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

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 money did Bob receive?

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

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

KarishmaB · Accepted Answer

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

BrentGMATPrepNow · Answer

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 -     = 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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mgtrinath · Answer

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.

rite2deepti · Answer

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 :-)

KarishmaB · Answer

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.

tfincham86 · Answer

Thanks for the explanation Karishma

BrentGMATPrepNow · Answer

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

SVaidyaraman · Answer

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

SOUMYAJIT_ · Answer

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.

KarishmaB · Answer

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.

SOUMYAJIT_ · Answer

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.

Yup!! Sorry.. Stupid question!!

JeffTargetTestPrep · Answer

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

4 + ⅓  = 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

Kinshook · Answer

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

hudacse6 · Answer

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

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