GMAT Maths | Number Properties Q3

GMAT Quant Questionbank | Division Algorithm | Remainders

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?

1. 13
2. 59
3. 35
4. 37
5. 12

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Step 1 of solving this GMAT Number Properties Question: Decode "A number when divided by a divisor leaves a remainder of 24"

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 Step 2 of solving this GMAT Number Properties Question: Decode "When twice the original number is divided by the same divisor, the remainder is 11" 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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