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Bag A contains red, white and blue marbles such that the red [#permalink]
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

Re: Marbles - ManhattanGMat [#permalink]
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.

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

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...

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...

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