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# 25+ Remainder Questions for CAT with SOLUTIONS

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Remainder Questions for the CAT exam are part of the Quant section in the CAT exam. Through Remainder Questions, aspirants are asked for the calculation and divisibility. The difficulty level of the Remainder questions can be moderate to difficult.

## CAT Remainder Practice questions for the CAT exam

Q 1: Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is
A. 75
B. 120
C. 60
D. 90

Q 2: If a certain amount of money is divided equally among n persons, each one receives Rs 352. However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330 . Then, the maximum possible value of n is

Q 3: For any natural numbers m, n, and k, such that k divides both m n + 2 and 3 4 m n + k must be a common divisor of
A. m and n
B. 2m and 3n
C. 2m and n
D. m and 2n

Q 4: How many values of A are possible if 3245684A is divisible by 3?

## Must-do Remainder questions for the CAT exam

Q 5: Example 16 How many pairs of A and B are possible in number 89765A4B if the number is divisible by 9, given that last digit of the number is even?

Q 6: Find the total number of even and prime divisors of N= 420

Q 7: What is the remainder when 50 is divided by 77?

Q 8: What is the remainder obtained when (1421 x 1423 x 1425) is divided by 127 ?

## Most Important Remainder Question for CAT

Q  9: What is the remainder when 9100 is divided by 8?

Q 10: For any natural number tt, suppose the sum of the first tt terms of an arithmetic progression is (n + 2n 2). If the nth term of the progression is divisible by 9, then the smallest possible value of n is
A. 4
B. 7
C. 9
D. 8

Q 11. Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the  mixture in order to make a profit of â‚¹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of â‚¹744. Then the amount, in rupees, that she had spent in buying almonds is
A. 1176
B. 2520
C. 1680
D. 1440

Q 12: The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is
A. 1 : 2
B. 4 : 1
C. 1 : 4
D. 3 : 1

## Find Some Previous Year Remainder Questions for CAT

Q 13. The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

Q 14: Let A be the largest positive integer that divides all the numbers of the form 3k + 4k + 5k and B be the largest positive integer that divides all the numbers of the form 4k + 3(4k) + 4k+2, where k is any positive integer. Then (A + B) equals