Arithmetic Mean(3)

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tsmith93: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Fri Feb 19, 2010 12:36 pm; Location: Pennsylvania; Thanked: 1 times

Arithmetic Mean(3)

by tsmith93 » Wed Mar 03, 2010 5:58 pm

The members of the French Club conducted a fund-raising drive. The average (arithmetic mean) amount of money raised per member was $85. Then Jean joined the club and raised $50. This lovered the average to $80. How many members were there before Jean joined?

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Source: Beat The GMAT — Problem Solving | Wed Mar 03, 2010 5:58 pm

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pm; Thanked: 653 times; Followed by:252 members

by papgust » Wed Mar 03, 2010 6:07 pm

Let X be the Sum of the money raised by members of french club and N be the number of members.

X / N = 85

X = 85N

X - 85N = 0 ... (1)

When Jean joined, average lowered to 80. He raised 50$,

X + 50 = 80 * (N+1)

X + 50 = 80N + 80

X - 80N = 30 ... (2)

Solving (1) and (2),

5N = 30

[spoiler]N = 6[/spoiler]

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GMATSUCKER: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sat Feb 27, 2010 2:58 am; Location: GMAT

by GMATSUCKER » Tue Mar 16, 2010 1:55 am

IMO6. What's the OA ?

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STEVEN SPIELBERG: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Sat Mar 13, 2010 4:11 am; Thanked: 1 times

by STEVEN SPIELBERG » Tue Mar 16, 2010 1:57 am

What's the OA ?

I want to win an OSCAR on the GMAT !!!

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Tue Mar 16, 2010 3:47 am

tsmith93 wrote:The members of the French Club conducted a fund-raising drive. The average (arithmetic mean) amount of money raised per member was $85. Then Jean joined the club and raised $50. This lovered the average to $80. How many members were there before Jean joined?

Before :

The group had 85 as the avg. You can view it as n 85s i.e. 85,85,85,........n terms

After Jean joined:

the avg became 80 i.e. 80,80,80...........(n+1)terms

Even Jean is considered to have raised 80 i.e additional $30. Where did this extra amount come from.

From rest of the members. In other words, rest of the members contributed $5 each to make that extra $30.

So, how many times 5 is 30 ?

Regards,
Harsha

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Tue Mar 16, 2010 3:59 am

tsmith93 wrote:The members of the French Club conducted a fund-raising drive. The average (arithmetic mean) amount of money raised per member was $85. Then Jean joined the club and raised $50. This lovered the average to $80. How many members were there before Jean joined?

There were x members before Jean joined, and those x must have raised $85 x already, Jean, the (x + 1)th member, raised $50 to make us write the following equation in x:

(85 x + 50) / (x + 1) = 80; solve and have

[spoiler]x = 6[/spoiler]

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