# Number Properties - Remainders & Divisors

Concept: Remainder of sum of two numbers

This GMAT quant practice question tests concepts in remainders and divisors. A Number Theory and Number Properties practice question.

#### Question: 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?

1. 11
2. 17
3. 13
4. 23
5. None of these

#### Video Explanation

##### When 242 is divided by a certain divisor the remainder obtained is 8.

Let the divisor be d.
When 242 is divided by d, let the quotient be 'x'. The remainder is 8.
Therefore, 242 = xd + 8

##### When 698 is divided by the same divisor the remainder obtained is 9.

Let y be the quotient when 698 is divided by d.
Then, 698 = yd + 9.

##### When the sum of the two numbers, 242 and 698, is divided by the divisor, the remainder obtained is 4.

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

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

Choice C is the correct answer.

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