Rectangle

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mmslf75: Legendary Member; Posts: 503; Joined: Sun Aug 09, 2009 9:53 pmFollowed by: 2 members; Thanked: 31 times

by mmslf75 » Mon Jan 18, 2010 12:30 am

Is the surface area of a rectangular pool larger than 1000 square feet?
(1) The pool measures fifty feet diagonally.
(2) One side of the pool measures twenty five feet.

OA is C

why noit A ?

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Source: Beat The GMAT — Data Sufficiency | Mon Jan 18, 2010 12:30 am

Lattefah84: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Mon Dec 14, 2009 4:15 am

by Lattefah84 » Mon Jan 18, 2010 1:33 am

so what is OA?

I would say that both are sufficient together and neather is sufficient alone...

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ct799: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sun Nov 22, 2009 8:38 am

by ct799 » Mon Jan 25, 2010 4:05 am

Does anybody have an answer-explanation why is C? I thought the maximum area on this case could be achieved by having the diagonal as a diagonal of a square?

any hints around???

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Jan 25, 2010 4:39 am

mmslf75 wrote:Is the surface area of a rectangular pool larger than 1000 square feet?
(1) The pool measures fifty feet diagonally.
(2) One side of the pool measures twenty five feet.

OA is C

why not A ?

Say the sides of the rectangle are a and b

the area of the pool = a*b

1) sqrt(a^2+b^2) = 50
2) a = 25

1 is not sufficient, nor is 2

but combining 1&2 ,we can find out b and a*b hence C

Always borrow money from a pessimist, he doesn't expect to be paid back.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Jan 25, 2010 4:55 am

mmslf75 wrote:Is the surface area of a rectangular pool larger than 1000 square feet?
(1) The pool measures fifty feet diagonally.

why noit A ?

the maximum area that a rectangle with diagonal measuring 50 feet is when it is square with side = 50/sqrt(2)

The area = side ^2 = 50*50/2 = 1250

It is above 1000 Sqft

had it been below 1000 we could have concluded that no pond can have area more than 1000 feet and we could have chosen A as sufficient.

[ say if the sides were sqrt(2450) and sqrt(50), the diagonal will be measuring 50 feet but the area is only sqrt(2 450) * sqrt(50) = 350 ]

Always borrow money from a pessimist, he doesn't expect to be paid back.

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ct799: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sun Nov 22, 2009 8:38 am

by ct799 » Mon Jan 25, 2010 5:24 am

ok smooth....i agree with you, thanks a lot for your help.

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