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# If wz < 2, is z < 1?

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Manager
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If wz < 2, is z < 1? [#permalink]

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02 Jan 2010, 17:16
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If wz < 2, is z < 1?

(1) w > 2
(2) z < 2
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 32959
Followers: 5743

Kudos [?]: 70328 [0], given: 9843

Re: Is z<1 [#permalink]

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02 Jan 2010, 17:41
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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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Re: Is z<1 [#permalink]

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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
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Re: If wz < 2, is z < 1? [#permalink]

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22 Feb 2014, 11:58
Expert's post
Bumping for review and further discussion.
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Re: If wz < 2, is z < 1? [#permalink]

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14 Apr 2014, 01:31
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.
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Re: If wz < 2, is z < 1? [#permalink]

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13 Mar 2016, 06:01
Here the simple way to conclude that statement 1 is sufficient is because w is always positive and greater than 2
for w=2 which it cant be => z=1
so as Z increases z will decrease => Z<1
Re: If wz < 2, is z < 1?   [#permalink] 13 Mar 2016, 06:01
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# If wz < 2, is z < 1?

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