Question rephrased: If x/y is an integer, is y=2?grandh01 wrote:If x and y are positive integers and x
is a multiple of y, is y = 2?
(1) y ≠1
(2) x + 2 is a multiple of y.
Statement 1: y ≠1
It's possible that x=3 and y=3, since 3/3 = 1 is an integer.
It's possible that x=4 and y=2, since 4/2 = 2 is an integer.
INSUFFICIENT.
Statement 2: x + 2 is a multiple of y
(x+2)/y = integer.
x/y + 2/y = integer.
2/y = integer - x/y.
Since x/y = integer, we get:
2/y = integer - integer = integer.
For 2/y to be an integer, y=1 or y=2.
INSUFFICIENT.
Combined:
Statement 2: y=1 or y=2.
Statement 1: y ≠1.
Thus, y=2.
SUFFICIENT.
The correct answer is C.
