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.
Given two positive integers A and B such that A>B...
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We are asked to get the remainder when (A^2 - B^2) is divided by 15.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 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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