ProGMAT wrote:If x and y are different integers and x² = xy, which of the following must be true?
I. x = 0
II. y = 0
Ill. x = -y
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
An alternate approach is to test values.
Try to show that I, II and III DON'T have to be true.
Let y=1.
If we plug y=1 into x² = xy, we get:
x² = x*1
x² = x.
The only values that satisfy the resulting equation are x=1 and x=0.
Since the question stem requires that x and y be different integers, x=1 is not allowed here.
Thus, x=0 and y=1 satisfy the constraint that x² = xy and that x and y are different integers.
Since it does not have to be true that y=0, eliminate any answer choice that includes statement II (B and E).
Since it does not have to be true that x=-y, eliminate any remaining answer choice that includes statement III (C and D).
The correct answer is
A.
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