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.

Brent@GMATPrepNow wrote: I checked the Quant-only text you refer to and the question says "x² = xy"
I've edited your question above.


Begin with: x² = xy
Rearrange: x² - xy = 0
Factor: x(x - y) = 0

From this, we can conclude that x = 0, or (x - y) = 0
HOWEVER, x - y cannot equal zero.
For x - y to equal zero, it must be the case that x = y, BUT the question tells us that x and y are different integers.

So, all we can conclude with certainty is that x = 0

Answer: A

Cheers,
Brent

Thanks for checking question.
I did it by inserting values from 3 value options and concluded the answer, but I think this one is easy and straight forward.