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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]

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

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

please explain
[Reveal] Spoiler: OA

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Re: If a < x < b and c < y < d, is x < y ? [#permalink]

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New post 28 Mar 2012, 09:54
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If a < x < b and c < y < d, is x < y ?

(1) a < c --> given: a<x, c<y and a<c. Now, if a<(c<y)<x then the answer is YES but if a<x<(c<y) then the answer is NO. Not sufficient.

(2) b < c --> given: x<b, c<y and b<c, so x<(b<c)<y, which means that x<y. Sufficient.

Answer: B.
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Re: If a < x < b and c < y < d, is x < y ? [#permalink]

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Re: If a < x < b and c < y < d, is x < y ? [#permalink]

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New post 03 Aug 2017, 13:41
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TomB wrote:
If a < x < b and c < y < d, is x < y ?

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

please explain


Target question: Is x < y?

Given: a < x < b and c < y < d

Statement 1: a < c
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several scenarios that satisfy statement 1 (AND the given information). Here are two:
Case a: a = 1, x = 2, b = 3, c = 4, y = 5 and d = 6. In this case, x < y
Case b: a = 1, x = 10, b = 11, c = 4, y = 5 and d = 6. In this case, x > y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b < c
Perfect, this information allows us to COMBINE the two given inequalities.
We get: a < x < b < c < y < d
At this point, it is clear that x < y
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:
[Reveal] Spoiler:
B


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Re: If a < x < b and c < y < d, is x < y ?   [#permalink] 03 Aug 2017, 13:41
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