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Re: If zy<xy<0 is |x-z|+|x|=|z| 1.z<x 2.y>0 A. [#permalink]
09 Jan 2013, 10:30
If zy<xy<0 is |x-z|+|x|=|z| 1.z<x 2.y>0
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.
Bunuel is right we don't need stmts (1) or (2) or both to solve this problem. Here how can we come to it.
squre both sides of the equation:
|x-z|+|x|=|z| |x-z|=|z|-|x| x^2-2xz+z^2=x^2-2|xz|+z^2 after that we have:
-2xz=-2|xz| divding this equation by -2 we have: xz=|xz| which means that question asks us: is xz=|xz|? here everything is clear i.e.If zy<xy<0 y must be positive or negative. If y positive x and z must be both negative or vice versa which means that if y is negative both x and z must be positive where the inequality zy<xy<0 will be correct.
So we don't need any statements to solve this problem