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bkk145
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Is x<y<z? (1) |z-x|=|z-y|+|y-x| (2) z>x 26 Oct 2007, 07:22
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young_gun
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Is x<y<z? (1) |z-x|=|z-y|+|y-x| (2) z>x 26 Oct 2007, 07:26
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I guessed E on this, so no explanation...just tried out a few diff numbers.
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KillerSquirrel
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Is x<y<z? (1) |z-x|=|z-y|+|y-x| (2) z>x 26 Oct 2007, 08:07
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the answer is (C)

statement 1

|z-x|=|z-y|+|y-x|

consider x=y=z

0 = 0+0 ---> true

consider z=3 y=2 x=1

2 = 1+1 ---> true

statement 2

clearly insufficient ---> no info on y

both statements

since z > x then y has to be in between to balance |z-x|

note that in |z-y|+|y-x| the effect of y is non existence (canceled out)

:)
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yuefei
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Is x<y<z? (1) |z-x|=|z-y|+|y-x| (2) z>x 26 Oct 2007, 13:41
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KillerS, is this an assumption we can infer:
"since z > x then y has to be in between to balance |z-x|"

This is not stated explicitly in the stem. I also tried integers and came up with E.
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Is x<y<z? (1) |z-x|=|z-y|+|y-x| (2) z>x 26 Oct 2007, 13:45
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bkk145
KillerSquirrel
the answer is (C)

statement 1

|z-x|=|z-y|+|y-x|

consider x=y=z

0 = 0+0 ---> true

consider z=3 y=2 x=1

2 = 1+1 ---> true

statement 2

clearly insufficient ---> no info on y

both statements

since z > x then y has to be in between to balance |z-x|

note that in |z-y|+|y-x| the effect of y is non existence (canceled out)

:)

What if x=0, y=0, z=1?
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Yes ! you got me there

:oops:
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bkk145
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Is x<y<z? (1) |z-x|=|z-y|+|y-x| (2) z>x 26 Oct 2007, 13:57
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KillerSquirrel
bkk145
KillerSquirrel
the answer is (C)

statement 1

|z-x|=|z-y|+|y-x|

consider x=y=z

0 = 0+0 ---> true

consider z=3 y=2 x=1

2 = 1+1 ---> true

statement 2

clearly insufficient ---> no info on y

both statements

since z > x then y has to be in between to balance |z-x|

note that in |z-y|+|y-x| the effect of y is non existence (canceled out)

:)

What if x=0, y=0, z=1?

Yes ! you got me there

:oops:
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I think it is best to think of this problem as a distance concept.
For example, |a - b| means distance from a to b
So, |z-x|=|z-y|+|y-x| can be interpret as:
distance from z to x = distance from z to y + distance from y to x
This means
z...y...x
OR
x...y...z
So (1) is INSUFFICIENT
(2) is obviously INSUFFICIENT, don't know y
Together, it must be true that
x...y...z
However, the problem says nothing about y or x being equal; thus, INSUFFICIENT.

OA=E
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KillerSquirrel
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Is x<y<z? (1) |z-x|=|z-y|+|y-x| (2) z>x 26 Oct 2007, 14:04
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bkk145
KillerSquirrel
bkk145
[quote="KillerSquirrel"]the answer is (C)

statement 1

|z-x|=|z-y|+|y-x|

consider x=y=z

0 = 0+0 ---> true

consider z=3 y=2 x=1

2 = 1+1 ---> true

statement 2

clearly insufficient ---> no info on y

both statements

since z > x then y has to be in between to balance |z-x|

note that in |z-y|+|y-x| the effect of y is non existence (canceled out)

:)

What if x=0, y=0, z=1?

Yes ! you got me there

:oops:

I think it is best to think of this problem as a distance concept.
For example, |a - b| means distance from a to b
So, |z-x|=|z-y|+|y-x| can be interpret as:
distance from z to x = distance from z to y + distance from y to x
This means
z...y...x
OR
x...y...z
So (1) is INSUFFICIENT
(2) is obviously INSUFFICIENT, don't know y
Together, it must be true that
x...y...z
However, the problem says nothing about y or x being equal; thus, INSUFFICIENT.[/quote]

Yes - this is a very good approach in absolute value problems - once again good question - touché !

:)



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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