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# Each person attending a fund raising party for a certain

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Manager
Joined: 22 Mar 2010
Posts: 56
Each person attending a fund raising party for a certain [#permalink]

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10 Jul 2010, 01:25
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Difficulty:

(N/A)

Question Stats:

75% (00:45) correct 25% (01:34) wrong based on 8 sessions

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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

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Manager
Joined: 04 May 2010
Posts: 86
WE 1: 2 yrs - Oilfield Service
Re: Each person attending a fund raising party for a certain [#permalink]

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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. Senior Manager Joined: 25 Feb 2010 Posts: 420 Re: Each person attending a fund raising party for a certain [#permalink] ### Show Tags 10 Jul 2010, 12:39 C straight forward, two variables can;t be solved from one equation... _________________ GGG (Gym / GMAT / Girl) -- Be Serious Its your duty to post OA afterwards; some one must be waiting for that... Math Expert Joined: 02 Sep 2009 Posts: 44416 Re: Each person attending a fund raising party for a certain [#permalink] ### Show Tags 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.

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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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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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