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Tough word problem - dividing $

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Tough word problem - dividing $

by Brent@GMATPrepNow » Sat Jan 03, 2009 4:17 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
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Re: Tough word problem - dividing $

by logitech » Sat Jan 03, 2009 4:46 pm
A) 4 + (x-4)/2

B) 4 + 1/3 [(X-12)/2]

C) 2/3 [(X-12)/2] = 32 ; (x-12) = 3 x 32

SO 4 + 1/3 [(X-12)/2] = 4+ 1/3 ( 3x32/2) = 20
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by logitech » Sat Jan 03, 2009 4:57 pm
So they had 108 dollars total

A ) 4 + 104/2 = 4+ 52 ( 52 remained )

B ) 4 + 1/3 ( 48 ) = 20 ( 32 remained )

C) 32
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by Brent@GMATPrepNow » Sat Jan 03, 2009 5:00 pm
Nice work, Logitech
My solution is below. Note that we don’t need to consider Ann’s portion in the solution. We can just let K be 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
The equation is K-4 – (K-4)/3 = 32
Solve for K (K=52) and then determine Bob’s portion ($20).
The answer is, indeed, A
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by logitech » Sat Jan 03, 2009 5:22 pm
Sweet!
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by mental » Sat Jan 03, 2009 11:35 pm
that was great Brent.
It shaved off half the steps.
B-)
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by kamu » Sat Feb 28, 2009 9:19 am
Bob took $4 + 1/3 of leftover..

that implies 2/3rds is left for Chloe..

if 2/3 of leftover = $32

1/3 of leftover = $16

$16+$4 = $20.
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Re: problem

by properz » Sun Mar 01, 2009 9:05 am
Where do you get x-12 for B?
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by deepoe » Sun Mar 01, 2009 9:23 am
The equation is K-4 – (K-4)/3 = 32 ?

K - 4 - k + 4 = 96?
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by kanha81 » Mon Mar 02, 2009 3:19 pm
kamu wrote:Bob took $4 + 1/3 of leftover..

that implies 2/3rds is left for Chloe..

if 2/3 of leftover = $32

1/3 of leftover = $16

$16+$4 = $20.
that's BRILLIANT!
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by shilpaqueen » Mon Nov 08, 2010 11:25 pm
Brent Hanneson wrote:Nice work, Logitech
My solution is below. Note that we don�t need to consider Ann�s portion in the solution. We can just let K be 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
The equation is K-4 � (K-4)/3 = 32
Solve for K (K=52) and then determine Bob�s portion ($20).
The answer is, indeed, A
One of the rules that I had read was that normally there is no 'useless' information that is provided, so in case you can solve a sum without using all the inforamation then you must be wrong.

How does one know that all the complicated information in this sum is not to be used??
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by Deepthi Subbu » Thu Nov 11, 2010 9:47 am
Hell All ,

The method that I am mentioning is quite long , but I want to know where I went wrong .

A - > 4 + (n-4) /2 - > (n+4)/2
B -> 4+ 1/3(n- (n+4)/2 -> (28+n)/6
C ->32

Hence , on solving this I get the total amount to be 116

Followed by Bob's share to be 24.
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by chendawg » Fri Nov 12, 2010 11:38 am
kamu wrote:Bob took $4 + 1/3 of leftover..

that implies 2/3rds is left for Chloe..

if 2/3 of leftover = $32

1/3 of leftover = $16

$16+$4 = $20.
Good way of thinking about it, even shorter than the way I did it. I thought of it as Anne taking 1/2, Bob took 1/3 of leftover, which is 1/3x1/2=1/6, so Chloe is left with 1/3 of total - 8 dollars. Since 1/3=32, Total =96. Plug back into equation for Bob = 1/6*96 + 4.

Your way was still much simpler!
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by anirudhbhalotia » Sun Dec 05, 2010 5:15 am
logitech wrote:A) 4 + (x-4)/2

B) 4 + 1/3 [(X-12)/2]

C) 2/3 [(X-12)/2] = 32 ; (x-12) = 3 x 32

SO 4 + 1/3 [(X-12)/2] = 4+ 1/3 ( 3x32/2) = 20


If X is the total amount.

Ann : 4 + (x-4)/2 (Ann receives $4 plus one-half of what remains)

Bob : 4 + 1/3(x- Share of Ann) (Bob receives $4 plus one-third of what remains)

Bob: 4+1/3[x-(4+(x-4)/2)]

Isn't it?


How did you get 4 + 1/3 [(X-12)/2] ?
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by badpoem » Tue Dec 28, 2010 1:41 am
I started with $100.

Ann receives a $4 plus one half of what remains -> 4 + 96/2 = 52.
Remaining = 100-52 = 48.
Bob receives $4 plus one third of what remains -> 4 + 44/3 = 56/3

Chloe receives the remaining $32. In this case Chloe receives 48 - 4 - 44/3 = 44*2/3.

Therefore, 44*2/3 equivalent to 32
and 56/3 (Bob's share) equivalent to (32*(56/3)*3)/(44*2) ~= 20.

Hence A.
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