If Every Donor to a Charity Drive Contributed at Least $14 and $237 was Collected, what is the Maximum Number of Donors GMAT Problem Solving

Question: If every donor to a charity drive contributed at least $14 and $237 was collected, what is the maximum number of donors?

1. 13
2. 14
3. 15
4. 16
5. 17

Correct Answer: (D)

Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given: 

• If every donor to a charity drive contributed at least $14.
• $237 was collected.

Find out:

• The maximum number of donors.

To get a baseline, let us start with option (C) 15
As per the problem statement, each person donates at least $14

If a total of 15 persons give a minimum of $14
then, (15∗$14) = (30∗$7) = $210

Can a 16th person give $14?
$210 + $14 = $224
$210 + $14 = $224
Since, the amount $224< $237, the answer is Yes.
Hence, 16 persons can give $14 each without exceeding $237

We can conclude that 15 persons are not the maximum number of donors.
So we will eliminate C, A and B whose number of donors is fewer than C.

Now, we will consider if 16 is the maximum number of donors
Let us consider option E. Can a 17th person donate $14?
We will Add $14 to $224
($224+$14=$238)
The answer is No since $238 > $237

17 cannot be the number of donors.
The extra $13 ($237-$224) indicates that one or more of the 16 donated more than $14.
The maximum number of donors is 16. 

Approach Solution 2:
The problem statement informs that:
Given: 

• If every donor to a charity drive contributed at least $14.
• $237 was collected.

Find out:

• The maximum number of donors.

The minimum donation per person = 14
Total Donation = 237
A maximum number of donors will be obtained when a minimum donation is received from each donor
237/14 = 16.9
i.e. 15 people will donate $14 and 16th person will donate $27
Therefore, the minimum number of donors = 16

Approach Solution 3:
The problem statement says that:
Given: 

• If every donor to a charity drive contributed at least $14.
• $237 was collected.

Find out:

• The maximum number of donors.

Since it is required to find the maximum number of donors, let us start with Option E i.e. 17.
Hence, 17*14 = 238(In this case, one of the donors would have to pay $13 for a total of $237 to be collected)
Therefore, the maximum number of donors must be 16 i.e. Option D since 15*$14 + 1*$27 = $237

“If every donor to a charity drive contributed at least $14 and $237 was collected, what is the maximum number of donors”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This GMAT Quantitative reasoning topic measures the numerical skills and abilities of the candidates. GMAT Problem Solving questions enable the candidates to evaluate knowledge and interpret numerical problems. GMAT Quant practice papers help the candidates to analyse several questions that will enable them to enhance their mathematical understanding.

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