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Word Problem

by beater » Mon Dec 01, 2008 9:18 am
Every member of a certain club volunteers to contribute equally to the purchase of $60 gift certificate. How many members does the club have?

1. Each members contribution is to be $4
2. If 5 club members fail to contribute, the share of each contributing member will increase by $2
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Source: — Data Sufficiency |
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by agoyal2 » Mon Dec 01, 2008 10:47 am
IMO D.

From I - Total members = 60/4 = 15 SUFFICIENT

From II -
Total Members = x
60x = (x-5)((60/x)+2)
Solving for x
x=-10, 15
Since number of members cannot be -ve, x=15

SUFFICIENT
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by beater » Mon Dec 01, 2008 6:37 pm
OA - D.

Could you please explain your workings for Stat2. Thanks!
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by agoyal2 » Tue Dec 02, 2008 1:18 am
Working for stat 2:

Take the total contributing members = x
Since they are contributing EQUALLY for the 60$ gift, individual contribution is = 60/x.

Now, from (2) -> 5 members do not contribute:
So, contributing members = x-5

Also from (2)-> the share of each contributing member will increase by $2
So, individual share = (60/x) + 2$

Now, the total has to be 60$ so,
(x-5)((60/x)+2) = 60
=> (x-5)((60+2x)/x)=60
=> 60x + 2x^2 - 300 - 10x = 60x
=> 2x^2 - 10x - 300 = 0
=> x^2 - 5x - 150=0
=> x^2 + 10x - 15x - 150 = 0
=> x(x+10)-15(x+10)=0
=> (x+10)(x-15)=0
=> x =15
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