Number Properties - Remainders and Divisors

Concept: Properties of remainders

The question is about finding the divisor given remainders of dividing a number and twice its value by the same divisor. Number Theory and Number Properties are favorite topics of GMAT test setters.

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
  5. 12

Explanatory Answer

Video explanation provided for this question
Decoding "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

Decoding "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 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 is "What number will leave a remainder of 11 when it divides 48?"
When 37 divides 48, the remainder is 11.

Hence, the divisor is 37.

Choice D is the correct answer.

Video Explanation

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