Can I ask someone to provide a solution for this? I don't understand the solution provided by Paul. Thank you.
Is (x^2 + y^2) a perfect square?
(1) x is even, y is odd --> clearly insufficient: if x=0
and the answer will YES but if x=2
and the answer will be NO. Not sufficient.
(2) x and y are odd --> x=2m+1
for some integers m
), so x^2+y^2
is not a perfect square (an even perfect square must be multiple of 2^2=4, in other words x^2+y^2
to be a perfect square since it's a multiple of 2 it must be multiple of 2^2 as a perfect square has even powers of its primes, but as x^2+y^2=2*odd
then it's not a multiple of 2^2). Sufficient.
But even though formal answer to the question is B (Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other,
and in this question (1) says that x is even and (2) says that x is odd, so the statements clearly contradict each other.
Hope it's clear.
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