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Algebra

by jainrahul1985 » Sat Jul 25, 2009 10:26 pm
If x and z are integers, is at least one of them even?

(1) x + z is odd.

(2) x - z is odd.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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by sreak1089 » Sat Jul 25, 2009 11:00 pm
stmt # 1: x + z is odd. => x or z is even, since odd + odd or even + even is even. So one of them has to be even. Hence stmt # 1 sufficient.

stmt # 2: x - z is odd. => x or z is even, since odd - odd is even and even - even is even and one of them have to be odd while the other being even. Hence stmt # 2 is sufficient.

Together, sufficient. Hence IMO ans is D
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