Brent@GMATPrepNow wrote:x and y are positive integers. When x is divided by 2y, the remainder is y. What is the value of y?
(1) x is even
(2) y is a prime number
Since dividing x by 2y leaves a remainder of y, x = (MULTIPLE OF 2y) + y:
x = a(2y) + y, where a is a nonzero integer.
Factoring out y on the right side, we get:
x =
y(2a+1).
Statement 1:
For x to be even, it must have an even factor.
2a+1 = even + odd = odd.
Since the blue factor above is odd, the red factor above -- in other words, the value of y -- must be even.
Thus, y can be any positive even integer.
INSUFFICIENT.
Statement 2:
Since y can be any prime number, INSUFFICIENT.
Statements combined:
Since y must be both even (from Statement 1) and prime (from Statement 2), x=2.
SUFFICIENT.
The correct answer is
C.
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