Harley1980 wrote:
If x > 1 is (x+y)(x-y) an even integer?
1) x+y is even
2) 2x = prime
Question: Is (x+y)(x-y) an even integer?
1) x+y is even
x = 4, y = 2, x+y = 6 (even integer), x-y = 2. So (x+y)(x-y) = 12, an even integer
x = 7/3, y = 5/3, x+y = 4 (even integer), x - y = 2/3 (not an integer so (x+y)(x-y) is not an integer)
Not Sufficient.
2) 2x = prime
Since 2x is prime, if it were 2, x would be 1 but we are given that x > 1.
So 2x must be an odd prime number. So x = Odd prime/2 such as 5/2, 7/2, 11/2 etc.
y can be anything so we cannot say that (x+y)(x-y) is an even integer.
Using both, x + y = Even integer
Odd prime/2 + y = Even integer
So y must be an Odd integer/2.
This means x - y = Odd integer/2 - Odd integer/2 = Even integer/2 = Integer
So (x+y)*(x-y) = Even integer * Integer = Even Integer
Sufficient.
Answer (C)
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Karishma
Veritas Prep GMAT Instructor
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