consider the integers x and y. when y is divided by x the remainder is 29. when y is divided by x/2 the remainder is 13. determine x
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GMAT Club Forum Index Data Sufficiency (DS)
If x and y are integer, what is the remainder when x^2 + y^2 : Data Sufficiency (DS)
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kt750
Updated on: Apr 26, 2012
00:00ABCDE
DIFFICULTY: 75% (hard) QUESTION STATS: based on 1393 sessions
57% (02:24) correct
43% (02:17) wrong
If x and y are integer, what is the remainder when x^2 + y^2 is divided by 5?
(1) When x-y is divided by 5, the remainder is 1
(2) When x+y is divided by 5, the remainder is 2
Spoiler: OA
Last edited by Bunuel on 26 Apr 2012, 20:56, edited 1 time in total.
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Bunuel
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Apr 26, 2012
If x and y are integer, what is the remainder when x^2 + y^2 is divided by 5?
(1) When x-y is divided by 5, the remainder is 1 --> , so can be 1, 6, 11, ... Now, and () then and thus the remainder is 0, but if and () then and thus the remainder is 3. Not sufficient.
(2) When x+y is divided by 5, the remainder is 2 --> , so can be 2, 7, 12, ... Now, and () then and thus the remainder is 2, but if and () then and thus the remainder is 4. Not sufficient.
(1)+(2) Square both expressions: and --> add them up: --> so is divisible by 5 (remainder 0), which means that so is . Sufficient.