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

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A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   10 Nov 2010, 10:14
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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
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A
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KarishmaB
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   10 Nov 2010, 11:36
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mrinal2100 wrote:
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


Start with Chloe.
Chloe got $32 which was 2/3rd 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
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BrentGMATPrepNow
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A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   Updated on: 11 May 2021, 06:59
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DensetsuNo wrote:
A sum of money was distributed among Lyle, Bob and Chloe. First, Lyle received 4 dollars plus one-half of what remained. Next, Bob received 4 dollars plus one-third of what remained. Finally, Chloe received the remaining $32. How many dollars did Bob receive?

A) 10
B) 20
C) 26
D) 40
E) 52

Kudos if you like!


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 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:
Show Spoiler
B


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Originally posted by BrentGMATPrepNow on 20 Jul 2016, 05:21.
Last edited by BrentGMATPrepNow on 11 May 2021, 06:59, edited 2 times in total.
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   10 Nov 2010, 11:01
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Total = s
Ann = 4+(1/2)(s-4) = (1/2)s+2
Bob = 4+(1/3)(s-4-(Ann)) = 4+(1/3)(s-4-((1/2)s+2)) = (1/6)s+2
Chlore = 32
A+B+C = s => s = 108
Bob = 20
Ans: A

OA pls.
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   11 Dec 2010, 02:27
Another way of solving this problem is by plugging in numbers :
Take total sum =108
Then the share of ann=4+104/2=56
104-52 =52 remains
The for Bob 4+48/3=20
For charlote $32 remains

:-)
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   11 Dec 2010, 04:03
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rite2deepti wrote:
Another way of solving this problem is by plugging in numbers :
Take total sum =108
Then the share of ann=4+104/2=56
104-52 =52 remains
The for Bob 4+48/3=20
For charlote $32 remains

:-)



Yes, plugging in numbers is a great strategy whenever applicable. The only small issue with it is that sometimes you need to go through the process multiple times before you get the answer. The more calculations you do, more time is lost and more are the chances of you making a calculation error. Though you will take a call according to your comfort with each question type, but if the question is straight forward and you know how to get the answer, my advice would be to solve it rather than going backwards.
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   11 Dec 2010, 09:45
Thanks for the explanation Karishma
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Re: A sum of money was distributed among Lyle, Bob and Chloe... [#permalink] New post   20 Jul 2016, 05:26
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DensetsuNo wrote:
A sum of money was distributed among Lyle, Bob and Chloe. First, Lyle received 4 dollars plus one-half of what remained. Next, Bob received 4 dollars plus one-third of what remained. Finally, Chloe received the remaining $32. How many dollars did Bob receive?

A) 10
B) 20
C) 26
D) 40
E) 52


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:
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B
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   20 Jul 2016, 21:46
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mrinal2100 wrote:
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



Let money remaining after Ann got her share and after Bob took $4 be x.
This is also equal to 32 +x/3.
So, 32 + x/3 = x
x=48 . So Bob got x/3 + 4 = 20
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   19 Jul 2017, 10:10
VeritasPrepKarishma wrote:
mrinal2100 wrote:
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


Start with Chloe.
Chloe got $32 which was 2/3rd 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


Can you explain how did you get 2/3rd of what was remaining was 32? As we keep on adding 4 to fractions of what was remaining in case of A and B.
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   20 Jul 2017, 01:55
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SOUMYAJIT_ wrote:
VeritasPrepKarishma wrote:
mrinal2100 wrote:
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


Start with Chloe.
Chloe got $32 which was 2/3rd 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


Can you explain how did you get 2/3rd of what was remaining was 32? As we keep on adding 4 to fractions of what was remaining in case of A and B.


Question tells us: "Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32."

Bob received $4 and a third a what remained. So 2/3rd was finally what was left for Chloe. That 2/3rd was $32.
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   20 Jul 2017, 03:09
[/quote]

Can you explain how did you get 2/3rd of what was remaining was 32? As we keep on adding 4 to fractions of what was remaining in case of A and B.[/quote]

Question tells us: "Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32."

Bob received $4 and a third a what remained. So 2/3rd was finally what was left for Chloe. That 2/3rd was $32.[/quote]

Yup!! Sorry.. Stupid question!!
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   25 Jul 2017, 10:50
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mrinal2100 wrote:
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


We can let the total amount of money = n.

Thus, Ann receives:

4 + ½(n - 4)

4 + ½n - 2

½n + 2

Bob receives:

4 + ⅓[n - 4 - Ann]

4 + ⅓[n - 4 - (½n + 2)]

4 + ⅓[n - 4 - ½n - 2]

4 + ⅓[½n - 6] = 4 + ⅙n - 2

⅙n + 2

Since we are given that Chloe receives the remaining $32, we can create the following equation, which combines Ann’s money, Bob’s money, and Chloe’s money:

½n + 2 + ⅙n + 2 + 32 = n

Multiplying both sides by 6, we have:

3n + 12 + n + 12 + 192 = 6n

4n + 216 = 6n

2n = 216

n = 108

Thus, Bob receives:

⅙(108) + 2 = 18 + 2 = $20

Answer: A
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   12 Aug 2019, 01:19
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mrinal2100 wrote:
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


Given: 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.

Asked: How much money did Bob receive?

Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32.
Chloe receives 2/3rd of what remains = $32
1/3 rd of what remains = $16
Bob receives = 16+4 =$20

IMO A
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   16 Nov 2019, 12:11
mrinal2100 wrote:
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




Lets, we (L, B, and C) have total 100$.

Now L received 4 + \(\frac{1}{2}\) of 96 ; (96, because after receiving 4 from 100, remaining is 96);

After that B received 4 + \(\frac{1}{3}\) of 48 ; (48, because after receiving \(\frac{1}{2 }\)of 96 we have remaining 48 only)

Now, we have remain only 32 which is C received. (32, because \(\frac{48}{3}\) = 16; 48 - 16 = 32 remaining lastly )

So, from B, ( 4 + \(\frac{1}{3}\) 48 ), we get, 4 + 16 = 20.
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Re: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann r [#permalink] New post   13 Apr 2024, 02:04
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