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If x, y, and z are nonzero integers and x > yz, which of the

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If x, y, and z are nonzero integers and x > yz, which of the [#permalink] New post 16 Nov 2005, 17:03
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A
B
C
D
E

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52% (01:51) correct 47% (00:52) wrong based on 73 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Aug 2012, 04:34, edited 1 time in total.
Edited the question and added the OA.
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 [#permalink] New post 16 Nov 2005, 17:09
A.

unless we know if they are +ve or -ve we cannot simply this inequality.
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 [#permalink] New post 16 Nov 2005, 17:13
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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[#permalink] New post 16 Nov 2005, 18:09
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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 [#permalink] New post 17 Nov 2005, 05:57
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] New post 08 Mar 2012, 20:07
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] New post 08 Mar 2012, 20:41
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] New post 08 Mar 2012, 21:17
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] New post 09 Mar 2012, 02:33
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] New post 14 Aug 2012, 04:46
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] New post 17 Aug 2012, 04:40
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Expert's post
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

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] New post 17 Aug 2012, 16:00
+1 A

We cannot infer anything. We need to know whether y and z are positive or negative.
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Re: If x, y, and z are nonzero integers and x > yz, which of the   [#permalink] 17 Aug 2012, 16:00
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