Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We need to determine whether the product of x and y is even.
Statement One Alone:
x^2 + y^2 − 1 is divisible by 4.
Since 4 is an even number, we need x^2 + y^2 − 1 to be even. In order for x^2 + y^2 − 1 to be even, we need x^2 + y^2 to be odd. If the sum of two squares is odd, one of them must be odd and the other must be even. This means that either x = odd and y = even OR x = even and y = odd. In either case, the product of x and y will be even. Statement one alone is sufficient to answer the question.
Statement Two Alone:
x + y is odd.
Since x + y = odd, either x = odd and y = even OR x = even and y = odd. In either case, the product of x and y will be even. Statement two alone is sufficient to answer the question.
Answer: D
