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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]

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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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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]

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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]

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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]

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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]

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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]

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18 Nov 2011, 07:52
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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]

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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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Re: Contribution to a charity Fund [#permalink]

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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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23 Sep 2013, 23:30
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06 Sep 2015, 07:23
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18 Sep 2016, 19:05
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Re: If john makes a contribution to a charity fund at school, th [#permalink]

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18 Oct 2016, 04:00
VeritasPrepKarishma wrote:
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

I got this wrong by attempting this problem logically (Fan of your logical approach ), please let me know what's wrong in my logic.

New avg - 75 per person
old avg- 50 per person
so 25 per person was extra added by john , that mean John had Extra $Extra John carried was = 25*(5+1) i.e. for 5 others and John Extra = 150, this is the extra amount. ..oh no! I think while writing this I got my mistake (silly one!) . I'll still continue so that people who find this interesting will adopt this and not make silly error as me So john contributed 150$ extra plus he also had the old avg amt. i.e. 50 $so total john contributed is 150+50 =$200

You must have figured what mistake I did. I picked B.150$. But that's just the extra amount John has apart from 50$.
Thanks.
Re: If john makes a contribution to a charity fund at school, th   [#permalink] 18 Oct 2016, 04:00
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