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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Four brothers Adam, Bill, Charles and David... tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Four brothers Adam, Bill, Charles and David... 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$9,900, find the contribution made by David.

A. $540 B.$580
C. $600 D.$660
E. $680 The OA is D. I'm really confused with this PS question. Experts, any suggestion? I think that I can solve it using an equations system in agree of the description, I know that the total price is$9900, the equation for it can be,
$$A+B+C+D=9900$$
Then for each one of the brothers contribution will be,
$$A=\frac{1}{2}\cdot\left(B+C+D\right)$$
$$B=\frac{1}{4}\cdot\left(A+C+D\right)$$
$$C=\frac{2}{3}\cdot\left(A+B+D\right)$$
I have 4 equations and 4 incognits, now I can get each contribution.

### GMAT/MBA Expert

GMAT Instructor
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Hello LUANDATO.

Let's take a look at your question.

Your answer is right. We have to set four equations with four variables. Your equations are great: $$(1) A+B+C+D=9900$$ $$(2) A=\frac{1}{2}\cdot\left(B+C+D\right)$$ $$(3) B=\frac{1}{4}\cdot\left(A+C+D\right)$$ $$(4) C=\frac{2}{3}\cdot\left(A+B+D\right)$$ Now, from equation (2) and (1) we can get $$2A=B+C+D\ \ \Leftrightarrow\ 3A=A+B+C+D=9900\ \Leftrightarrow\ A=\frac{9900}{3}=3300.$$ Now we know A. From equation (3) and (1) we can get $$4B=A+C+D\ \Leftrightarrow\ 5B=A+B+C+D=9900\ \Leftrightarrow\ B=\frac{9900}{5}=1980.$$ From the equation (4) and (1) we can get $$3C=2\left(A+B+D\right)\ \Leftrightarrow\ 5C=2\left(A+B+D\right)+2C=2\left(A+B+C+D\right)$$ $$5C=2\left(9900\right)=19800\ \Leftrightarrow\ C=\frac{19800}{5}=3960.$$ Finally, from equation (1) we can conclude: $$3300+1980+3960+D=9900\ \Leftrightarrow\ D=9900-9240=660\ \text{dollars}.$$ Hence, the correct answer is the option D=$660. I hope this answer can help you. Feel free to contact me again if you have a doubt. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1465 messages Followed by: 19 members Upvotes: 39 LUANDATO 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$9,900, find the contribution made by David.

A. $540 B.$580
C. $600 D.$660
E. $680 We can let the contribution made by Adam, Bill, Charles and David be A, B, C, and D respectively. Since Adam contributes A dollars, the other three boys contribute 9900 - A dollars; so we have: A = (1/2)(9900 - A) 2A = 9900 - A 3A = 9900 A = 3,300 Similarly, since Bill contributes B dollars, the other three boys contribute 9900 - B dollars and we have: B = 1/4(9900 - B) 4B = 9900 - B 5B = 9900 B = 1,980 Finally, since Charles contributed C dollars, the other three boys contributed 9900 - C dollars and thus: C = 2/3(9900 - C) 3C = 2(9900) - 2C 5C = 2(9900) C = 3,960 Now that we know A = 3,300, B = 1,980 and C = 3,960, we can easily find D by the following equation: 3,300 + 1,980 + 3,960 + D = 9,900 9,240 + D = 9,900 D = 660 Answer: D _________________ Jeffrey Miller Head of GMAT Instruction jeff@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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