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If (x + y) / z > 0, is x < 0? 1) x < y 2) z < 0

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Director
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If (x + y) / z > 0, is x < 0? 1) x < y 2) z < 0 [#permalink] New post 20 Apr 2008, 11:26
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C
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If (x + y) / z > 0, is x < 0?

1) x < y
2) z < 0
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Intern
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Re: DS OG Number Prop [#permalink] New post 20 Apr 2008, 11:36
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jimmyjamesdonkey wrote:
If (x + y) / z > 0, is x < 0?

1) x < y
2) z < 0


Answer C

1) insuf. try numbers (-2-1)/-2 or (1+2)/2 --> x<0 and x>0
2) means numerator has to be negative. still insuff because no relationship betwee x and y is given.

Combined, x<y from (1) and x+y<0 from (2). It follows that x cant be >0. Sufficient
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Re: DS OG Number Prop [#permalink] New post 20 Apr 2008, 11:42
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I also get c.

from stat 1, we know nothing about sign of z. insuff.

from stat 2, we know that z is negative, but nothing about x or y. insuff.

together, z is negative, and therefore to meet the condition in the stem, the numerator (x+y) has to be negative. Since x+y<0, this leads to x<-y, and so we can answer the question. sufficient.
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Re: DS OG Number Prop [#permalink] New post 20 Apr 2008, 11:45
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1)
assume z positive
x+y must be positive for (x+y)/z to be greater than 0
let x =-1 and y=1000
let x=1000 and y=-1
1 fails

2)
z is negative
x+y must be negative for (x+y)/z to be greater than 0
let x=-1000 and y=1
let x=1 and y=-1000
2 fails

1+2)
from 2 (x+y) must be negative
from 1 x<y
using 2, either x or y must be negative
if x is negative this confirms x<0
using 1, if y is negative, x must be less than y so x<0

C
Director
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Re: DS OG Number Prop [#permalink] New post 20 Apr 2008, 11:51
OA is C. Question..Are we allowed to cross multiply across a inequality?
Re: DS OG Number Prop   [#permalink] 20 Apr 2008, 11:51
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If (x + y) / z > 0, is x < 0? 1) x < y 2) z < 0

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