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# x, y, z are numbers on the number line. Is x<y<z? 1)

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Senior Manager
Joined: 08 Aug 2005
Posts: 251
x, y, z are numbers on the number line. Is x<y<z? 1) [#permalink]

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27 Apr 2006, 23:41
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

x, y, z are numbers on the number line. Is x<y<z?

1) |y-x| + |y-z| = |z-x|

2) x<z
Manager
Joined: 20 Mar 2005
Posts: 201
Location: Colombia, South America
Re: xyz on number line [#permalink]

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28 Apr 2006, 00:32
getzgetzu wrote:
x, y, z are numbers on the number line. Is x<y<z?

1) |y-x| + |y-z| = |z-x|

2) x<z

(1) remainds me of the triangle inequality
|x-y| + |y-z| >= |x-z|

so is just equal if x<y<z or x>y>z
insuff.

(2) insuff.

together works

C
VP
Joined: 21 Sep 2003
Posts: 1057
Location: USA
Re: xyz on number line [#permalink]

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28 Apr 2006, 00:34
conocieur wrote:
getzgetzu wrote:
x, y, z are numbers on the number line. Is x<y<z?

1) |y-x| + |y-z| = |z-x|

2) x<z

(1) remainds me of the triangle inequality
|x-y| + |y-z| >= |x-z|

so is just equal if x<y<z or x>y>z
insuff.

(2) insuff.

together works

C

What happens if y=z or y=x?
_________________

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- Bernard Edmonds

Manager
Joined: 20 Mar 2005
Posts: 201
Location: Colombia, South America
Re: xyz on number line [#permalink]

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28 Apr 2006, 00:57
giddi77 wrote:
conocieur wrote:
getzgetzu wrote:
x, y, z are numbers on the number line. Is x<y<z?

1) |y-x| + |y-z| = |z-x|

2) x<z

(1) remainds me of the triangle inequality
|x-y| + |y-z| >= |x-z|

so is just equal if x<y<z or x>y>z
insuff.

(2) insuff.

together works

C

What happens if y=z or y=x?

yes, I didn't notice that one, mmm, should we go for E then?
VP
Joined: 29 Apr 2003
Posts: 1403

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28 Apr 2006, 01:44
It works for x=y or y=z

if x=0, y=0, z=2

0 + 2 = 2

if x=0, y=2, z=2

2 + 0 = 2
Manager
Joined: 20 Mar 2005
Posts: 201
Location: Colombia, South America

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28 Apr 2006, 01:46
sm176811 wrote:
It works for x=y or y=z

if x=0, y=0, z=2

0 + 2 = 2

if x=0, y=2, z=2

2 + 0 = 2

o yeah, the triangle inequality yes, but what about x<y<z

i guess that one doesn't hold
VP
Joined: 29 Apr 2003
Posts: 1403

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28 Apr 2006, 01:47
conocieur wrote:
sm176811 wrote:
It works for x=y or y=z

if x=0, y=0, z=2

0 + 2 = 2

if x=0, y=2, z=2

2 + 0 = 2

o yeah, the triangle inequality yes, but what about x<y<z

i guess that one doesn't hold

What do you mean.. give an example!
Manager
Joined: 20 Mar 2005
Posts: 201
Location: Colombia, South America

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28 Apr 2006, 01:50
sm176811 wrote:
conocieur wrote:
sm176811 wrote:
It works for x=y or y=z

if x=0, y=0, z=2

0 + 2 = 2

if x=0, y=2, z=2

2 + 0 = 2

o yeah, the triangle inequality yes, but what about x<y<z

i guess that one doesn't hold

What do you mean.. give an example!

x=0, y=2, z=2
both hold in (1) and (2)
but since y=z
then x<y<z doesn't work

also x=0 y=1 z=2
hold in (1) and (2)
then x<y<z does work

since can obtain two different answers there is no enough info
VP
Joined: 29 Apr 2003
Posts: 1403

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28 Apr 2006, 01:56
Ah!! Missed that I guess the answer is E then!
28 Apr 2006, 01:56
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