List of top Quantitative Aptitude Questions asked in CAT

A and B started a business with their initial investments of Rs.180 and X respectively. After 2 years from the start of the business, another person C joins them with investment Rs.300 and A and B invested additional amounts in the ratio of 1:5 respectively. If at the end of 5 years C receives (\(\frac{10}{33}\)) of total profit and the ratio of total profit of B to total profit of C is 7:6, what was the additional amount invested by B?
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 = ?
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 ?
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) ?
At what exact time between 3:00 PM and 4:00 PM do the hour and minute hands of a standard clock coincide?
Let R1 and R2 respectively denote the maximum and the minimum possible remainders when 276\(^n\) is divided by 91 for any natural number n, n ≥ 144. Find R1 + R2.
What is the value of 'x' in the expression given below ?
\(\frac{x^4-16}{x^2-6x+9}\times\frac{x^3-27}{(x^2+4)(x+2)}\div\frac{x^2+3x+9}{x-3}=\frac{3}{2}\)
For how many values of ‘n < 50’ are possible, such that n! is divisible by n2.
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?
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 remainder when (345672) in base 9 is divided by 8.
Find the value of \(36(\frac{a}{2}+\frac{b}{6}+\frac{c}{3})^2\)
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’.
A shopkeeper has two jars P and Q containing almond oil in the ratio 2 : 3 respectively. He mixes '3x' litres and '2x' litres of olive oil in P and Q, respectively, after which the percentage of olive oil in jar P becomes 80% more than that in jar Q. If mixtures from jar P and jar Q are then mixed in the ratio of 3 : 1, what will be the percentage of olive oil in the resultant mixture?
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?
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 x and y are integers and – 5 ≤ x ≤ 6 and 4 ≤ y ≤ 9, then the minimum value of \(\frac{2x-y}{x} \) is____.
If a + b + c = 4, (a + b)2 + (b + c)2 + (c + a)2 = 20. Find the value of (a2 + b2 + c2).
Nitin raised a fund for the national environmental day. The amount (in thousands) on any given day after the start of fundraising event is given by a quadratic function f(x) = ax2 + bx + c , where f(x) is the money in thousand and x is the given day. If the amount collected on the first 3 days is 9, 10, and 13, then find the amount raised on the 10th day.