CAT Quant Practice Test 1

In a survey of 800 students, 65% preferred online classes over offline classes. Among those who preferred online classes, 40% also said they would pay extra for personalized tutoring. How many students preferred online classes but would NOT pay extra for personalized tutoring?

The ages of A, B and C are in the ratio 2:3:5. The sum of the ages of A and C exceeds twice the age of B by 14 years. Find the age of B.

A shopkeeper marks an item 40% above its cost price. He then offers a discount of 20% on the marked price, but due to a billing error an additional 5% discount is applied on the already discounted price. What is the shopkeeper's overall percentage profit?

Two cars start simultaneously from towns X and Y, 420 km apart, and travel towards each other along the same road. The car from X travels at 45 km/h and the car from Y travels at a speed 15 km/h faster than the car from X. After how many hours will the two cars meet?

A can complete a piece of work in 18 days and B can complete the same work in 24 days. They work together for 6 days, after which A leaves. In how many more days will B alone complete the remaining work?

If 3x + 2y = 34 and 5x − 2y = 30, what is the value of x + y?

A function f is defined for all real numbers x by f(x) = 2x² − 3x + 1. If f(a) = f(a + 1) for some real number a, what is the value of a?

How many positive integers x satisfy both 3x − 7 < 2x + 8 and x² < 100?

A chord of length 16 cm is drawn in a circle of radius 10 cm. What is the perpendicular distance of the chord from the center of the circle?

A cylindrical tank has a radius of 7 m and height of 10 m. A cone-shaped tank has the same radius and a height of 15 m. What is the ratio of the volume of the cylinder to the volume of the cone?

What is the remainder when 7¹⁰⁰ is divided by 5?

Find the smallest positive integer that leaves a remainder of 3 when divided by 7 and a remainder of 5 when divided by 9.

In how many ways can a committee of 4 people be selected from a group of 6 men and 5 women such that the committee has at least 2 women?

A bag contains 4 red balls, 5 blue balls, and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are of the same color?

The sum of the first n terms of an arithmetic progression is given by Sₙ = 3n² + 5n. Find the 10th term of the progression.

The average weight of 12 students in a class is 48 kg. When a new student joins, the average weight becomes 49 kg. What is the weight of the new student?

The product of two consecutive positive even integers is 624. Find the sum of the two integers.

A line passes through the points (2, 3) and (6, 11). What is the y-intercept of this line?

A sum of money invested at compound interest, compounded annually, amounts to ₹13,310 in 2 years and ₹14,641 in 3 years. What is the rate of interest per annum?

What is the remainder when 15! is divided by 17?

A rectangular sheet of metal measuring 24 cm by 18 cm has squares of side 3 cm cut from each corner. The sheet is then folded up along the cuts to form an open box. What is the volume of the box?

Two numbers are such that twice the larger number exceeds three times the smaller number by 9, and the sum of the two numbers is 32. Find the larger number.