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Bag A contains red, white and blue marbles such that the red [#permalink]
 28 May 2007, 20:12
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
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Re: Marbles - ManhattanGMat [#permalink]
28 May 2007, 20:44
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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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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6 it is! Same logic. Bag A ratio - 2-6-9 , bag B 1-4
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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...
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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
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