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If john makes a contribution to a charity fund at school

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by BTGmoderatorDC » Sun Jul 22, 2018 7:10 pm

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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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by GMATGuruNY » Mon Jul 23, 2018 3:17 am
BTGmoderatorDC 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
Since $75 is 50% more than $50, the first 5 contributions were worth an average of $50.
Thus, the sum of the first 5 contributions = 5*50 = 250.
Since the average of all 6 contributions = $75, the sum of all 6 contributions = 6*75 = 450.
Thus, John's contribution = (sum of all 6 contributions) - (sum of the first 5 contributions) = 450-250 = 200.

The correct answer is C.
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by Brent@GMATPrepNow » Mon Jul 23, 2018 6:42 am
BTGmoderatorDC 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
Mitch's approach is the most straightforward. However, here's an algebraic version:
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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by Jeff@TargetTestPrep » Wed Jul 25, 2018 4:28 pm
BTGmoderatorDC 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

Answer: C

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