himu wrote:If (x−y)^2 = x^2 − y^2 what is the value of nonzero integer xy?
(1) x=5
(2) x−y=0
Target question:
What is the value of nonzero integer xy?
Given: (x−y)^2 = x^2 − y^2
Expand left-side to get: x^2 - 2xy + y^2 = x^2 − y^2
Simplify: 2y^2 - 2xy = 0
Divide both sides by 2: y^2 - xy = 0
Factor: y(y - x) = 0
This means that y = 0 or x - y = 0
IMPORTANT: Since we're told that xy is a nonzero integer, we know that y cannot equal 0, which means x - y = 0
So, the given information is essentially telling us that
x - y = 0, and our goal is to
find the value of xy.
Statement 1: x = 5
Since we also know that
x - y = 0, we can conclude that y = 5 as well.
So, we can be certain that
xy = (5)(5) = 25
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x - y = 0
We already knew that
x - y = 0 from the given information.
As such statement 2 does not provide any new information.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
