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# C individuals pledged to pay equal contributions so that a charity...

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Manager
Joined: 24 May 2016
Posts: 149
C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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28 Jul 2016, 08:41
2
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:21) correct 38% (02:21) wrong based on 73 sessions

C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal? A) dx / C B) x / (C-d) C) d / (C-dx) D) x / (C(C-d)) E) dx / (C(C-d)) Please develop in detail your answer. Thank you. SC Moderator Joined: 13 Apr 2015 Posts: 1693 Location: India Concentration: Strategy, General Management GMAT 1: 200 Q1 V1 GPA: 4 WE: Analyst (Retail) Re: C individuals pledged to pay equal contributions so that a charity... [#permalink] ### Show Tags 28 Jul 2016, 09:12 Number of individuals = C Amount paid by each individual = n Total expected amount = Charity's goal = nC = x n = x/C Number of individuals who fail to pay = d Contribution from individuals who would fail to pay = dx/C --> Additional amount Number of individuals who are paying = C - d Additional amount has to be divided among the (C - d) individuals --> dx/C(C - d) Answer: E Senior Manager Joined: 02 Mar 2012 Posts: 317 Schools: Schulich '16 Re: C individuals pledged to pay equal contributions so that a charity... [#permalink] ### Show Tags 29 Jul 2016, 02:05 c people would pay x 1)so contra would be =x/c 2)but d people refused or didn't pay , so for same x contra increased to =x/(c-d) note 2 nd point above has more contribution than 1 point above so increase in contri is 2 statement - 1 statement above x/c-d - x/c which will give you E as answer Manager Joined: 07 Jul 2016 Posts: 79 GPA: 4 Re: C individuals pledged to pay equal contributions so that a charity... [#permalink] ### Show Tags 06 Aug 2016, 01:43 1 EBITDA wrote: C individuals pledged to pay equal contributions so that a charity’s goal of$x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?

$$\frac{x}{C} \text{ - original cost}\\ \frac{x}{C-d} \text{ - new cost}\\ \text{additional cost = new cost - original cost}\\ \frac{x}{C-d} - \frac{x}{C} = \frac{x(C)}{C(C-d)} - \frac{x(C-d)}{C(C-d)} = \frac{xd}{C(C-D)}$$

E) dx / (C(C-d))

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Re: C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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29 Jan 2018, 10:56
EBITDA wrote:
C individuals pledged to pay equal contributions so that a charity’s goal of \$x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?

A) dx / C
B) x / (C-d)
C) d / (C-dx)
D) x / (C(C-d))
E) dx / (C(C-d))

Had all C individuals paid their contributions, each would have paid x/C dollars. Since d of them failed to pay theirs, each of the remaining individuals would now have to pay x/(C - d) dollars. Thus, the difference in the number of dollars contributed by each person is:

x/(C - d) - x/C

Obtaining the common denominator C(C - d), we have:

xC/[C(C - d)] - x(C - d)/[C(C - d)]

[xC - x(C - d)]/[C(C - d)]

(xC - xC + xd)/[C(C - d)]

xd/[C(C - d)]

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Re: C individuals pledged to pay equal contributions so that a charity... &nbs [#permalink] 29 Jan 2018, 10:56
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