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If every donor to a charity drive contributed at least $14 and $237 wa

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If every donor to a charity drive contributed at least $14 and $237 wa [#permalink]

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New post 09 Jun 2018, 00:10
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If every donor to a charity drive contributed at least $14 and $237 was collected, what is the maximum number of donors?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17

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Re: If every donor to a charity drive contributed at least $14 and $237 wa [#permalink]

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New post 09 Jun 2018, 01:27
Bunuel wrote:
If every donor to a charity drive contributed at least $14 and $237 was collected, what is the maximum number of donors?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17


Minimum Donation per person = 14

Total Donation = 237

Maximum Number of donors will be obtained when minimum donation is received from each donor

237/14 = 16.9

i.e. 15 people will donate $14 and 16th person will donate $27

So minimum Number of donors = 16

Abswer: option D
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If every donor to a charity drive contributed at least $14 and $237 wa [#permalink]

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New post 10 Jun 2018, 13:47
Bunuel wrote:
If every donor to a charity drive contributed at least $14 and $237 was collected, what is the maximum number of donors?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17

Answer choices
To get a baseline, start with (C) 15
Each person donates at least $14

Total if 15 persons give the minimum of $14?
\((15*$14)=(30*$7)=$210\)

Can a 16th person give $14?
\($210 + $14 = $224\)
\($224 < $237\)
Yes. 16 persons can give $14 each without exceeding $237

15 persons is not the maximum.

Eliminate C (and A and B whose number of donors is fewer than C)

Is 16 the maximum number of donors?

Answer E? Can a 17th person donate $14?
Add $14 to $224
\(($224+$14=$238)\)

No. $238 > $237 Too high

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

Maximum number of donors: 16

Answer D
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If every donor to a charity drive contributed at least $14 and $237 wa [#permalink]

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New post 11 Jun 2018, 02:13
Bunuel wrote:
If every donor to a charity drive contributed at least $14 and $237 was collected, what is the maximum number of donors?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17


Since we need the maximum number of donors, lets start with Option E(17)

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 dollars must be 16(Option D) - 15*$14 + 1*$27 = $237
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If every donor to a charity drive contributed at least $14 and $237 wa   [#permalink] 11 Jun 2018, 02:13
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If every donor to a charity drive contributed at least $14 and $237 wa

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