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Number Theory : Remainders, Finding Divisors

Remainders of division of different numbers by the same divisor

Question

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?

(1) 13
(2) 59
(3) 35
(4) 37

Correct Choice - (4). Correct Answer is 37

Explanatory Answer

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.

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