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# Each person attending a fund-raising party for a certain

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Manager
Joined: 21 Mar 2007
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Each person attending a fund-raising party for a certain [#permalink]  07 Mar 2008, 03:15
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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 $.75 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.
Manager
Joined: 31 Oct 2007
Posts: 113
Location: Frankfurt, Germany
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Re: GMAT Prep DS [#permalink]  07 Mar 2008, 03:33
1
KUDOS
In this question, we are looking for the no. of people.

Statements 1 and 2 alone are not sufficient because by itself, each statement has 3 variables for you to solve. 1st variable, the admission fee, 2nd variable the no of people attended and 3rd the total amount. Neither statement alone allows you to solve.

--

If this question is a PS question, the working as follows:
Let x be the admission fee per person
Let y be the no of person
Let z be the total admission fees

Statement 1:
(x - 0.75) * (y + 100) = z

Statment 2:
(x + 1.50) * (y - 100) = z

Thus, statement 1 = statment 2

(x - 0.75) * (y + 100) = (x + 1.50) * (y - 100)
=> xy + 100x - 0.75y -75 = xy - 100x + 1.50y - 150
=> - 0.75y - 75 = 1.50y - 150
=> 2.25y = 75
=> y = 75/2.25
=> ~33ppl
_________________

Jimmy Low, Frankfurt, Germany
Blog: http://mytrainmaster.wordpress.com
GMAT Malaysia: http://gmatmalaysia.blogspot.com

Last edited by jimmylow on 07 Mar 2008, 21:16, edited 1 time in total.
Manager
Joined: 21 Mar 2007
Posts: 75
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Kudos [?]: 24 [0], given: 0

Re: GMAT Prep DS [#permalink]  12 Mar 2008, 03:59
jimmylow wrote:
In this question, we are looking for the no. of people.

Statements 1 and 2 alone are not sufficient because by itself, each statement has 3 variables for you to solve. 1st variable, the admission fee, 2nd variable the no of people attended and 3rd the total amount. Neither statement alone allows you to solve.

--

If this question is a PS question, the working as follows:
Let x be the admission fee per person
Let y be the no of person
Let z be the total admission fees

Statement 1:
(x - 0.75) * (y + 100) = z

Statment 2:
(x + 1.50) * (y - 100) = z

Thus, statement 1 = statment 2

(x - 0.75) * (y + 100) = (x + 1.50) * (y - 100)
=> xy + 100x - 0.75y -75 = xy - 100x + 1.50y - 150
=> - 0.75y - 75 = 1.50y - 150
=> 2.25y = 75
=> y = 75/2.25
=> ~33ppl

What happens to the 200x that appears when the -100x from the right is added on to the 100x on the left?
CEO
Joined: 29 Mar 2007
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Re: GMAT Prep DS [#permalink]  12 Mar 2008, 04:16
japped187 wrote:
jimmylow wrote:
In this question, we are looking for the no. of people.

Statements 1 and 2 alone are not sufficient because by itself, each statement has 3 variables for you to solve. 1st variable, the admission fee, 2nd variable the no of people attended and 3rd the total amount. Neither statement alone allows you to solve.

--

If this question is a PS question, the working as follows:
Let x be the admission fee per person
Let y be the no of person
Let z be the total admission fees

Statement 1:
(x - 0.75) * (y + 100) = z

Statment 2:
(x + 1.50) * (y - 100) = z

Thus, statement 1 = statment 2

(x - 0.75) * (y + 100) = (x + 1.50) * (y - 100)
=> xy + 100x - 0.75y -75 = xy - 100x + 1.50y - 150
=> - 0.75y - 75 = 1.50y - 150
=> 2.25y = 75
=> y = 75/2.25
=> ~33ppl

What happens to the 200x that appears when the -100x from the right is added on to the 100x on the left?

Yes what happened to that 200x...

I get E for this problem b/c we are left with 200x+75=2.25y
Manager
Joined: 11 Apr 2007
Posts: 143
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Re: GMAT Prep DS [#permalink]  12 Mar 2008, 06:19
That's not how I did it.
Since in the question we have that x*y=z
(1) (x-0.75)*(y+100)=z => (x-0.75)*(y+100)=xy from here we remain with 100x-0.75y=75 not suff
(2) (x+1.50)*(y-100)=z => (x+1.50)*(y-100)=xy from here we remain with -100x+1.50y=150 not suff

(1)(2) we have 100x-0.75y=75
-100x+1.50y=150
If we add these 2 equations we have 0.75y=225, y =300
100x-225=75, x=3
So sufficient C
Re: GMAT Prep DS   [#permalink] 12 Mar 2008, 06:19
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