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05 Dec 2023, 11:40
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Scholarships funded: (3/4)(S)
Alumni donating: A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
63% (03:24) correct
37%
(03:40)
wrong
based on 949
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Data Insights (DI) Butler 2023-24 [Question #142, Date: Dec-05-2023] [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.
| Scholarships funded | Alumni donating | |
| 3S/4A | ||
| 4A/3S | ||
| (3/4)(S) | ||
| A | ||
| 3A/S | ||
| (3/4)(A) |
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Official Answer
Scholarships funded: (3/4)(S)
Alumni donating: A
18 Dec 2023, 07:40
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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
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
General Discussion
17 Apr 2024, 02:49
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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: \(\frac{3A}{2} \div \frac{3}{2} = A\)
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: \(\frac{3A}{2} \div \frac{3}{2} = A\)
