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# If john makes a contribution to a charity fund at school, th

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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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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
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Re: 700-800 level problem Statistics [#permalink]  22 Jan 2010, 10:20
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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.
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Re: 700-800 level problem Statistics [#permalink]  22 Jan 2010, 10:33
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yes 200 is the ans.

final avg = 75 = 1.5 of old

i.e old avg = 50 = total of five/5

total of five = 250

new avg = 75 = total of six/6

total of 6 = 450

so John's contribution = 450-250 =200
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Re: 700-800 level problem Statistics [#permalink]  22 Jan 2010, 10:35
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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

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.

$$1.5a=75$$ --> $$a=50$$

$$a=50=\frac{c}{5}$$ --> $$c=250$$

$$\frac{c+x}{6}=75$$ --> $$\frac{250+x}{6}=75$$ --> $$x=200$$

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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.

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Re: Contribution to a charity Fund [#permalink]  18 Nov 2011, 01:43
ok here is how I approached this question:

I, first, got the original average before the increase and without john's:

1.5x=75
x=50

then, I got the sum of the contributions of the 5 dominees without John:

5x/5=50
hence, 5x=250

after that, i set up the average equation with john's contribution:

250+x/6=75

250+x=75(6)

250+x=450
hence, x, which is John's amouts= 200
so the answer I got is C, hope this helps
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Last edited by manalq8 on 18 Nov 2011, 13:48, edited 1 time in total.
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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.
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Re: Contribution to a charity Fund [#permalink]  20 Nov 2011, 00:07
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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

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Joined: 28 Jul 2011 Posts: 563 Location: United States Concentration: International Business, General Management GPA: 3.86 WE: Accounting (Commercial Banking) Followers: 2 Kudos [?]: 132 [0], given: 16 Re: Contribution to a charity Fund [#permalink] 20 Nov 2011, 00:12 Thanks VeritasPrepKarishma _________________ +1 Kudos If found helpful.. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6238 Location: Pune, India Followers: 1683 Kudos [?]: 9665 [1] , given: 198 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Contribution to a charity Fund [#permalink]  21 Nov 2011, 06:02
I do not understand at all, but thanks for your time. I think I'll spend a little extra time in the ol' GMAT book today.
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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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Re: If john makes a contribution to a charity fund at school, th   [#permalink] 06 Sep 2015, 07:23
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