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If a<y<z<b is I y-a I < I y-b I 1) I z-a I <

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Manager
Joined: 13 Apr 2008
Posts: 64
If a<y<z<b is I y-a I < I y-b I 1) I z-a I < [#permalink]

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29 Jul 2008, 02:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If a<y<z<b is I y-a I < I y-b I

1) I z-a I < I z-b I

2) I y-a I < I z-b I

SVP
Joined: 17 Jun 2008
Posts: 1529

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29 Jul 2008, 02:30
I would go with answer D.

If I plot the four points a,y,z and b on number line, then
Stmt1: If absolute distance between z and a is less than absolute distance between z and b and since y is to the left of z, hence absolute distance between y and a will be less than the absolute distance between y and b.

Stmt2: Similar logic as in Stmt 1.
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Joined: 24 Jun 2008
Posts: 1346

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29 Jul 2008, 08:58
Value wrote:
If a<y<z<b is I y-a I < I y-b I

1) I z-a I < I z-b I

2) I y-a I < I z-b I

Yes, agree with the post above. Remember that | y - a | just means "the distance between y and a on the number line". So the question is asking, "is y closer to a than it is to b?"

Statement 1 tells us "z is closer to a than it is to b". We know y is even closer to a than z is (from a<y<z<b) so this statement is sufficient.

Statement 2 tells us that "y is closer to a than z is to b". Since y is further from b than z is, y must be closer to a than to b. This statement is sufficient.

Much easier to see all of this if you draw the number line.
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Senior Manager
Joined: 19 Mar 2008
Posts: 351

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30 Jul 2008, 08:24
i got E

could someone explain why it is D?
SVP
Joined: 07 Nov 2007
Posts: 1789
Location: New York

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30 Jul 2008, 08:53
judokan wrote:
i got E

could someone explain why it is D?

See the attachment.
Attachments

distance.doc [23.5 KiB]

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Intern
Joined: 01 Jul 2008
Posts: 40

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30 Jul 2008, 08:55
IanStewart wrote:
Value wrote:
If a<y<z<b is I y-a I < I y-b I

1) I z-a I < I z-b I

2) I y-a I < I z-b I

Yes, agree with the post above. Remember that | y - a | just means "the distance between y and a on the number line". So the question is asking, "is y closer to a than it is to b?"

Statement 1 tells us "z is closer to a than it is to b". We know y is even closer to a than z is (from a<y<z<b) so this statement is sufficient.

Statement 2 tells us that "y is closer to a than z is to b". Since y is further from b than z is, y must be closer to a than to b. This statement is sufficient.

Much easier to see all of this if you draw the number line.

a<y<z<b => I y-a I + I z-y I = I z-a I -(1)

& a<y<z<b => I z-y I + I b-z I = I b-y I => I b-z I < I b-y I -(2)

1) I z-a I < I z-b I => I y-a I + I z-y I < I z-b I (from (1))
& I b-z I < I b-y I (from (2))
=> I y-a I + I z-y I < I b-y I
=> I y-a I < I b-y I

2) I y-a I < I z-b I
=> I y-a I < I z-b I < I b-y I from (2)
hence I y-a I < I b-y I
Re: GMATPREP-Absolute Values   [#permalink] 30 Jul 2008, 08:55
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