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# Is x<y<z? (1) |z-x|=|z-y|+|y-x| (2) z>x

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VP
Joined: 10 Jun 2007
Posts: 1439
Is x<y<z? (1) |z-x|=|z-y|+|y-x| (2) z>x [#permalink]

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26 Oct 2007, 07:22
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Is x<y<z?
(1) |z-x|=|z-y|+|y-x|
(2) z>x
Current Student
Joined: 31 Aug 2007
Posts: 369

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26 Oct 2007, 07:26
I guessed E on this, so no explanation...just tried out a few diff numbers.
VP
Joined: 08 Jun 2005
Posts: 1145

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26 Oct 2007, 08:07

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)

Manager
Joined: 02 Aug 2007
Posts: 145

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26 Oct 2007, 13:41
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.
VP
Joined: 08 Jun 2005
Posts: 1145

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26 Oct 2007, 13:45
bkk145 wrote:
KillerSquirrel wrote:

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

VP
Joined: 10 Jun 2007
Posts: 1439

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26 Oct 2007, 13:57
KillerSquirrel wrote:
bkk145 wrote:
KillerSquirrel wrote:

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

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
VP
Joined: 08 Jun 2005
Posts: 1145

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26 Oct 2007, 14:04
bkk145 wrote:
KillerSquirrel wrote:
bkk145 wrote:
KillerSquirrel wrote:

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

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.

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

26 Oct 2007, 14:04
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