List of top Quantitative Aptitude Questions asked in CAT

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

Let f(x) = 2x-5and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if

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

Consider the expression (xxx)_b = (62)_b , where b is the base and x is any digit in base b. Find the value of (b + x).

If (x - 1)³ + (y - 2)³ + (z - 3)³ + 3(x + y - 3)(y + z - 5)(x + z - 4) = 0, then what is the value of (x + y + z) ?

What is the value of 'x' in the expression given below ?
\(\frac{x^4-16}{x^2-6x+9}\times\frac{x^3-27}{(x^2+4)(x+2)}\div\frac{x^2+3x+9}{x-3}=\frac{3}{2}\)

How many natural numbers, when converted to base 5 are four- digit numbers ?

What is the value of \((x^4+y^4+x^2y^2)\frac{x^2-2xy+y^2}{x^2-xy+y^2}\div(x^3-y^3)\) ?

At what exact time between 3:00 PM and 4:00 PM do the hour and minute hands of a standard clock coincide?

If a³ + b³ + c³ = 62, abc = -6 and (a + b + c) = 5, then what is the value of ab + bc + ac ?

A factory produces a certain number of toys in a week using a team of 40 workers who work for 8 hours daily. Due to an increase in demand, the factory needs to double the production while maintaining the same work schedule. How many additional workers should be hired?

‘A’ while working 40% more efficiently can complete a piece of work in 25 days and ‘B’ while working 25% more efficiently can complete the same work in 21 days. While working with their original efficiencies ‘A’ and ‘B’ together worked for 9 days, then find the time taken by ‘A’ alone to complete the remaining work with his original efficiency.

How many natural numbers, when converted to base 3, are four-digit numbers, but when converted to base 4, are three-digit numbers ?

If a, b and c are integers such that a² + b² + c² = 228, a + b + c = 26 and b = c, then what is the value of a ?

If \((4x^2+\frac{1}{4x^2})=2\), then what is the value of \((8x^3+\frac{1}{8x^3})\) ?
A) +2
B) -2
C) +4
D) -4

If a + b + c = 4, (a + b)² + (b + c)² + (c + a)² = 20. Find the value of (a² + b² + c²).

How many four-digit numbers in base 4, when converted to base 5, will have unit digit zero ?

A rectangular plot of land measures 55 meters by 25 meters. A path of uniform width surrounds the plot. If the area of the path is equal to the area of the plot, what is the width of the path in meters?

All the vertices of a rhombus lie on a circle of radius R. If the length of one diagonal of the rhombus is D, then the area of the rhombus is:

If f(x)=x-5, and f²(x)=f(f(x)), f³(x)=f(f(f(x))) and so on, then find the value of f⁸(9).

A triangular garden has its corners at points A(2, 3), B(5, 7), and C(1, 6) on a coordinate plane. If a fourth point D is added to form a parallelogram ABCD, what are the coordinates of point D?

Find the remainder when (345672) in base 9 is divided by 8.

If x and y are integers and – 5 ≤ x ≤ 6 and 4 ≤ y ≤ 9, then the minimum value of \(\frac{2x-y}{x} \) is____.

Eight years hence from now, ratio of ages of ‘A’ and ‘B’ will be 10 : 9, respectively. Present age of ‘B’ is 60% more than age of ‘C’ 8 years ago from now. If ratio of present ages of ‘A’ and ‘C’ is 3:2, respectively then find the present age of ‘C’.

In a box there are (x + 5) red balls, ‘x’ blue balls and (x + 1) black balls. If the probability of picking two blue balls at random is 1/35, then find the value of ‘x’.