is |x|=y-z ? 1. x+y=z 2. x<0 first we know that y-z=|x|, : DS Archive
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# is |x|=y-z ? 1. x+y=z 2. x<0 first we know that y-z=|x|,

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is |x|=y-z ? 1. x+y=z 2. x<0 first we know that y-z=|x|, [#permalink]

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07 Oct 2006, 18:23
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is |x|=y-z ?

1. x+y=z

2. x<0

first we know that y-z=|x|, so

-x=y-z
-x=y-z

from 1. we know that x=z-y, so -x=y-z, so why do we need 2?
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07 Oct 2006, 19:31
Here is what I think.

Since |x| is positive, y-z should be greater than 0. (i)
Equation 1 says: x = z-y
if x is a positive number, z-y>0 i.e y-z < 0, which will contradict the conclusion in (i)
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08 Oct 2006, 01:24
is |x|=y-z ?

1. x+y=z

2. x<0

from stem

x = y-z x>=0 or x = z-y x<0

from one x = z-y ie x<0.....insuff

from two x<0 ...insuff

both insuff my answer is E
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08 Oct 2006, 09:30
It must be C.
Is |X| =Y-Z.

1: x+y =z
2+3 = 5 ie x=2 y=3 and z=5
These values will not satisfy |x|=y-z

-2+3 =1 i.e x=-2 y=3 and z=1
These values will satisfy |x|=y-z.

So 1 is not sufficient

2: x<0 Clearly alone not sufficient.

Let's combine both.

Since x<0, |x| =-x.------------(1)
given x+y= z
ie x=z-y
ie -x = y-z
ie |x| = y-z from (1)

So it is C
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08 Oct 2006, 10:08
Another one for C.

I wasn't sure how to explain my answer till Cicerone did a great job of it.
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08 Oct 2006, 10:47
C

|x| = y - z

I) x + y = z
x = z - y

if x is negative |x| = y - z, however it may be positive & x = z - y

so we need II

II) x < 0
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08 Oct 2006, 11:37
I guess i ve a lot to learn and practise thanks everyone
08 Oct 2006, 11:37
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