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If john makes a contribution to a charity fund at school, th [#permalink]
22 Jan 2010, 10:16

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Difficulty:

45% (medium)

Question Stats:

62% (02:10) correct
38% (01:29) wrong based on 275 sessions

If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 5 other contributions made before john's, what is the size of his donation?

Re: 700-800 level problem Statistics [#permalink]
22 Jan 2010, 10:20

3

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Cavg = average contribution before John

Cavg*1.5 = 75, therefore the average cont is $50 before John.

If he needs to increase the average contribution by $25, he must put in $25 for each of the 5 people. so $125. But, he also has to put in the average for himself (the sixth person), so add $75.

So $200 is your answer. _________________

________________________________________________________________________ Andrew http://www.RenoRaters.com

Re: 700-800 level problem Statistics [#permalink]
22 Jan 2010, 10:35

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Expert's post

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GMAT10 wrote:

If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person.If there were 5 other contributions made before john's,what is the size of his donation? a)$100 b)$150 c)$200 d)$250 e)$450

Please solve?

Let \(a\) be the average contribution size before John makes his contribution. Let \(c\) be the total contribution size before John makes his contribution. Let \(x\) be John's contribution.

Re: Contribution to a charity Fund [#permalink]
17 Nov 2011, 16:25

If, after John's donation, the average was $75 per person then the total is $75(6) which comes to a total of 450 contributed dollars by all donees. If John's donation increases the total contributions by 50% then it is now 150% of what it was and John's contribution was 1/3 of that, which would be 1/3 of the $450. John contributed $150.

Re: Contribution to a charity Fund [#permalink]
18 Nov 2011, 07:52

Thought I'd write my reasoning out in a more quantitative form.

J = {6($75)}/3, or J = [{1($75) +5($75)}/150]*50. The key, I think, is to realize that John's contribution was 1/3 of all the current contributions. Since we know the total contribution is 6($75)=$450, then we know his contribution was 1/3 of that. 1/3*450=$150.

Re: Contribution to a charity Fund [#permalink]
20 Nov 2011, 00:07

1

This post received KUDOS

Expert's post

enigma123 wrote:

If John makes a contribution to a charity fund at school, the average contribution size will increase by 50%, reaching $75 per person. If there were 5 other contributions made before John’s, what is the size of his donation? (A) $100 (B) $150 (C) $200 (D) $250 (E) $450

OA is not provided, but I have got C. Do you guys think C is the right answer?

Responding to a pm:

After John's contribution, the average size increases by 50% and reaches $75. What must have been the average size of contribution before John's donation? It must have been $50 since a 50% increase would lead us to $75. $50 was the average size for 5 donations. Total amount donated = $250 $75 is the average size for 6 donations. Total amount donated = $450 John's contribution must have been 450 - 250 = $200

Re: Contribution to a charity Fund [#permalink]
20 Nov 2011, 08:04

1

This post received KUDOS

Expert's post

Stoneface wrote:

If, after John's donation, the average was $75 per person then the total is $75(6) which comes to a total of 450 contributed dollars by all donees. If John's donation increases the total contributions by 50% then it is now 150% of what it was and John's contribution was 1/3 of that, which would be 1/3 of the $450. John contributed $150.

Answer B.

Responding to a pm:

We cannot say that John's contribution is a third. To increase the average by 50%, you need to invest more than a third of the total. The reason is that previous average is for 5 people. New average has another person so the total contribution needs to be higher.

The total contribution now = 75*6 = 450 Out of this, if 150 were contributed by John, the previous total contribution must have been 300. With 5 people, that would mean an average of 60. We need 6 people to make the average 50 but before John made the contribution, there were only 5 people. That's where you made a mistake. Since a person increases, the contribution needs to be even higher than a third. _________________

Re: If john makes a contribution to a charity fund at school, th [#permalink]
23 Sep 2013, 23:30

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Re: If john makes a contribution to a charity fund at school, th [#permalink]
06 Sep 2015, 07:23

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