BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Four brothers Adam, Bill, Charles and David...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Four brothers Adam, Bill, Charles and David...

by BTGmoderatorLU » Wed Jan 24, 2018 5:43 am
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.

Thanks in advance.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

by EconomistGMATTutor » Wed Jan 24, 2018 8:07 am
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 [spoiler]D=$660[/spoiler].

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.

Image
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Fri Jan 26, 2018 9:56 am
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
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1