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The question is about remainders and divisors. Number Theory and Number Properties are hot favorites in GMAT.

When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?

A. 11
B. 17
C. 13
D. 23
E. None of these

The correct choice is (C) and the correct answer is 13.

Let the divisor be d.

When 242 is divided by the divisor, let the quotient be 'x' and we know that the remainder is 8.

Therefore, 242 = xd + 8

Similarly, let y be the quotient when 698 is divided by d.

Then, 698 = yd + 9.

242 + 698 = 940 = xd + yd + 8 + 9

940 = xd + yd + 17

As xd and yd are divisible by d, the remainder when 940 is divided by d should have been 17.

However, as the question states that the remainder is 4, it would be possible only when leaves a remainder of 4.

If the remainder obtained is 4 when 17 is divided by d, then d has to be 13.

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