This GMAT quant practice question tests concepts in remainders and divisors. A GMAT 650 to 700 level Number Theory and Number Properties problem solving sample question.

Question 5: 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?

- 11
- 17
- 13
- 23
- None of these

@ INR

Let the divisor be d.

When 242 is divided by d, let the quotient be 'x'. The remainder is 8.

Therefore, 242 = xd + 8

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

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

However, because we know that the remainder is 4, it would be possible only when \\frac{17}{d}) leaves a remainder of 4.

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