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# If X+Y/Z > 0, is X<0 ? 1. X<Y 2. Z<0

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Manager
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If X+Y/Z > 0, is X<0 ? 1. X<Y 2. Z<0 [#permalink]

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03 Feb 2008, 13:07
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If X+Y/Z > 0, is X<0 ?

1. X<Y
2. Z<0
CEO
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03 Feb 2008, 14:17
E

x=1, y=2, z=-4
x=-2, y=-1, z=-0.1

satisfy both conditions. Insuff.
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Manager
Joined: 23 Jan 2008
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03 Feb 2008, 16:18
walker wrote:
E

x=1, y=2, z=-4
x=-2, y=-1, z=-0.1

satisfy both conditions. Insuff.

here answer is C. together they are sufficient.
SVP
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03 Feb 2008, 19:09
hmm . im getting E as well. i reduced stem to -x*z<y

stat 1 doesnt tell us about z. insuff

stat 2 doesnt tell us about x or y. insuff.

together, i can have a negative x and positive y (since x<y) and a positive x and positive y. z is negative given from second statement.

consider x=-2, z=-1 and y=-1 --> (-2)*(-1)<-1 --> 2<-1 ... not true

consider x=2, z=-1 and y=4 --> (2)*(-1) <4 --> -2<4 ... true
Manager
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03 Feb 2008, 21:03

1 STATEMENT : X=4 Y=5 Z=5
X=-4 Y=15 Z=3

SO X CAN BE POSITIVE OR NEGATIVE

2 STATEMENT : X=2 Y=1 Z=-1
X=-2 Y=-10 Z=-1

SO X CAN BE POSITIVE OR NEGATIVE

BOTH STATEMENTS TOGETHER

X=-4 Y=-2 Z=-1/6
X HAS TO BE NEGATIVE IN ORDER TO FULFILL ALL CONDITIONS
SVP
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03 Feb 2008, 22:33
neeraj.kaushal wrote:

1 STATEMENT : X=4 Y=5 Z=5
X=-4 Y=15 Z=3

SO X CAN BE POSITIVE OR NEGATIVE

2 STATEMENT : X=2 Y=1 Z=-1
X=-2 Y=-10 Z=-1

SO X CAN BE POSITIVE OR NEGATIVE

BOTH STATEMENTS TOGETHER

X=-4 Y=-2 Z=-1/6
X HAS TO BE NEGATIVE IN ORDER TO FULFILL ALL CONDITIONS

I can not see why X must be negative! x can be positive: x =3, y = 4, z =-2

1. 3 + 4/(-2) =1 >0 satify
2. 3< 4
3. -2 < 0

All the conditions satified, why x must be negative?

E
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Manager
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04 Feb 2008, 14:30
Just a quick question, can I do

X+Y/Z > 0
X > -(Y/Z)
X < Y/Z

Given Z -ve Y/Z is -Ve and Hence X is -ve. So, B only.

Not sure if this is correct.

-Jack
Director
Joined: 01 Jan 2008
Posts: 624
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04 Feb 2008, 14:31
blog wrote:
If X+Y/Z > 0, is X<0 ?

1. X<Y
2. Z<0

1: insufficient (-1,1,0.5), (0.5,1,0.5)
2: insufficient (-1,-2,-1), (1,-2,-1)

1&2: insufficient:

(-4,-3,-0.25) and (3,4,-2) -> E
Senior Manager
Joined: 06 Jul 2006
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Schools: Berkeley Haas
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04 Feb 2008, 16:37
Has to be E.

As per St1: X can be both -ve and +ve to meet the result.
X Y Z
-4 -3 -0.5 > 0
2 4 2 > 0

Not suff.

As per St2 again: X can be both -ve and +ve to meet the result.
X Y Z
-3 -4 -1 > 0
3 -2 -1 > 0
3 2 -1 > 0

Not suff.

Combining 1 & 2:
X Y Z
-4 -3 -1 > 0...YES
3 4 -1 < 0...NO
3 4 -4 > 0...YES

X can be both -ve and +ve..
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Last edited by suntaurian on 04 Feb 2008, 16:49, edited 1 time in total.
Senior Manager
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Schools: Berkeley Haas
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04 Feb 2008, 16:39
jackychamp wrote:
Just a quick question, can I do

X+Y/Z > 0
X > -(Y/Z)
X < Y/Z

Given Z -ve Y/Z is -Ve and Hence X is -ve. So, B only.

Not sure if this is correct.

-Jack

Jack, How do you know that given Z is -ve, Y/Z can not be positive ? Y can be both positive or negative...hence so can X.
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When you come to the end of your rope, tie a knot and hang on.

Senior Manager
Joined: 26 Jan 2008
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05 Feb 2008, 00:35
blog wrote:
walker wrote:
E

x=1, y=2, z=-4
x=-2, y=-1, z=-0.1

satisfy both conditions. Insuff.

here answer is C. together they are sufficient.

blog, based on your feedback, I think the question is supposed to be:

If (X+Y)/Z > 0, is X<0 ?

1. X<Y
2. Z<0

Then the answer would be (C). Otherwise its (E)
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Manager
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05 Feb 2008, 11:38
incognito1 wrote:
blog wrote:
walker wrote:
E

x=1, y=2, z=-4
x=-2, y=-1, z=-0.1

satisfy both conditions. Insuff.

here answer is C. together they are sufficient.

blog, based on your feedback, I think the question is supposed to be:

If (X+Y)/Z > 0, is X<0 ?

1. X<Y
2. Z<0

Then the answer would be (C). Otherwise its (E)

yeah Z is below both (X+Y) ?
Senior Manager
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Posts: 263
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Kudos [?]: 109 [0], given: 16

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05 Feb 2008, 12:24
blog wrote:
yeah Z is below both (X+Y) ?

The equation (X+Y)/Z > 0 is different from X+Y/Z > 0

The latter would be evaluated as:
X+(Y/Z) > 0
since when parenthesis are not specified, division is performed prior to addition.

for instance:
2 + 4/2 = 2 + (4/2) = 2 + 2 = 4
whereas
(2+4)/2 = 6/2 = 3

But I think you already knew this!
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Re: is X<0 ?   [#permalink] 05 Feb 2008, 12:24
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