jjjinapinch wrote:If x and y are positive integers, is xy even?
(1) x^2 + y^2 - 1 is divisible by 4
(1) x + y is odd
xy will not be even -- in other words, xy will be ODD -- only if x and y are both odd.
Question stem, rephrased:
Are x and y both odd?
Statement 1: x² + y² - 1 is divisible by 4
x² + y² - 1 = (multiple of 4)
x² + y² = (multiple of 4) + 1
x² + y² = EVEN + ODD
x² + y² = ODD.
The equation in blue implies that x and y CANNOT both be odd, since ODD² + ODD ² = EVEN.
Thus, the answer to the rephrased question stem is NO.
SUFFICIENT.
Statement 2: x + y is odd
The statement above implies that x and y CANNOT both be odd, since ODD + ODD = EVEN.
Thus, the answer to the rephrased question stem is NO.
SUFFICIENT.
The correct answer is
D.
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