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If x, y, and z are nonzero integers and x > yz, which of the [#permalink]
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16 Nov 2005, 18:03
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If x, y, and z are nonzero integers and x > yz, which of the following must be true I. x/y > z II. x/z> y III. x/(yz) > 1 A. None of the above B. I only C. III only D. I and II only E. I, II, III
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Last edited by Bunuel on 17 Aug 2012, 05:34, edited 1 time in total.
Edited the question and added the OA.



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A.
unless we know if they are +ve or ve we cannot simply this inequality.
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I am inclined to pick A as well...we dont know the signs
we know that X>yz
so lets say x=1 YZ=3
1/3=1/3 <1
if X is 3 YZ=2
3/2 > 1....
likewise others dont add up either...



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I think A as well.
I picked a couple of numbers
1. x = 4, y = 2, z= 5
2. x= 4, y=2, z=3
none have to work



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I pick C. Seems to me that it is always correct to say x/yz > 1



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Re: Q: If X,Y, and Z are nonzero integers and X>YZ, which of [#permalink]
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08 Mar 2012, 21:07
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None of the options satisfies all the cases Good example for plugging in question type .. + kudos if U like this post
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Re: Q: If X,Y, and Z are nonzero integers and X>YZ, which of [#permalink]
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08 Mar 2012, 21:41
Well waiting for Bunuel's reply to this question. I am sure there will be something special in store.



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Re: Q: If X,Y, and Z are nonzero integers and X>YZ, which of [#permalink]
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08 Mar 2012, 22:17
if u consider y & z are negative numbers and plugin cases 1 and 2 fail.
However 3 seems to be correct coz x>yz is the given condition so x/yz>1 always.
Hope this helps.



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Re: Q: If X,Y, and Z are nonzero integers and X>YZ, which of [#permalink]
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09 Mar 2012, 03:33
faisalt wrote: Q: If X,Y, and Z are nonzero integers and X>YZ, which of the following must be true 1. X/Y>Z 2. X/Z>Y 3. X/YZ>1
A. None of the above B. 1 only C. 3 only D. 1 and 2 only E. 1, 2, 3 I used numbers Case a X = 8 , Y = 2 , Z = 3 Option 1 and 2 fails Case b X = 3 , Y = 3 , Z = 2 Option 2 fails None of them satisfies. Ans should be A



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Re: Q: If X,Y, and Z are nonzero integers and X>YZ, which of [#permalink]
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14 Aug 2012, 05:46
pratikbais wrote: Well waiting for Bunuel's reply to this question. I am sure there will be something special in store. True , expert solution will reenforce our solutions, I am also getting A simple pick easy numbers x= 16 y = 2 and Z=4 as X>YZ satisfies all but if we pick x= 4 y= 2 and Z=4 as X>YZ so option 1 x/y> Z need not be true and X/YZ > 1( option 3 ) also need not be true also x= 4 Y=2 and Z= 4 as X>YZ so option 2 , X/Z > Y also need not be true so none of the answer choices have to be true for X>YZ condition to hold
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Re: If x, y, and z are nonzero integers and x > yz, which of the [#permalink]
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17 Aug 2012, 05:40
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If x, y, and z are nonzero integers and x > yz, which of the following must be trueI. x/y > z II. x/z> y III. x/(yz) > 1 A. None of the above B. I only C. III only D. I and II only E. I, II, III Remember, when we divide both sides of an inequality by a negative number we should flip the sign. Given: \(x > yz\). If \(y<0\), then when we divide both parts by \(y\) we'll get \(\frac{x}{y}<z\). Thus option I is not necessarily true; If \(z<0\), then when we divide both parts by \(z\) we'll get \(\frac{x}{z}<y\). Thus option II is not necessarily true; If \(yz<0\), then when we divide both parts by \(yz\) we'll get \(\frac{x}{yz}<1\). Thus option III is not necessarily true. So, none of the options must be true. Answer: A. Hope it's clear.
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Re: If x, y, and z are nonzero integers and x > yz, which of the [#permalink]
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