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Each person attending a fund-raising party for a certain clu [#permalink]
23 Sep 2010, 11:15

00:00

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Difficulty:

25% (medium)

Question Stats:

78% (01:55) correct
22% (00:49) wrong based on 46 sessions

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

Re: Club Admission Fee [#permalink]
24 Sep 2010, 11:13

let assume x=admin fee,y=no.of. people x*y=100. 1) (x-.75)* (y+100)= 100 (statement 1 mentioned same amount,so i assume the amount as 100) from question stem x*y=100 so x=100/y, sufficient to know x value.

2) (x+1.50) * (y-100) =100 x*y =100 x=100/y,sufficient to know x value.

Bunnel, plz explain why should we solve the problem like this.

Each person attending a party was charged the same admission [#permalink]
09 Nov 2012, 06:28

Each person attending a party was charged the same admission fee. How many people attended the party?

(1) If the fee had been 0.75$ less and 100 more people had attended, the club would have made the same amount of money. (2) If the fee had been 1.50$ more and 100 fewer people had attended, the club would have made the same amount of money.

I have a specific question regarding this problem :

Obviously Statement 1 and 2 are insufficient alone, however once we find out equation 1: xy = (x-3/4)(y+100) from statement 1 and xy = (x+3/2)(y-100) from statement 2, why can't we simply equate them? (x-3/4)(y+100) = (x+3/2)(y-100)

I'd appreciate any help! Thanks

Last edited by Bunuel on 09 Nov 2012, 06:32, edited 1 time in total.

Re: Each person attending a party was charged the same admission [#permalink]
09 Nov 2012, 06:43

Expert's post

mockney wrote:

Each person attending a party was charged the same admission fee. How many people attended the party?

(1) If the fee had been 0.75$ less and 100 more people had attended, the club would have made the same amount of money. (2) If the fee had been 1.50$ more and 100 fewer people had attended, the club would have made the same amount of money.

I have a specific question regarding this problem :

Obviously Statement 1 and 2 are insufficient alone, however once we find out equation 1: xy = (x-3/4)(y+100) from statement 1 and xy = (x+3/2)(y-100) from statement 2, why can't we simply equate them? (x-3/4)(y+100) = (x+3/2)(y-100)

I'd appreciate any help! Thanks

Well, actually you can: (x-3/4)(y+100) = (x+3/2)(y-100) --> 9y=800x+300.

From xy = (x-3/4)(y+100) we'll have that 3y=400x-300, so 9y=1200x-900. Equating again: 800x+300=1200x-900 --> x=3 --> y=300.

Though you can directly simplify xy = (x-3/4)(y+100) to get 3y=400x-300 and xy = (x+3/2)(y-100) to get 3y=200x+300 --> 400x-300=200x+300 --> x=3 --> y=300.

Re: Each person attending a party was charged the same admission [#permalink]
09 Nov 2012, 06:54

Thank you Bunuel for your help! I was just expecting to find a value for either x or y directly without needing to isolate for y from one of the 2 equations!

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

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

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

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 official answer is C, but the solution is very complicated. So, please, can somebody over there help me to handle this problem?

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

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

Merging similar topics. Please refer to the solutions above. _________________

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

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

Merging similar topics. Please refer to the solutions above.

Thanks. I found out why the problem was so confusing. There is a big difference between %0.75 and $0.75. I thought that 0.75 was a percentage increase which was wrong.