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Is absolute value x equal to y minus z? 1) x+y=z 2) x<0

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Manager
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Is absolute value x equal to y minus z? 1) x+y=z 2) x<0 [#permalink]  20 Apr 2006, 15:55
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Is absolute value x equal to y minus z?

1) x+y=z

2) x<0
Senior Manager
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Q) is |x| = y-z ?

1) x+y=z

=> x = z-y or -x = y-z
can't tell unless we know the sign of x.

2) x<0
=> |x| = -x

from 1 and 2, |x| = -x = y-z

C.

Thanks,
Vipin
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Re: DS: absolute value [#permalink]  20 Apr 2006, 16:13
jlui4477 wrote:
Is absolute value x equal to y minus z?

1) x+y=z

2) x<0

Question is, is |x| = y - z?

This holds true when x = y -z, or when x = z - y.

(1) Tells us precisely that.
(2) Doesn't.

Hence A.
_________________

Who says elephants can't dance?

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Re: DS: absolute value [#permalink]  20 Apr 2006, 19:41
kapslock wrote:
jlui4477 wrote:
Is absolute value x equal to y minus z?

1) x+y=z

2) x<0

Question is, is |x| = y - z?

This holds true when x = y -z, or when x = z - y.

(1) Tells us precisely that.
(2) Doesn't.

Hence A.

From the (1) y-z =-x which is not sufficient by itself.
(2) is not suff by itself as well.
Together they are sufficient, so the correct answer is 'C'.
GMAT Club Legend
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1) x = z-y.

If x = 2, z-y = 4-2 and y-z will not be equal to |x|
If x = -2, z-y = 2-4 and y-z will be equal to |x|.

Insufficient.

2) x < 0. It doesn't mean a thing.
x could be -3, and so |x| = 3 but y-z could be any value. Insufficient.

Using both,
we know it's sufficient. y-z must be equal to |x|

Ans C
Intern
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If Abs(X)=Y-Z is true then: X=Y-Z or X=-Y+Z

1) tells us that X=Z-Y => Sufficient
2) doesn't provide enough information to answer=> Insifficient

to me should it be answer A
Manager
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ywilfred wrote:
1) x = z-y.

If x = 2, z-y = 4-2 and y-z will not be equal to |x|
If x = -2, z-y = 2-4 and y-z will be equal to |x|.

Insufficient.

2) x < 0. It doesn't mean a thing.
x could be -3, and so |x| = 3 but y-z could be any value. Insufficient.

Using both,
we know it's sufficient. y-z must be equal to |x|

Ans C

Aren't we out to prove that |x| = y-z and not that x =/ <> y-z. Correct me if my understanding is incorrect. I feel that if x = z-y the |x| = y-x, thus A.
Senior Manager
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either -x = y-z or x=y-z will satisfy the given condition

i) x+y = z => -x = y-z sufficient since |-x| = |x|
ii) not sufficient

hence A
Manager
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Still confused
If x = 2 or -2; |x| will always be 2.
thus if y-z = 2 then (y = 4; z =2) x =2==> |x| = true
if y-z = -2 (y =2; z=4) then x=-2; even though |x| = 2; y-z <> 2
Director
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What is the source of this problem? Is it OG?
Director
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can someone explain this with numbers ?
Senior Manager
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(C)

I. tells usthat x = z - y
lets take x = 2, z = 5, y = 3
then, I holds, but |x| != y - z
as |x| = 2 and y - z = -2

II. tells nothing

Combining, we know that x is -ve,
since, x = z - y
and x < 0, |x| = -(z-y) = y -z
(C)
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