List of top Quantitative Aptitude Questions asked in CAT

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

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

Is\( (\sqrt{x}-\frac{1}{\sqrt{x}})=\sqrt{-5}\) and x≠ 0, then what is the value of \(\frac{3(x^2+3)-6-3x}{4x}\) ?

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)

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

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

In triangle ABC, ‘D’ and ‘E’ are two points on sides AB and AC, respectively such that DE is parallel to BC. If AD=16 cm, BD=(5x-16) cm, AE=2x cm and EC=(25-2x) cm, then find the value of ‘x’.

PQRS is a rhombus such that length of its each side is 30 cm. If PR=36 cm and QS=\(4\sqrt{x}\) cm then the length of each side of the rhombus (in terms of ‘x’) 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?

In the given figure, ‘O’ is the centre of the semi-circle and ∠MON =48°, Find ∠MRP.

How many numbers between 90 and 600 have exactly three factors?

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

How many factors of N=2⁶ x 3⁸ x 5¹⁰ x 7¹² are perfect squares as well as perfect cubes?

If \(x=a^2+1\ \text{and} \ y=a^2-a+1\), then find the value of \(\frac{x^3-y^3-xy^2+x^2y}{(x+y)^2}\)

The radii of three concentric circles are in the ratio 2: 3: 4. What is the ratio of sum of areas of two inner circles to the area of the region between outermost circle and innermost circle?

If the LCM of three natural numbers 24¹², 18¹⁶ and a is 36¹⁸, then how many values of a are possible?

Find the HCF of (81²⁵-1) and (2⁷⁴-1).

In a ∆PQR, internal angle bisectors of ∠Q and ∠R meet at I while external angle bisectors of ∠Q and ∠R meet at X. If ∠P = 54°, then find the measures of ∠QIR and ∠QXR, respectively.

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?

Find the value of \(36(\frac{a}{2}+\frac{b}{6}+\frac{c}{3})^2\)

If (Ax + By - Cz)² = 4x²+ 3y²+ 2z²+ \(4\sqrt{3xy} \)-\( 2\sqrt{6yz}\) - 4√2xz, then find the value of A2+ B2C2.

If 25^(3a-2b) = 5^(b-a) = 5² and , then find the value of ab - c.

If log₈ 9, log₈ (2y+7) and log₈ (3y+6) are in arithmetic progression with non-zero common difference, find the value of y.

In the questions two columns are given. You are required to solve the equations given in the "equations" column and match them with the correct statement given about the desired equation in the "conditions" column.

	Equations		Conditions
(a)	2x2 – 11x + 12 = 0	(d)	Product of roots is negative
(b)	5x2 21x – 20 = 0	(e)	Product of roots is completely divisible by 6
( c)	x2 – 17x + 72 = 0	(f)	Sum of both roots is positive