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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
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x, y, z are numbers on the number line. Is x<y<z? 1) [#permalink]  27 Apr 2006, 22:41
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
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Re: xyz on number line [#permalink]  27 Apr 2006, 23:32
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
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Re: xyz on number line [#permalink]  27 Apr 2006, 23:34
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?
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Manager
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Re: xyz on number line [#permalink]  27 Apr 2006, 23:57
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
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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
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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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Kudos [?]: 18 [0], given: 0

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
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Location: Colombia, South America
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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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Kudos [?]: 18 [0], given: 0

Ah!! Missed that I guess the answer is E then!
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