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# If a < x < b and c < y < d, is x < y ?

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If a < x < b and c < y < d, is x < y ? [#permalink]  24 Sep 2012, 04:19
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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If a < x < b and c < y < d, is x < y ?

(1) a < c
(2) b < c

Practice Questions
Question: 48
Page: 279
Difficulty: 600

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Re: If a < x < b and c < y < d, is x < y ? [#permalink]  24 Sep 2012, 07:51
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Statement 1: A <c... insufficient...

Statement. 2 ...sufficient..because B<c.. X must be less than Y..
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Re: If a < x < b and c < y < d, is x < y ? [#permalink]  24 Sep 2012, 04:19
Expert's post
SOLUTION

If a < x < b and c < y < d, is x < y ?

(1) a < c. From this statement we cannot determine whether $$x < y$$. For example, consider that $$a$$ and $$c$$ are some negative numbers and $$x$$ and $$y$$ are some positive numbers, we can have that $$x<y$$ as well as $$y<x$$. Not sufficient.

(2) b < c. Since, $$b<c$$, then $$a < x < b<c < y < d$$ --> $$x<y$$. Sufficient.

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Re: If a < x < b and c < y < d, is x < y ? [#permalink]  24 Sep 2012, 04:34
1) Insufficient
2) Sufficient

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Re: If a < x < b and c < y < d, is x < y ? [#permalink]  24 Sep 2012, 08:21
Bunuel wrote:
If a < x < b and c < y < d, is x < y ?

(1) a < c
(2) b < c

x < y?

(1)
a < x < b
c < y < d
and a < c
these 2 eqns can be combined in multiple ways

a...x...b...c...y...d
or
a...c..y...d...x..b
etc.
Thus, x can be greater or lesser than y
So, this is not sufficient

(2)
a < x < b
c < y < d
and b < c

these 3 eqns can be fit only in one way
a...x...b...c...y...d
=> x < y

Thus this is sufficient.

Hence B
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Re: If a < x < b and c < y < d, is x < y ? [#permalink]  28 Sep 2012, 04:38
Expert's post
SOLUTION

If a < x < b and c < y < d, is x < y ?

(1) a < c. From this statement we cannot determine whether $$x < y$$. For example, consider that $$a$$ and $$c$$ are some negative numbers and $$x$$ and $$y$$ are some positive numbers, we can have that $$x<y$$ as well as $$y<x$$. Not sufficient.

(2) b < c. Since, $$b<c$$, then $$a < x < b<c < y < d$$ --> $$x<y$$. Sufficient.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: If a < x < b and c < y < d, is x < y ? [#permalink]  28 Sep 2012, 06:19
Expert's post
This one is tricky because we could assume right away that we need both stats ar at least 3 elements to have an answer

1) a < c we do not know nothing about B (in this case we can see B as a pivotal element)

2) b < c thi is suff because in the chain a < b AND b < c the c < d........

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Re: If a < x < b and c < y < d, is x < y ?   [#permalink] 28 Sep 2012, 06:19
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