List of top Quantitative Aptitude Questions asked in CAT

In a trinary base system, how many numbers from 0 to 100 end with digit 1?

What is the number of factors of the number formed by the last three digits of 1005¹⁰⁰¹?

A fruit basket contains 80 apples, 70 oranges, and 60 bananas. Some fruits might be rotten and discarded. What is the difference between the maximum and minimum possible number of fruits that are both apples and oranges?

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

If 25x² + y² = 41 and xy = 4 where x, y > 0, then the value of (125x³ + y³) is :

If x²-4x+3=0, then what is the value of (x³+4x²+7x+24)(x²+2x+3)^-1?

If \(A=\frac{x^2-y^2}{x^2-y^2}\), \(B=\frac{x+y}{x^2+y^2+xy}\) and \(C=\frac{ 3xy^2-3x^2y}{x^2-y^2}\), then find the value of AB (A+C)

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

If x² - 12x + 1 = 0, then find the value of {x⁶ + x + x⁵ + 1}/x³

If x² - 8x = 1, then find the value of {(x⁶ + 12x³ - 1)/(x⁶ - 24x³- 1)}

Let X=11×12×13×_____×75. Suppose ‘X’ is divisible by 10^2k (where ‘k’ is a natural no.). Find the maximum value of ‘k’.

If (x² - xy + y²) = 8 and (x⁴ + x²y² + y⁴) = 16, then find the value of (x² + xy + y²).

Find the greatest integral power of 2 in 41! + 42! + 43! + ……………+ 50!

For any natural number n, suppose the sum of the first n terms of an arithmetic progression is n(n+1). If the nth term of the progression is divisible by 7, then the smallest possible value of n is:

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

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

If \(\frac{5(4x^2+1)-3x}{4x}=8\) and x ≠ 0, then what is the value of \((√2x-\frac{1}{√2x}) \)?

Let A be the largest positive integer that divides all the numbers of the form\( (2^{k}+3^{k}+5^{k})\) and B be the largest positive integer that divides all the numbers of the form \((3^{k}+4^{k}+5^{k}) \), where k is any positive integer. Then (A + B) equals

What is the minimum value of (a + b) such that 4a x 5b will be a multiple of 5000?

How many odd factors of the number 45⁶ x 56⁵ x 77⁶ are multiples of 63?

The LCM and product of two numbers X and Y are 180 and 2700, respectively. If X is completely divisible by Y, then the value of (X-Y) is _____.

If \(N = 2^5 \times 3^4 \times 5^5 \times 11^2\), then how many factors of N are multiples of 66 but not of 72?

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 (3x-\(\frac{1}{3x}\))=4, , then what is the value of (27x³-\(\frac{1}{27x^3}\)) ?

If=\(\frac{2x^2+x-6}{(x+2)^2-(x-2)^2}\), Q=\(\frac{x^2+3x+9}{(2x-3)(x^2-4)}\) and \(R=\frac{x^2-27}{x^4-4}\), then find the value of PXQ÷R