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# Is xy > z? 1). xyz=1 2). xyz^2 > 1

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Senior Manager
Joined: 08 Aug 2005
Posts: 251
Is xy > z? 1). xyz=1 2). xyz^2 > 1 [#permalink]

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27 Nov 2005, 03:52
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Is xy > z?

1). xyz=1
2). xyz^2 > 1
SVP
Joined: 24 Sep 2005
Posts: 1885

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27 Nov 2005, 04:26
getzgetzu wrote:
Is xy > z?

1). xyz=1
2). xyz^2 > 1

1. x=1, y=2, x=1/2 ...xy>z? YES
x=y=1/2 , z= 4 ....xy>z? NO
--->insuff

2. xyz^2>1
x=y= 1, z= 2 ....xy>z? NO
x=2, y=5, z=1/3 .....xy>z? YES
--->insuff

1 and 2:
divide the 2nd inequality two sides by xyz , we have : z>1 ..xyz=1 ---> xy<1<z

--->suff

C.
SVP
Joined: 05 Apr 2005
Posts: 1710

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27 Nov 2005, 13:09
i and ii alone are not suff.

from i and ii, z>1. if z>1, then xy must be <1. so xy is not greater than z.
Re: DS inequality   [#permalink] 27 Nov 2005, 13:09
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