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题库 / Prep2007E2-DS-138
If zy < xy < 0, is |x - z| + |x| = |z| ?
(1) z < x
(2) y > 0
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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If zy < xy < 0，xz>0（即两者同正负）
条件一：z < x，
则z < x< 0，|x| = -x, |z| = -z , |x - z|=x-z
|x - z| + |x| =x-z-x=-z=|z|, 故原题可证；
条件二： y > 0
则z < x< 0，论证同条件一。
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