List of top Quantitative Aptitude Questions asked in CAT

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

For how many integers n, will the inequality \((n – 5) (n – 10) – 3(n – 2) ≤ 0\) be satisfied?

If the top left and the top right entries of the grid are 6 and 2, respectively, then the bottom middle entry is

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

How many different pairs (a, b) of positive integers are there such that a ≤ b and 1/a+1/b=1/9=?

If \(f_1 (x) = x^2 + 11x + n\) and \(f_2 (x) = x,\) then the largest positive integer n for which the equation \(f_1 (x) = f_2 (x)\) has two distinct real roots, is

The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is

An infinite geometric progression a1 , a2 , a3 ,... has the property that an = 3(an+ l + an+2 +….) for every n ≥ 1. If the sum a1 + a2 + a3 +….... = 32, then a5 is

If log (2a × 3b × 5C) is the arithmetic mean of log (22 × 33 × 5), log (26 × 3 × 57 ), and log (2 × 32 × 54 ), then a equals

Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is

The shortest distance of the point \((\frac{1}{2},1)\) from the curve \(y = |x -1| + |x + 1|\) is

An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?

If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2:1, then which one of the following is a possible value of (a + b + c)?

In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

If \(f(x)=\frac{5x+2 }{3x-5}\) and \(g(x)=x^2-2x-1\),then the value of \(g(f(f(3)))\) is 

Suppose, \(log_3 \ x = log_{12} \ y = a\), where x, y are positive numbers. If G is the geometric mean of x and y, and \(log_6\) G is equal to

In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?

If 9x-1/2-22x-2=4x-32x-3, then x is

If a and b are integers of opposite signs such that \((a+3)^2:b^2= 9:1\) and \((a -1)^2:(b - 1)^2=4:1\),then the ratio \(a:b\) is

Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is

If a1=1/2×5, a2=1/5×8, a3=1/8×11,...,then a1, +a2, +a3, +....a100 is

If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(l) is

How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?