List of top Quantitative Aptitude Questions asked in CAT

Out of 40 members of team A only 60% are selected for the tour and out of 60 members of team B only 40% are selected for the tour. Ratio of male members to female members on the tour is 5:3. Ratio of male members who are selected from team A to female members who are selected from team A is 5:1. Find total number of female members who are selected for tour from team B.

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

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

X, Y, Z and W can do a certain piece of work in 10, 15, 25 and 30 days respectively. All of them started the work together but X left the job 2 days before the completion of work, Z left the work 1 day before completion of work, W worked with double of his efficiency. Find total time taken by them to complete the work is how much more or less than the total time taken by X alone to complete the work.

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:

Boat 'A' takes 60 seconds to cover entire length of the river when travelling with the stream. Had the speed of the stream been double, then the boat would've saved 10 seconds to complete the same journey. Find the time taken by a hat that is floating in the river to cover the same distance, if the stream is flowing at the original speed.

The sets \( P_n \) are defined as \( \{ n, n+1, n+2, n+3, n+4, n+5, n+6, n+7, n+8 \} \), where \( n = 1, 2, 3, \ldots, 520 \). How many of these sets contain a multiple of 17?

Let \( y = (1^2) + (2^2) + \cdots + (10000^2) \), what is the remainder when \( y \) is divided by 1152?

What is the remainder when \( 13^{2013} \) is divided by 100?

Solution P contains three liquids A, B, and C in the ratio 2:3:5 respectively. Another solution Q contains A, B, and C in the ratio 5:3:2 respectively. Solutions P and Q are mixed in the ratio 7:3 to obtain another solution R. Now 50% volume of R is replaced with another solution having A and B in the ratio 7:3. The resulting solution is Z. Find the percentage amount of B in solution Z.

Perimeter of \(\Delta ABC\) is 32 m. If AB = BC and altitude BD measures 8 m, find area of triangle ABC.

If 150! is converted to base 7, how many consecutive zeros would be there at the end of it?

Find the sum of the digits of \( 100^{100} - 10 \).

In an examination of 12600 students, the ratio of the number of boys to the number of girls is 3:4. The ratio of the number of students who passed the exam to those who failed the exam is in the ratio of 11:3. Among the girls, the ratio of the number of students who passed to those who failed the exam is in ratio 11:4. Find the difference between the number of boys who passed and failed the exam.

All natural numbers that give remainders 1 and 2 when divided by 6 and 5, respectively, are written in ascending order, side by side, from left to right. What is the 99th digit from the left of the number thus formed?

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?

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.

In a group of 100 people, 70 like coffee, 60 like tea, and 45 like both coffee and tea. How many people like neither coffee nor tea?

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’.

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

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 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 ?

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?

Upstream speed of a motorboat is 70% of that downstream speed. The motorboat goes 220 km downstream but while returning the same distance in upstream, the rate of stream was double of itself. In this way, the motorboat takes the total time of 31 hours. What was the difference between time taken to go 220 km downstream and return the same distance in upstream?