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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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Kudos [?]: 28 [1] , given: 0

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.

Thus, the answer is C.

--

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
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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.

Thus, the answer is C.

--

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
Posts: 2591
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Kudos [?]: 233 [0], given: 0

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.

Thus, the answer is C.

--

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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Kudos [?]: 20 [0], given: 0

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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