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Given two positive integers A and B such that A>B...

by AAPL » Mon Nov 06, 2017 1:46 pm
Given two positive integers A and B such that A>B, what is the remainder when the square of B is subtracted from the square of A and then divided by 15?

(1) When the sum of A and B is divided by 5, the remainder is 1.
(2) When B is subtracted from A and then divided by 3, the remainder is 1.

The OA is E.

Please, can any expert assist me with this DS question? I don't have it clear why that is the correct answer and I appreciate if any explain it for me. Thanks.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Nov 06, 2017 9:38 pm
AAPL wrote:Given two positive integers A and B such that A>B, what is the remainder when the square of B is subtracted from the square of A and then divided by 15?

(1) When the sum of A and B is divided by 5, the remainder is 1.
(2) When B is subtracted from A and then divided by 3, the remainder is 1.

The OA is E.

Please, can any expert assist me with this DS question? I don't have it clear why that is the correct answer and I appreciate if any explain it for me. Thanks.
We are asked to get the remainder when (A^2 - B^2) is divided by 15.

=> We have to get the remainder when (A + B)(A - B) is divided by 15.

(1) When the sum of A and B is divided by 5, the remainder is 1.

Say A + B = 5n + 1. But we do not know about (A - B). Insufficient.

(2) When B is subtracted from A and then divided by 3, the remainder is 1.

Say A - B = 3m + 1. But we do not know about (A + B). Insufficient.

(1) and (2) combined:

We have A + B = 5n + 1 and A - B = 3m + 1

Thus, (A + B)(A - B) = (5n + 1)(3m + 1) = 15mn + 3m + 5n + 1.

So, we have to the remainder when (15mn + 3m + 5n + 1) is divided by 15. It will depend on the values of m and n, which are not known. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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