List of top Quantitative Aptitude Questions asked in CAT

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).

∆ABC is inscribed inside a circle and there is a point D on the arc BC opposite to A such that BD = CD. If ∠BAC = 70° and ∠ABD = 85°, then find the measure of ∠BCA.

If a² + 32 + b² + 8(a + b) = 0, then find the value of (a3 + b3).

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

If 4^(4b-3a) = 2^(2b+c) = 8^(c-a) and a + b + c = 11, then find the value of \(4(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca})\)

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.

In triangle PQR, PM is perpendicular to QR. If ‘T’ is a point in between ‘Q’ and ‘M’ such that PT = \(5\sqrt3\) cm, PM = \(\sqrt{39}\) cm then find the value of PQ such that QM : TM = 5 : 2.

In the given figure, AB is the chord of the circle with centre ‘O’. A tangent AT is drawn at point ‘A’ so that angle BAT = 48°, then measure of angle ADB is :

In triangle PQR, the straight line parallel to side QR meets PQ and PR at points ‘A’ and ‘B’, respectively. If PA = BR, PQ = 36 cm and PB = 6 cm, then BR = ?

For how many values of ‘n < 50’ are possible, such that n! is divisible by n².

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

If (Ax + By - Cz)² + 4\(\sqrt3\)xy - 2\(\sqrt6\)yz - 4\(\sqrt2\)xz, then find the value of A² + B²C².

If 25^{(3a - 2b)} = 5^{(b - a)} = 5² and \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{35}\), then find the value of ab - c.

If 4^{4b - 3a} = 2^{2b + c} = 8^{c - a} and a + b + c = 11 , then find the value of \(4(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca})\)

Find the number of zeros at the end of the product :
5 × 10 × 15 × 20 × 25 × ……………………..× 500

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

Find the number of zeros at the end of
P = 35! + 36! + 37! + 38! + 39! + 40!

Find the minimum numbers starting from 74 that are multiplied to get 50 zeros at the end ?

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

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

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

A solid wooden cylindrical log of radius 35 cm and height 20 cm is used to make a glass holder box. 12 conical holes of height 15 cm and radius 3.5 cm are drilled into the upper surface of the log to accommodate glasses. The remaining upper surface area which is solid is covered with woolen cloth that costs Rs.4 per sq. cm and the inner surfaces of the holes are polished at the rate of Rs.0.25 per sq. cm. What is the total cost incurred ?

An overhead water tank of 7200 m³ capacity is being filled with water. The delivery of the pump filling the tank is 5/6^th of the delivery of the pump discharging the same tank. As a result, 24 minutes more is needed to fill the tank than discharge it. Determine the delivery of the pump in filling the tank.