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# If wz < 2, is z < 1? (1) w > 2 (2) z < 2 A.

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If wz < 2, is z < 1? (1) w > 2 (2) z < 2 A. [#permalink]  02 Jan 2010, 17:16
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If wz < 2, is z < 1?
(1) w > 2
(2) z < 2

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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Re: Is z<1 [#permalink]  02 Jan 2010, 17:41
If wz < 2, is z < 1?

(1) w > 2, subtract the equations (we can do it as the signs are in opposite direction)

wz-w<2-2 --> w(z-1)<0, as w is positive (given w>2), thus z-1 must be negative, product to be negative --> z-1<0 --> z<1. Sufficient.

(2) z < 2. We can take z=1.5>1 and w=0 --> wz<2 or z=0<1 and w=0 wz<0. Not sufficient.

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Kudos [?]: 61 [0], given: 25

Re: Is z<1 [#permalink]  02 Jan 2010, 17:46
Thanks Bunuel

Even i got A. However, the OA given in the GMAC paper test is D.

I guess the OA (like many others in the paper tests) is wrong
Re: Is z<1   [#permalink] 02 Jan 2010, 17:46
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