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Number Systems - April 14, 2004
The GMAT Sample Math question for the day is from the topic Number Systems.
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?
A. 13
B. 59
C. 35
D. 37
E. 12
The correct choice is (D) and the 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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