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Find the divisor.

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by Vincen » Fri Sep 15, 2017 6:43 pm
Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.

A. 276
B. 552
C. 414
D. 1104
E. 2202

OA is B.

How can I solve this PS question?
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by Jay@ManhattanReview » Tue Sep 19, 2017 1:22 am
Vincen wrote:Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.

A. 276
B. 552
C. 414
D. 1104
E. 2202

OA is B.

How can I solve this PS question?
We have the sum of remainders = 248 + 372 = 620

Since the sum (620) would also be divisible by the divisor, and we have the remainder = 68, the divisor would be a factor of 620 - 68 = 552 and is less than 68.

We see that option A (276) and option B (552) are the factors of 552. But option A (276) cannot be the divisor since the second number when divided by 276 cannot leave a remainder (372) greater than the divisor (276).

Thus, the correct answer is B.

Hope this helps!

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