GMAT Problem Solving - A Certain Sum of Money is Divided Among A, B and C such that A Gets One

Question: A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $12.4 more than that received by B, find the total amount shared by A, B and C.

1. $345.20
2. $386.40
3. $520.30
4. $446.40
5. None

“A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get” - this is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

 It is asked,find the total amount shared by A, B and C, If the amount received by A is $12.4 more than that received by B.

It is given,

• A, B, and C each receive a particular amount of money.
• A receives a third of what B and C combined receive.
• B receives 2/7 of what A and C combined receive.
• A received $12.4 more than B did in terms of money

It is asked
To Find the total amount shared by A, B and C.

Lets solve further,
A receives a third of what B and C combined receive.
This means,
if A gets ‘a’ then B+C= 3a
A+B+C = 4a

B receives two-seventh of what A and C combined receive.
This means
B gets 2b, then A+C = 7b
A+B+C = 9b

Now, A+B+C is equal to 4a as well as 9b.
Therefore, we can assume A+B+C= 36k.
This means,
A= 9k, B= 8k, c= 19k
9k= 8k+12.4
k= 12.4
so, total amount shared by A, B, and C= 36k=446.40

The answer is D which is 446.40

Correct Answer: D

Approach Solution 2:
There is another approach to answering this question

It is given, A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $12.4 more than that received by B, find the total amount shared by A, B and C.

If you understand the logic behind the problem, it is not at all difficult.

If A has ⅓ of B and C, then B and C together hold 3/3.

Thus, A has 1 peace, B and C each have 3,

A holds a share of ¼ of the total.

B has 2/9 if we apply the same argument to B.

We can now create equality.

\(\frac{1}{4}x-\frac{1}{9}x=12.4\)

\(\frac{[9-8]}{36}x = 12.4\)

\(\frac{1}{36}x= 12.4\)

x= 12.4*36=446.4

The answer is D which is 446.40

Correct Answer: D

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