2. 外语
  3. If x and z are integers, is x + z2 odd? (1) x is odd and z is even. (2) x-z is odd.

If x and z are integers, is x + z2 odd? (1) x is odd and z is even. (2) x-z is odd.

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问题 If x and z are integers, is x + z2 odd?
(1) x is odd and z is even.
(2) x-z is odd.
选项 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.
答案D
解析 (1)     We are given that x is odd and z is even. Therefore, z2 is even and hence x + z2 is odd, because an odd integer added to an even integer is an odd integer; SUFFICIENT.
(2)     We are given that x - z is odd. Since there is not a readily apparent useful algebraic relation between x - z and x + z2, we consider all possible cases.

From the table it is clear that if x - z is odd, then x + z2 is odd; SUFFICIENT.
The correct answer is D;
each statement alone is sufficient.
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