party

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party

by grandh01 » Thu Jul 12, 2012 11:14 pm
Each person attending a fund-raising party for a certain club was charged the same admission fee. How many people attended the party?

1) If the admission fee had been $0.75 cents less and 100 more people had attended, the club would have received the same amount in admission fees.

2) If the admission fee had been $1.50 more and 100 fewer people had attended, the club would have received the same amount in admission fees.

Having trouble in understanding the question, thanks in advance.
Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Jul 12, 2012 11:44 pm
grandh01 wrote:Each person attending a fund-raising party for a certain club was charged the same admission fee. How many people attended the party?

1) If the admission fee had been $0.75 cents less and 100 more people had attended, the club would have received the same amount in admission fees.
2) If the admission fee had been $1.50 more and 100 fewer people had attended, the club would have received the same amount in admission fees.
The red part should be either $0.75 or 75 cents.

Say, the admission fee was $F and N people attended the party.
Hence, total amount of admission fee received = $FN

Statement 1: (F + 0.75)(N + 100) = FN ---> (0.75N + 100F + 75) = 0
We can't solve for N without any extra information.

Not sufficient

Statement 2: (F + 1.50)(N - 100) = FN ---> (1.5N - 100F - 150) = 0
We can't solve for N without any extra information.

Not sufficient

1 & 2 Together: Now we have two different equations in two unknowns. Hence, we can solve for both N and F.

Sufficient

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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