fantaisie wrote:
\(x^2\) - \(y^2\) = (x-y)*(x+y)
1) We know that (x - y) is even, but don't know if (x+y) is even or odd
If (x-y) & (x+y) is odd: (x+y)(x-y) = O*O = O
If (x-y) is odd & (x+y) is even: O*E = E
NOT SUFFICIENT
2) x is an odd integer
If x is odd, & y is odd, then:
(x-y) = O - O = E or 0
(x+y) = O + O = E or 0
(x+y)(x-y) = E * E = E
If x is odd, & y is even, then:
(x-y) = O - E = O
(x+y) = O + E = O
(x+y)(x-y) = O * O = O
NOT SUFFICIENT
1 & 2)
We know that (x-y) is even & that x is odd.
Given those circumstances, we can conclude that y is also odd:
(x-y) = O - O = E (In the formulas above we can see, that if y is even, then (x-y) would be odd)
If x is odd and y is odd, then:
(x-y)*(x+y) = E * E = E
Answer: C
Thanks for pointing out such a careless mistake! My new take on the question:
1) We know that (x - y) is even, but don't know if (x+y) is even or odd
If (x-y) even & (x+y) is odd: (x+y)(x-y) = E*O = E
If (x-y) even & (x+y) is even: E*E = E
SUFFICIENT
2) x is an odd integer
If x is odd, & y is odd, then:
(x-y) = O - O = E or 0
(x+y) = O + O = E or 0
(x+y)(x-y) = E * E = E
If x is odd, & y is even, then:
(x-y) = O - E = O
(x+y) = O + E = O
(x+y)(x-y) = O * O = O
NOT SUFFICIENT
Answer: A