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Data Sufficiency Question - Easy but a challenging assumptio

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by Ankush Soni » Mon Sep 22, 2008 8:33 am
Q: A rectangle has length, width and diagonal as L, W and D resp. What is the length of the rectangle ?

1. L+W = 6
2. D^2 = 20 i.e D to the power of 2 = 20

Which choice would you mark (C) or (E). Thanks.
My assumption is the length of a rectangle is always the longest side.

Thanks

Ankush
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Source: — Data Sufficiency |
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by tendays2go » Mon Sep 22, 2008 9:32 am
if D^2 = 20 => L^2 + W^2 = 20
Also, L+W = 6 => L^2 + W^2 + 2L*W = 36 i.e. L*W = 8
so, we have L* ( 6 - L) = 8 or L=2/4

now, the question says clearly that L is the length, so for me,
L = 4 is the correct answer.

What is the OA?
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by 4meonly » Mon Sep 22, 2008 9:56 am
NEither 1 nor 2 alone are not suff

Combining:
we have
l+w=6, w=6-l
d^2=20
l^2 + (6-l)^2 = 20 solving we get
l^2 - 6l + 8 = 0
(l-2)(l-4)=0
l can be as 2 as 4, so I think answer wil be E until we are told that l>w.

I don't know whether lenght is always more than width in GMAT
Can anybody resolve my doubts?
I will choose E in this case

I think we need Stuart and Ian here! :idea:
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Hi Tendaysago and 4meonly

by Ankush Soni » Mon Sep 22, 2008 11:47 am
answering to ten days ago
......the original question was what is the area of the rectangle ?
I just extended the question to calculating the length.


answering to 4meonly

How do we get Stuart or Ian here ?
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by mals24 » Mon Sep 22, 2008 11:49 am
Agree with 4meonly the answer should be E

The length of a rectangle is not necessarily greater than the width. So L could be 2 or 4.
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by mals24 » Mon Sep 22, 2008 11:55 am
@ Ankush Soni

If the question is asking for area of the rectangle then the answer is clearly C. The solution is explained very clearly by tendays2go
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by Ian Stewart » Mon Sep 22, 2008 2:38 pm
The 'length' of a rectangle is normally equal to its longest side, so the answer here should be C, as I think has been explained adequately above. Still, the GMAT does *not* test whether you know obscure details about mathematical definitions. There is no chance that you would see a question exactly like this on the GMAT- if it were a real GMAT question, they would tell you that l > w. So don't worry about the minor technicality here that makes the answer C; if you found that 2 and 4 are the two side lengths, you've learned what you need to from the question.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Hi

by Ankush Soni » Wed Sep 24, 2008 10:42 am
Thanks Ian
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