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Does the rectangle have an area less than 30?

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Does the rectangle have an area less than 30? [#permalink] New post 18 Aug 2009, 17:43
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A
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80% (01:50) correct 20% (01:53) wrong based on 23 sessions
Does the rectangle have an area less than 30?

(1) Perimeter = 20
(2) Diagonal < 10
[Reveal] Spoiler: OA
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Re: Does the rectangle have an area less than 30? [#permalink] New post 19 Aug 2009, 06:08
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yezz wrote:
Does the rectangle have an area less than 30?
(1) Perimeter = 20
(2) Diagonal < 10


for (1), perimeter = 20, therefore the Smax=(20/4)^2=25<30
A sufficient

for (2), suppose X^2+Y^2=100
the area is S=XY=X\(\sqrt{100-X^2}\)

when X^2=50 or X=\(\sqrt{50}\), Smax=50>30

So the answer is A
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Re: Does the rectangle have an area less than 30? [#permalink] New post 05 Jan 2010, 13:17
flyingbunny wrote:
yezz wrote:
Does the rectangle have an area less than 30?
(1) Perimeter = 20
(2) Diagonal < 10


for (1), perimeter = 20, therefore the Smax=(20/4)^2=25<30
A sufficient

for (2), suppose X^2+Y^2=100
the area is S=XY=X\(\sqrt{100-X^2}\)

when X^2=50 or X=\(\sqrt{50}\), Smax=50>30

So the answer is A


Dont think this is correct....

ST1 - SUFF for sure....
ST2 - gives that area is more than 30... therefore is very much sufficient to answer the question....

Hence answer should be D....
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Re: Does the rectangle have an area less than 30? [#permalink] New post 05 Jan 2010, 13:20
jeeteshsingh wrote:
flyingbunny wrote:
yezz wrote:
Does the rectangle have an area less than 30?
(1) Perimeter = 20
(2) Diagonal < 10


for (1), perimeter = 20, therefore the Smax=(20/4)^2=25<30
A sufficient

for (2), suppose X^2+Y^2=100
the area is S=XY=X\(\sqrt{100-X^2}\)

when X^2=50 or X=\(\sqrt{50}\), Smax=50>30

So the answer is A


Dont think this is correct....

ST1 - SUFF for sure....
ST2 - gives that area is more than 30... therefore is very much sufficient to answer the question....

Hence answer should be D....


Oops.... sorry its A.... :) My mistake... I failed to consider that diagonal is less than 10.. hence the area could be 50 or less.....
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Re: Does the rectangle have an area less than 30? [#permalink] New post 05 Jan 2010, 14:31
Clearly answer is A
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Re: Does the rectangle have an area less than 30? [#permalink] New post 09 Jan 2010, 20:20
Can someone provide another example for why STMT 2 is insufficient?
I can see that the area's < 48 since the diagonal's < 10.
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Re: Does the rectangle have an area less than 30? [#permalink] New post 09 Jan 2010, 20:40
gottabwise wrote:
Can someone provide another example for why STMT 2 is insufficient?
I can see that the area's < 48 since the diagonal's < 10.


Rephrase of ? - Are l & w < 5 & 6?
(1) 2l+2w=20 l+w=10 max 5, 5; max area 25; 25<30 SUFF
(2) 1/2 rectangle=right triangle; a^2+b^2=c^2 c<10 (6-8-10 right triangle); sides less than 6 & 8
given that, does the possibility of the l & w being any combo of #'s < 6&8 make it INS?
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Re: Does the rectangle have an area less than 30? [#permalink] New post 09 Jan 2010, 22:47
Thanks for the g8 explanation
Re: Does the rectangle have an area less than 30?   [#permalink] 09 Jan 2010, 22:47
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