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A sum of money is to be divided among Ann, Bob and Chloe.

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A sum of money is to be divided among Ann, Bob and Chloe.

by BTGModeratorVI » Sun Jul 19, 2020 1:36 pm

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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 money did Bob receive?

A) 20
B) 22
C) 24
D) 26
E) 52

Answer: B
Source: Magoosh
Last edited by BTGModeratorVI on Mon Jul 20, 2020 8:45 am, edited 1 time in total.
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Re: A sum of money is to be divided among Ann, Bob and Chloe.

by Jay@ManhattanReview » Mon Jul 20, 2020 1:13 am
BTGModeratorVI wrote: ↑
Sun Jul 19, 2020 1:36 pm
 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 money did Bob receive?

A) 20
B) 22
C) 24
D) 26
E) 52

Answer: A
Source: Magoosh
Say the sum of money if $x.

Thus, Ann's share = 4 + 1/2 of (x – 4) = (x + 4)/2;

Sum remains x – (x + 4)/2 = (x – 4)/2

Bob's share = 4 + 1/3 of [(x – 4)/2 – 4] = (x + 12)/6

Sum remains (x – 4)/2 – (x + 12)/6 = (x – 12)/3

=> (x – 12)/3 = 32

x = $108

Bob's share = (x + 12)/6 = (108 + 12)/6 = $20

Correct answer: A

Hope this helps!

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Re: A sum of money is to be divided among Ann, Bob and Chloe.

by Brent@GMATPrepNow » Mon Jul 20, 2020 8:44 am
BTGModeratorVI wrote: ↑
Sun Jul 19, 2020 1:36 pm
 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 money did Bob receive?

A) 20
B) 22
C) 24
D) 26
E) 52

Answer: B
Source: Magoosh
Notice that we need not consider Ann'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 receives $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

Answer: B
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Re: A sum of money is to be divided among Ann, Bob and Chloe.

by Brent@GMATPrepNow » Mon Jul 20, 2020 8:44 am
BTGModeratorVI wrote: ↑
Sun Jul 19, 2020 1:36 pm
 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 money did Bob receive?

A) 20
B) 22
C) 24
D) 26
E) 52

Answer: B
Source: Magoosh
Another approach:

This time, let K = the money REMAINING after Ann has received her portion AND after Bob has taken $4.
At this point, Bob receives 1/3 of K, and Chloe gets the rest.
This means that Chloe receives 2/3 of K

Since Chloe receives $32, we can say that: (2/3)K = 32
Multiply both sides by 3/2 to get: K = 48

Since Bob receives 1/3 of K plus $4, we can see that the amount Bob gets = (1/3)(48) + 4 = $20

Answer: B
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