This GMAT sample question is about finding the divisor given remainders of dividing a number and twice the number by the same divisor. Number Theory and Number Properties are often-tested topics in the GMAT quant section.

Question 3: 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?

- 13
- 59
- 35
- 37
- 12

@ INR

Let the original number be 'a'.

Let the divisor be 'd'.

Let the quotient of dividing 'a' by 'd' be 'x'.

Therefore, we can write the division as \\frac{a}{d}) = x and the remainder is 24.

i.e., a = dx + 24

Twice the original number is divided by 'd' means 2a is divided by d.

We know from Step 1 that a = dx + 24.

Therefore, 2a = 2(dx + 48) or 2a = 2dx + 48

When (2dx + 48) is divided by 'd' the remainder is 11.

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

The remainder of 11 would be the remainder of dividing 48 by d.

The question essentially becomes **"What number will leave a remainder of 11 when it divides 48?"**

When 37 divides 48, the remainder is 11.

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