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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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55% (hard)

Question Stats:

67% (01:53) correct 33% (02:11) wrong based on 663 sessions

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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]

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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: 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, 10:20
3
1
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: 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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Updated on: 18 Nov 2011, 13:48
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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Originally posted by manalq8 on 18 Nov 2011, 01:43.
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
1
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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1
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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20 Nov 2011, 08:04
1
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.

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.
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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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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.
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Re: If john makes a contribution to a charity fund at school, th  [#permalink]

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11 Dec 2016, 08:00
Here is my take on this one -->
Mean 1=>50
Mean 2=>75
Sum(1)=50*5=250
Sum(2)=75*6=450.
Hence,John's contribution => 450-250=200.

Alternatively =>
John donated => 50+25*6=> 50+150=200.

Great explanation by VeritasPrepKarishma

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

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23 Jul 2018, 06:49
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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 J = the John's donation
Let a, b, c, d and e = the donations of the other 5 donors.

John makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If the average contribution for all 6 donors =$75, we can write: (a + b + c + d + e + J)/6 = $75 Multiply both sides by 6 to get: a + b + c + d + e + J =$450

John makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If we let x = the OLD (before John) average donation, then we can write 1.5x =$75
Solve for x to get x = $50 So,$50 is the OLD (before John) average donation for donors a, b, c, d and e
We can write: (a + b + c + d + e)/5 = $50 Multiply both sides by 5 to get: a + b + c + d + e =$250

We now have two equations:
a + b + c + d + e + J = $450 a + b + c + d + e =$250

Subtract the bottom equation from the top equation to get: J = $200 Answer: C RELATED VIDEO FROM OUR COURSE _________________ Test confidently with gmatprepnow.com Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2827 Re: If john makes a contribution to a charity fund at school, th [#permalink] Show Tags 25 Jul 2018, 16:35 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

We can let the old average = a and create the equation:

1.5a = 75

a = 50

Thus, the original sum was 250.

So we can create another equation, where j = the size of John’s contribution:

75 = (j + 250)/6

450 = j + 250

200 = j

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Re: If john makes a contribution to a charity fund at school, th   [#permalink] 25 Jul 2018, 16:35
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