List of top Quantitative Aptitude Questions asked in CAT

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?

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’.

The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?

The average weight of ‘b’ boys in a group is 63 kg. A boy whose weight is 147 kg joins the group such that the average weight of the group becomes a prime number in between 65 and 91. Find the value of ‘b+1’.

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:

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

Given below are 3 equations I, II and III where 'a' and 'b' are the roots of equation I where (a < b) and 'c' and’d’ are roots of equation II where (c < d). On this basis, solve for equation III and find the relationship between 'z' and 'k' given that k = 11
I. 3x(x - 12) + 72 = x² - 11x - 5
II. 5y(y - 3) - 64 = y(3y - 2) – 19
III. (z + 2a - d)² = 169

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:

‘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.

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.

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).

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

Find the range of x that satisfies the equation: || 3x-6| +4|<10.

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

If a²+b²=89 and a²-b²=39, then find the value of a³ - b³-3ab, (a, b >0).

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

Nitish booked movie tickets online which collects the same internet handling charges for normal movies and 3D movies, whereas the cost price of each normal movie ticket is 80% of the 3D movie ticket. Nitish paid Rs. 1030 for two 3D movie tickets and 3 normal tickets and Rs. 610 for one 3D movie ticket and 2 normal tickets. Find the internet handling charges per ticket.

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

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 ?

α and β are the roots of the equation x²+9x+18=0, where α>β. Then for the equation x²-ax+b=0 with its roots as (α+β) and (-3α), find the value of (a+b).

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

In a bag there are 100 coins. The coins in the bag are of denomination Rs.1 or Rs.2 or Rs.5. There are at least 10 coins and at most 60 coins of each denomination. Urvashi takes out 40 coins, which consist at least one coin of each denomination from the bag and finds that total worth of coins that she has taken out is Rs.148. The total worth of coins that are still in the bag is Rs.212. Which of the following can be the total number of coins of denomination Rs.1 that are still in the bag?

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

If 35% of x% of y=700% of y% of z, find the relation between ‘x’ and ‘z’.