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Bag A contains red, white and blue marbles such that the red

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Intern
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Bag A contains red, white and blue marbles such that the red [#permalink] New post 28 May 2007, 19:12
Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 30 white marbles. How many red marbles could be in bag A?
1
3
4
6
8


I really dislike their explanation so could someone come up with a clean one?thanks
Director
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Re: Marbles - ManhattanGMat [#permalink] New post 28 May 2007, 19:44
nxrfelix wrote:
Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 30 white marbles. How many red marbles could be in bag A?
1
3
4
6
8


I really dislike their explanation so could someone come up with a clean one?thanks

W(a) = 4r(a)
W(b) = 3r(b)

W(a) + W(b) = 30
4r(a) + 3r(b) = 30

if r(a) = 3 and r(b) = 6, then the sum becoms 30. therefore, r(a) = 3.
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 [#permalink] New post 29 May 2007, 11:06
I got 6

I am assuming I have only whole marbles in each bag.

The problem says that for bag A:
r:w = 1:3 and w:b = 2:3
this means that r:w:b = 1: 3: 4.5
So out of all answer choices the only ones that give you combinations of whole marbles are:
4 -> 4red, 12white, 18blue
6 -> 6red, 18white, 27blue
8 -> 8red, 24white, 36blue

For bag B, a ratio of r:w = 1:4 means that we have the following combinations possible:
1red, 4white
2red, 8white
3red, 12white
4red, 16white
5red, 20white
6red, 24white
7red, 28white and so on...

The only possible combination b/w bag A and bag B such that the white marbles in bag A plus the white marbles in bag B equal 30 is:
Bag A:
6 red, 18white, 27blue, and
Bag B:
3 red, 12 white

18+12 = 30, so

Answer is 6
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 [#permalink] New post 29 May 2007, 11:21
6 it is! Same logic. Bag A ratio - 2-6-9 , bag B 1-4
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 [#permalink] New post 29 May 2007, 18:55
joroivanov wrote:
I got 6

I am assuming I have only whole marbles in each bag.

The problem says that for bag A:
r:w = 1:3 and w:b = 2:3
this means that r:w:b = 1: 3: 4.5
So out of all answer choices the only ones that give you combinations of whole marbles are:
4 -> 4red, 12white, 18blue
6 -> 6red, 18white, 27blue
8 -> 8red, 24white, 36blue

For bag B, a ratio of r:w = 1:4 means that we have the following combinations possible:
1red, 4white
2red, 8white
3red, 12white
4red, 16white
5red, 20white
6red, 24white
7red, 28white and so on...

The only possible combination b/w bag A and bag B such that the white marbles in bag A plus the white marbles in bag B equal 30 is:
Bag A:
6 red, 18white, 27blue, and
Bag B:
3 red, 12 white

18+12 = 30, so

Answer is 6


this is a great solution!much better than what mgmat gave...
Director
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Posts: 889
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 [#permalink] New post 29 May 2007, 20:28
nxrfelix wrote:
joroivanov wrote:
I got 6

I am assuming I have only whole marbles in each bag.

The problem says that for bag A:
r:w = 1:3 and w:b = 2:3
this means that r:w:b = 1: 3: 4.5
So out of all answer choices the only ones that give you combinations of whole marbles are:
4 -> 4red, 12white, 18blue
6 -> 6red, 18white, 27blue
8 -> 8red, 24white, 36blue

For bag B, a ratio of r:w = 1:4 means that we have the following combinations possible:
1red, 4white
2red, 8white
3red, 12white
4red, 16white
5red, 20white
6red, 24white
7red, 28white and so on...

The only possible combination b/w bag A and bag B such that the white marbles in bag A plus the white marbles in bag B equal 30 is:
Bag A:
6 red, 18white, 27blue, and
Bag B:
3 red, 12 white

18+12 = 30, so

Answer is 6


this is a great solution!much better than what mgmat gave...


Answer is 6

BAG A

2:6:9

Bag B

1:4

after that it's easy
  [#permalink] 29 May 2007, 20:28
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Bag A contains red, white and blue marbles such that the red

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