Word Problems!

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Ahmed MS: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Wed Apr 06, 2011 8:35 pmFollowed by: 1 member

by Ahmed MS » Sun Jun 12, 2011 11:28 pm

If everyone was charged the same fee, how many people came?

a. If the fee had been %0.75 less and 100 more people came the club would have received the same amount.
b. If fee had been $1.50 more and 100 fewer people came, the club would have received the same amount.

The answer is C, but according to me it should be E. Please help me out!

Cheers!

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Source: Beat The GMAT — Data Sufficiency | Sun Jun 12, 2011 11:28 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jun 13, 2011 12:35 am

Ahmed MS wrote:If everyone was charged the same fee, how many people came?

a. If the fee had been %0.75 less and 100 more people came the club would have received the same amount.
b. If fee had been $1.50 more and 100 fewer people came, the club would have received the same amount.

I think the % in statement 1 should be $.

Say, the fee was $P and n people came.

Statement 1: (n + 100)(P - 0.75) = nP
Hence, 100P - 0.75n - 75 = 0
We cannot find n as we have one equation but two unknown.

Not sufficient

Statement 1: (n - 100)(P + 1.5) = nP
Hence, 100P - 1.5n + 150 = 0
We cannot find n as we have one equation but two unknown.

Not sufficient

S1 & 2 Together: We can uniquely determine n as we have two equations in two unknown.

Sufficient

The correct answer is C.

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Ahmed MS: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Wed Apr 06, 2011 8:35 pmFollowed by: 1 member

by Ahmed MS » Mon Jun 13, 2011 9:37 am

Thanks Anurag! I am sorry about the error as I said I download from the web.

Cheers!

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