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Each person attending a fund raising party for a certain

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Each person attending a fund raising party for a certain [#permalink]

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New post 10 Jul 2010, 01:25
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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 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/each-person-a ... 01572.html
[Reveal] Spoiler: OA

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Re: Each person attending a fund raising party for a certain [#permalink]

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New post 10 Jul 2010, 01:34
Let's say there were N people and they each paid X$. We need to find N.

1. Let's translate the words into algebra:

Original amount received = N*X

New amount received = (N + 100) * (X - 0.75)

We are told these two are equal quantities. Equate them

N*X = (N+100)*(X-0.75)

A glance at this should suffice to say that thought the NX term would cancel out, we cannot find N independent of the value of X.

INSUFFICIENT

2. Similar situation which works out to:

N*X = (N - 100)*(X - 1.5)

INSUFFICIENT (cannot isolate N)

Both 1 and 2

We have two independent simultaneous equations in two variables. Sufficient to find each of N and X

SUFFICIENT

Pick C.

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New post 10 Jul 2010, 12:39
C straight forward, two variables can;t be solved from one equation...
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Re: Each person attending a fund raising party for a certain [#permalink]

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New post 11 Aug 2017, 03:23
Each person attending a fund raising party for a certain club was charged the same admission fee. How many people attended the party?

Let the original admission fee be \(x\) and the original # of people be \(n\). Question: \(n=?\)

(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 the admission fee

\(xn=(x-0.75)(n+100)\) --> \(100x-0.75n=75\). Two unknowns, one equation, not sufficient to calculate \(n\).

(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 the admission fee

\(xn=(x-1.5)(n-100)\) --> \(100x-1.5n=-150\). Two unknowns, one equation, not sufficient to calculate \(n\).

(1)+(2) \(100x-0.75n=75\) and \(100x-1.5n=-150\) --> we have two distinct linear equation with two unknowns, hence we can solve for \(n\). Sufficient.

Answer: C.

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Re: Each person attending a fund raising party for a certain   [#permalink] 11 Aug 2017, 03:23
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