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

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.

\(1.5a=75\) --> \(a=50\)

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

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

Answer: C.
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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

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.

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.

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

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.

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

Answer (C)
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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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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.

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.

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


Regards
Stone Cold
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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

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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

Answer: C
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hi,
i tried this for every mean Q: gap between added value-mean 1 divided by number people/days)= change in mean, hence:
mean was 50.
Anna added X value.
mean changed by + 25, so:
x-50/6 people=25
x-50=150
x=200

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