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If wz < 2, is z < 1?

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If wz < 2, is z < 1? [#permalink] New post 02 Jan 2010, 16:16
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If wz < 2, is z < 1?

(1) w > 2
(2) z < 2
[Reveal] Spoiler: OA
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Re: Is z<1 [#permalink] New post 02 Jan 2010, 16:41
Expert's post
If wz < 2, is z < 1?

(1) w > 2. Subtract w > 2 from wz < 2 (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), then the product to be negative z-1 must be negative --> z-1<0 --> z<1. Sufficient.

(2) z < 2. If z=1.5>1 and w=0 (wz<2), then the answer is YES but if z=0<1 and w=0 (wz<0), then the answer is NO. Not sufficient.

Answer: A.
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Manager
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Joined: 17 Aug 2009
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Kudos [?]: 93 [0], given: 25

Re: Is z<1 [#permalink] New post 02 Jan 2010, 16:46
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
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Re: If wz < 2, is z < 1? [#permalink] New post 22 Feb 2014, 10:58
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Re: If wz < 2, is z < 1? [#permalink] New post 14 Apr 2014, 00:31
If wz < 2, is z < 1?

(1) w > 2
(2) z < 2

Sol.
opt.1 => w>2
i.e. z(something>2)<2
=> z<2/(something >2)
in the step above, R.H.S will always be <1. Hence Z<1

opt.2 => z<2
from this we can't say whether z will be less then 1.
Hence, A.
Re: If wz < 2, is z < 1?   [#permalink] 14 Apr 2014, 00:31
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