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# Four brothers Adam, Bill, Charles and David together

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Manager
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Kudos [?]: 23 [2] , given: 8

Four brothers Adam, Bill, Charles and David together [#permalink]  01 Apr 2010, 03:37
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74% (03:24) correct 26% (03:52) wrong based on 67 sessions
Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is $9900, find the contribution made by David. A.$540
B. $580 C.$600
D. $660 E.$680
[Reveal] Spoiler: OA

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Last edited by Bunuel on 02 Dec 2012, 03:27, edited 1 time in total.
Renamed the topic and edited the question.
Senior Manager
Joined: 31 Mar 2010
Posts: 415
Location: Europe
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Kudos [?]: 34 [0], given: 26

Re: Hard Ratio question [#permalink]  01 Apr 2010, 04:02
Hmm, if you write it down you get literally:

A = \frac{1}{2}(B + C + D)

B = \frac{1}{4}(A + C + D)

C = \frac{2}{3}(A + B + D)

A + B + C + D = 9900

Therefore you have a system of 4 unknowns and 4 equations, so it's solvable (too bad it's not a DS problem we could just stop here ). Now I guess the easiest way to solve it is to use Gauss' Pivot Method? Remember you are only interested in D, so no need to calculate A, B and C, that would be a waste of time
Manager
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Re: Hard Ratio question [#permalink]  01 Apr 2010, 04:40
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Given that A:(B+C+D)= 1:2.
Hence A contributed 1/3rd of the total price.

Given B:(A+C+D)=1:4
Hence B contributed 1/5th of the total price.

Given C:(A+B+D)=2:3
Hence C contributed 2/5th of the total price.

Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15

So, the remaining 1/15th of the price is contributed by David.
Hence David's contribution= 1/15×9900=660$. Last edited by sh00nya on 01 Apr 2010, 05:04, edited 1 time in total. Senior Manager Joined: 31 Mar 2010 Posts: 415 Location: Europe Followers: 2 Kudos [?]: 34 [0], given: 26 Re: Hard Ratio question [#permalink] 01 Apr 2010, 05:43 sh00nya wrote: Given that A:(B+C+D)= 1:2. Hence A contributed 1/3rd of the total price. Hi, I don't understand where you get the 1/3 from? Manager Joined: 19 Jul 2009 Posts: 53 Location: baltimore, md Schools: kellogg, booth, stern, ann arbor Followers: 1 Kudos [?]: 17 [0], given: 3 Re: Hard Ratio question [#permalink] 06 Apr 2010, 09:47 sh00nya wrote: Given that A:(B+C+D)= 1:2. Hence A contributed 1/3rd of the total price. Given B:(A+C+D)=1:4 Hence B contributed 1/5th of the total price. Given C:(A+B+D)=2:3 Hence C contributed 2/5th of the total price. Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15 So, the remaining 1/15th of the price is contributed by David. Hence David's contribution= 1/15×9900=660$.

how did you get the contributed amounts? for example A contributed 1/3, B contributed 1/5th, etc?
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Intern
Joined: 04 Feb 2010
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Re: Hard Ratio question [#permalink]  08 Apr 2010, 13:18
azule45 wrote:
sh00nya wrote:
Given that A:(B+C+D)= 1:2.
Hence A contributed 1/3rd of the total price.

Given B:(A+C+D)=1:4
Hence B contributed 1/5th of the total price.

Given C:(A+B+D)=2:3
Hence C contributed 2/5th of the total price.

Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15

So, the remaining 1/15th of the price is contributed by David.
Hence David's contribution= 1/15×9900=660$. how did you get the contributed amounts? for example A contributed 1/3, B contributed 1/5th, etc? Add the portions of the ratio. 1:2 => 3 parts total, A is 1/3 1:4 => 5 parts total, B is 1/5 2:3 => 5 parts total, C is 2/5 Manager Joined: 29 Dec 2009 Posts: 122 Location: india Followers: 1 Kudos [?]: 13 [2] , given: 10 Re: Hard Ratio question [#permalink] 01 May 2010, 00:50 2 This post received KUDOS there is another simple way ---- a+b+c+d=t a= .5(t-a) b= .25(t-b) c=2/3(t-c) so t = 9900 so a=3300 , b= 1980 , c= 3960 so d= 660 Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 14 Kudos [?]: 187 [2] , given: 11 Re: Hard Ratio question [#permalink] 02 Dec 2012, 00:01 2 This post received KUDOS (1) A = (B + C + D)/2 (2) B = (A + C + D)/4 (3) C = 2(B + D + A)/3 (4) A + B + C + D = 9900 Combine (1) and (4) A = (9900 - A)/2 ==> A=3300 Combine (2) and (4) B = (9900 - B)/4==>B=1980 Combine (3) and (4) C = 2(9900-C)/3==>C=3960 D = 9900 - (3300 + 1980 + 3960) D = 660 Answer: 660 _________________ Impossible is nothing to God. Math Expert Joined: 02 Sep 2009 Posts: 19041 Followers: 3364 Kudos [?]: 24474 [0], given: 2680 Re: Four brothers Adam, Bill, Charles and David together [#permalink] 02 Dec 2012, 03:30 Expert's post hardnstrong wrote: Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is$9900, find the contribution made by David.

A. $540 B.$580
C. $600 D.$660
E. $680 Similar question to practice: baker-s-dozen-128782-20.html#p1057509 _________________ SVP Joined: 09 Sep 2013 Posts: 2093 Followers: 180 Kudos [?]: 35 [0], given: 0 Re: Four brothers Adam, Bill, Charles and David together [#permalink] 25 Feb 2014, 04:15 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Director Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 811 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 4 Kudos [?]: 196 [0], given: 165 Re: Hard Ratio question [#permalink] 04 Mar 2014, 21:13 sh00nya wrote: Given that A:(B+C+D)= 1:2. Hence A contributed 1/3rd of the total price. Given B:(A+C+D)=1:4 Hence B contributed 1/5th of the total price. Given C:(A+B+D)=2:3 Hence C contributed 2/5th of the total price. Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15 So, the remaining 1/15th of the price is contributed by David. Hence David's contribution= 1/15×9900=660$.

Nice method to solve this kind of problems, when only 1 variable value is required
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Re: Hard Ratio question   [#permalink] 04 Mar 2014, 21:13
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# Four brothers Adam, Bill, Charles and David together

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