chetan2u wrote:
If x and y are integers, is x an even integer?
1) \(8y^2+x^2=x^4+y^4\)
2) \(y=6-x\)
A modified version of a Q on GMATCLUB chat..
1) \(8y^2+x^2=x^4+y^4\)
2) \(y=6-x\)
A modified version of a Q on GMATCLUB chat..
Statement 1 implies y must be even but is insufficient to conclude anything about x.
Explanation - \(8y^2\) is even.
Case 1 - x is even, therefore \(x^2\) and \(x^4\) are even. LHS is even, for RHS to be even, \(y^4\) must be even, thus y is even.
Case 2 - x is odd, then \(x^2\) and \(x^4\) are odd. LHS is odd, and \(y^4\) must be even for RHS to be odd.
Not sufficient
Statement -2
x + y = 6 implies either both are even or both are odd. Not sufficient.
Statement 1 + 2
y is even from (1), thus x is even from (2)
Answer - C