A prep school in Europe is soliciting donations from its alumni for it

Question

Data Insights (DI) Butler 2023-24       Click here for Details ]

A prep school in Europe is soliciting donations from its alumni for its scholarship fund. The total number of the school’s alumni is A, and a donation of €1 per month for one year from each alumnus will fund exactly S full tuition scholarships for the upcoming school year.

In terms of A and S, select the expression that represents how many full-tuition scholarships will be funded if half the alumni donate €1.50 per month each for one year, and select the expression that represents how many alumni must donate €1.50 per month each for one year in order to fund collectively exactly 1.5S full-tuition scholarships for the upcoming school year. Make only one selection in each column.

as.hish404 · Accepted Answer

Language of the question is tricky but its very easy if we try to solve it logically.

if A people €1 per month than 
total amount is 12*1*A= €12A
which is equals to S (total scholarship)
12A=S.....A=S/12

1st question (Scholarships funded) 
Now if half the alumni donate €1.50 per month each for one year
= (A/2)*1.5*12= 18A
NOW..... 18A= 18*(S/12) 
 18A= (3/4)S

2nd question (Alumni donating)
how many alumni must donate €1.50 per month each for one year in order to fund collectively exactly 1.5S full-tuition scholarships 
as we know tha 12A=1*S
so for 1.5S....
1.5S=1.5*(12A)= 18A
So for 1.5S Scholarships it require 18A amount of donation
which will be collected if every alimini (A) donates = 18A/12A= 1.5 per month 
So the ans is A

Gemmie · Answer

Amount per each Scholarship:  \frac{A*1}{S} = \frac{A}{S}

How many full-tuition scholarships will be funded if half the alumni donate €1.50 per month each for one year

Total donated:  \frac{3}{2} * \frac{1}{2} * A = \frac{3A}{4} 
=> Number of scholarships:  \frac{3A}{4} \div \frac{A}{S}= \frac{3A}{4} * \frac{S}{A} = \frac{3}{4} * S

How many alumni must donate €1.50 per month each for one year in order to fund collectively exactly 1.5S full-tuition scholarships

Total amount to be donated:  (\frac{3}{2} * S) * \frac{A}{S} = \frac{3}{2} * A 
Total number of alumni to donate €1.50 per month:  \frac{3A}{2} \div \frac{3}{2} = A

sanjitscorps18 · Answer

Sajjad1994

This is trickily worded. The phrase "In terms of A and S, select the expression that represents how many full-tuition scholarships will be funded if half the alumni donate €1.50 per month each for one year"

appears to say that half of the Alumni decided to do €1.5 instead of €1 while the other half continues to do €1.

It would be clear if this is changed to

"In terms of A and S, select the expression that represents how many full-tuition scholarships will be funded if  ONLY  half the alumni donate €1.50 per month each for one year"

The other thing that somewhat helps and avoids the confusion are the answer choices. the solution with the ambiguous wordings don't feature in the answer choices.

cheshire · Answer

I agree that adding "only half" would make the problem clearer.

Vivek1707 · Answer

Using unitary method  this can be done more intuitively with fewer calculations.

A alumini are there, each person is paying 1 euro for one month ---> 12 months. You ll collect  12A euros.  Since total funding would be for S scholarships. i.e  12A = S  ..... i

Now when half of the guys are paying 1.5 that means the total collection become  9A  i.e 0.5 * A * 1.5*12

So since the  12A  ---->  9A  there is a  25% decrease . The number of scolarships will also  decrease by 25%  i.e  (3/4)S

2nd part:

Now if S becomes  1.5S  and the collection becomes  1.5 * 12  i.e  18
 
So total number of people required would be (1.5*S)/18 ---> To find this in terms of A ---> replace S by 12A
You ll get (1.5 * 12A) /18 i.e A

*** The  more logical  way to see this part 2 would be that since S ---> increases by 50% i.e becomes 1.5S
 12A  ----> should increase by  50%  i.e should become  18A  but since each person contributes  1.5  instead the number of people would be (18A)/18 i.e  A number of people would be there

Scholarships funded	Alumni donating
		3S/4A
		4A/3S
		(3/4)(S)
		A
		3A/S
		(3/4)(A)

A prep school in Europe is soliciting donations from its alumni for it

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A prep school in Europe is soliciting donations from its alumni for it

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