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

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SVP
Joined: 21 Jul 2006
Posts: 1550
Followers: 7

Kudos [?]: 178 [0], given: 1

Each person attending a fund-raising party for a certain [#permalink]  11 Dec 2007, 14:48
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Difficulty:

5% (low)

Question Stats:

100% (01:02) correct 0% (00:00) wrong based on 5 sessions
Each person attending a fund-raising party for a certain club was charged the same admission fee. How many people attended the party?

Director
Joined: 12 Jul 2007
Posts: 868
Followers: 12

Kudos [?]: 192 [0], given: 0

wow...this one is deceptively tricky for me. I'm not sure anymore
Intern
Joined: 13 Jun 2007
Posts: 48
Followers: 1

Kudos [?]: 3 [0], given: 0

P- original number of people

1) AP=(A-0.75)(P+100)
AP=AP+100A-0.75P -75
0=100A-0.75P-75
1 equation, 2 unknowns

2) AP=(A+1.5)(P-100)
AP=AP-100A+1.5P-150
0=-100A+1.5P-150
1 equation, 2 unknowns

1) + 2) 0=0+0.75P-225=> P=225*4/3=300
SVP
Joined: 21 Jul 2006
Posts: 1550
Followers: 7

Kudos [?]: 178 [0], given: 1

the OA is C. Anyone else wanna try this?
CIO
Joined: 09 Mar 2003
Posts: 466
Followers: 1

Kudos [?]: 23 [0], given: 0

alexperi wrote:
P- original number of people

1) AP=(A-0.75)(P+100)
AP=AP+100A-0.75P -75
0=100A-0.75P-75
1 equation, 2 unknowns

2) AP=(A+1.5)(P-100)
AP=AP-100A+1.5P-150
0=-100A+1.5P-150
1 equation, 2 unknowns

1) + 2) 0=0+0.75P-225=> P=225*4/3=300

I completely agree with this, but it's a little too much. The moment you have the first equation, you should know you can't solve, and the same with the second one. Together, you've got two equations and two variables, so you should be able to solve.

The only risk here is that sometimes, with two equations, you can't solve. But if you learn the times when you can't, you can do a quick check for them and move on. They are:

1) When the equations are the same but look different
Example:
y = 3x + 6
6x = 2y - 12
These are actually the same equation.

2) When there are powers in one or both equation
Example:
y^2 + x = 9
x + 2y = 6

3) When one of the variables actually disappears, and you should have picked A or B
Example:
3x + 2y = 18
x + y = 4x + y + 12 <-- the y's cancel here so there's actually only 1 variable.

So look at the two equations and make sure quickly that you're not in any of those three situations (a very fast test when you get used to looking for them) and then the answer is C right away.
Director
Joined: 03 May 2007
Posts: 899
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 39 [0], given: 6

Re: DS: another good one [#permalink]  14 Dec 2007, 11:27
tarek99 wrote:
Each person attending a fund-raising party for a certain club was charged the same admission fee. How many people attended the party?

C.
1: xy = (x-0.75) (y+100)
100x -0.75y = 75
100x = 0.75y + 75

2: xy = (x+1.50) (y-100)
xy = xy - 100x + 1.50y - 150
1.50y - 100x = 150
1.50y - 150 = 100x

togather, solve for 1 and 2:

0.75y + 75 = 1.50y - 150
0.75y = 225
y = 300
x = 2.25
Re: DS: another good one   [#permalink] 14 Dec 2007, 11:27
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