A college has raised 75% of the amount it needs for a new building by

Question

A college has raised 75% of the amount it needs for a new building by receiving an average donation of $60 from the people already solicited. The people already solicited represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, how much must the remaining people donate per person?

A) $25
B) $30
C) $40
D) $50
E) $60

A) $25 
B) $30 
C) $40 
D) $50 
E) $60

giobas · Accepted Answer

lets assume there are 100 people. so 60 people donated 60 each, that 60x60=3600
3600 is 75% of needed.

so remaining 25% needed = 3600*0.25/0.75 = 1200

1200$ is for 40 people, so 30$ each

answer is b

saswata4s · Answer

Suppose, there are x people.

So, total donated = .6x;
remaining people = .4x;

Total donation = .6x*60 = $36x = 75% of required donation;
Therefore, remaining 25% of denation = {(36x)/(3/4)} *(1/4) = $12x;

then required donation per person = 12x/.4x = $30;
Hence, answer B.

Najmul · Answer

You need to convert the 75% of required donation to 100% of the donation. 
Then. calculate the remaining 25% of the donation.

and, 36/4 doesn't result in 12. 
It would be like as follows :- 
 75% of required donation = 36x
 so, required donation = 36x/.75 = 48x.
Thus, remaining 25% of donation = 48x *(1/4) = $12x;

saswata4s · Answer

Thanks for pointing out. Corrected now.

KanishkM · Answer

Lets plug in a number => Total students = 10

60% solicited = 6

75% of x = 360(6*60,average donation/person)
Total money(x) = 480

25% of x = 120

remaining students = 4

Average = 120/4 = 30

B

CrackverbalGMAT · Answer

Since we have percentage values,  let’s assume the total number of people as 100x . Therefore,

People already solicited = 60x  and  people not solicited = 40x .

Now, we know that the  60x persons have donated $60 on an average per person . Therefore,  their total contribution = 60x * 60 = 3600x . From the first sentence of the question, we know that  this 3600x represents 75% of the amount that the college needs . So,

3600x = ¾ * (Amount needed by the college).
Amount needed by the college =  \frac{4}{3}  *3600x = 4800x.

So another 1200x needs to be collected from the remaining 40x persons. This would amount to  (\frac{1200x}{40x} ) i.e. $30 per person on an average. 
 The correct answer option is B .

When you deal with problems like these, remember to take the unknown as 100 since you are dealing with percentages; even better would be if you take it as a multiple of 100 (say 100x as I have done). The 100 will deal with percentage value and the x will take care of any uncertainties that may crop up in some situations. It also makes problem solving easier and faster compared to just assuming x as the unknown.

Hope that helps!

ScottTargetTestPrep · Answer

Let n = the total number of people solicited and d = the amount of donation per person of the remaining 40% of the people solicited. We can create the following proportion, in which we state: the number of dollars already donated is to 75% of the total money needed AS the remaining number of dollars needed is to 25% of the total money needed:

60(0.6n) / 0.75 = d(0.4n) / 0.25

36n/0.75 = 0.4dn/0.25

9n = 0.3dn

30 = d

Answer: B

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A college has raised 75% of the amount it needs for a new building by

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