A Sum of Money is to be Divided Among Ann, Bob, and Chloe GMAT Problem Solving

Question: A sum of money is to be divided among Ann, Bob, and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much did Bob receive?

1. 20
2. 22
3. 24
4. 26
5. 52

Answer:
Approach Solution (1):
Start with Chloe
Chloe got $32 which was 2/3^rd of what was remaining after Bob received $4
So 1/3 that Bob received must have been $16
This was remaining when Bob had already been given $4
In all, Bob received $16 + $4 = $20

Correct option: A

Approach Solution (2):
Total = s
Ann = \({{{4+{1\over2}}}\over{s-4}}={1\over2}{(s+2)}\)
Bob =\({{{4+{1\over3}}}\over{s-4-Ann}}=4+{(\frac{1}{3})}(s-4-{(\frac{1}{2})}s+2)=\frac{1}{6}s+2 \)
Chloe = 32
A + B + C = s
s = 108
Bob = 20

Correct option: A

Approach Solution (3):
Notice that we need not consider Lyle’s portion in the solution. We can just let K = the money remaining after Ann has received her portion and go from there
Our equation will use the fact that, once we remove Bob’s portion, we have $32 for Chloe
So, we get K – Bob’s $ = 32
Bob received 4 dollars plus one-third of what remained
Once bob received $4, the amount remaining is K – 4 dollars. So, bob gets a 1/3 of that as well
1/3 of K – 4 is (K – 4) / 3
So altogether, Bob receives 4 + (K + 4) / 3
So our equation becomes: K – [4 + (K – 4) / 3] = 32
Simplify to get: K – 4 – (K – 4) / 3 = 32
Multiply both sides by 3 to get: 3K – 12 – K + 4 = 96
Simplify: 2K – 8 = 96
Solve: K = 52
Plug this K-value into K – Bob’s $ = 32 to get: 52 – Bob’s $ = 32
So, Bob’s $ = 20

Correct option: A

“A sum of money is to be divided among Ann, Bob, and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much did Bob receive?”- 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 amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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