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

Question

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?

A. $100
B. $150
C. $200
D. $250
E. $450

Bunuel · Accepted Answer

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.

gurpreetsingh · Answer

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

andrewcs · Answer

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.

Stoneface · 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.

Answer B.

manalq8 · Answer

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

Stoneface · Answer

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

J = {6($75)}/3, or J =  *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.

KarishmaB · 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

Answer (C)

KarishmaB · Answer

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.

Stoneface · Answer

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.

deepak268 · Answer

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.

stonecold · Answer

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 :-D

Regards
Stone Cold

Regards Stone Cold

BrentGMATPrepNow · Answer

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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JeffTargetTestPrep · Answer

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

dimri10 · Answer

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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