List of top Quantitative Aptitude Questions asked in CAT

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 \(4(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca})\)

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?

The digit at the unit place of P would be: Given, P=(6+1) (6²+1) (6³+1) ......... (6100+1)

Aman bought '3x' shares for Rs. 420 per share, '4x' shares for Rs. 450 per share and '3x' shares for Rs. 430 per share. He sold 40% of the shares at Rs. 480 per share and the rest at Rs. 'y' per share. If he made a total profit of 20% on the whole transaction, find the value of 'y'.

Scheme A offers 25% interest and scheme B offers 20% interest. M invested Rs.4000 in scheme A and Rs.6000 in scheme B at compound interest. After 2 years, he invested the amount received from scheme A and B in schemes B and A respectively at simple interest for 2 more years. If another person N invested Rs.6000 in scheme A and Rs.4000 in scheme B at compound interest. After 2 years, he invested the amount received from scheme A and B in schemes B and A respectively at simple interest for 2 more years, then what is the difference between total amount received by M and N after 4 years?