You are here: Home » GMAT Test Prep Questions » Number Properties & Theory » Question 3

The question is about finding the divisor given remainders. Number Theory and Number Properties are hot favorites in GMAT.

A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

A. 13
B. 59
C. 35
D. 37
E. 12

The correct choice is (D) and the correct answer is 37.

Let the original number be 'a'

Let the divisor be 'd'

Let the quotient of the division of a by d be 'x'

Therefore, we can write the relation as = x and the remainder is 24.

i.e., a = dx + 24

When twice the original number is divided by d, 2a is divided by d.

We know that a = dx + 24. Therefore, 2a = 2dx + 48

The problem states that leaves a remainder of 11.

2dx is perfectly divisible by d and will therefore, not leave a remainder.

The remainder of 11 was obtained by dividing 48 by d.

When 48 is divided by 37, the remainder that one will obtain is 11.

Hence, the divisor is 37.

Number Theory and Inequalities eBook @ USD 6.99

This eBook covers all the topics in Number Theory and Inequalities related to GMAT. Explanation of topics provide in-depth knowledge of concepts such as LCM, HCF, remainder theorem in number theory and the rules governing inequalities.

The book contains over 50 solved examples and illustrative examples. In addition, the eBook contains 44 exercise questions covering a wide variety of questions from these two topics for you to practise.