked as TITA]

The number of pairs of integers \((x , y)\) satisfying \(x≥y≥-20\) and \(2x+5y=99\) is
[This Question was asked as TITA]

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3.
[This Question was asked as TITA]

If \(x_m +1\) and \(x_m=x_{m+1}+(m+1)\) for every positive integer \(m\), then \(x_{100 }\) equals

The mean of all 4 -digit even natural numbers of the form 'aabb', where a >0, is

Let \(N\), \(x\) and \(y\) be positive integers such that \(N=x+y\), \(2<x<10\) and \(14<y<23\). If \(N>25\), then how many distinct values are possible for \(N\)? [This Question was asked as TITA]

If \(a, b, c\) are non-zero and \(14^a = 36^b = 84^c\), then \(6b \bigg(\frac{1}{c}-\frac{1}{a}\bigg)\)is equal to [This Question was asked as TITA]

How many pairs \((a, b)\) of positive integers are there such that \(a≤b\) and \(ab=4^{2017}\) ?

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7? [This Question was asked as TITA]

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is s. Then the area of the triangle is

In how many ways can a pair of integers \((x , a)\) be chosen such that \(x^2-2|x|+|a-2|=0\) ?

If \(log_a\) \(30\) = \(A\), \(log_a\) \(\bigg(\frac{5}{3}\bigg)\) = \(-B\) and \(log_2\; a\) = \(\frac{1}{3}\), then \(log_3\) \(a\) equals.

The value of \(log_a\bigg(\frac{a}{b}\bigg)+log_b\bigg(\frac{b}{a}\bigg)\), for \(1<a≤b\) cannot be equal to

The number of distinct real roots of the equation \(\bigg(\frac{x+1}{x}\bigg)^2-3\bigg(\frac{x+1}{x}\bigg)+2=0\) equals
[This Question was asked as TITA]

Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is ₹ 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is

Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is