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

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Intern
Joined: 07 Apr 2007
Posts: 9

Kudos [?]: 13 [0], given: 0

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

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28 May 2007, 20:12
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Kudos [?]: 13 [0], given: 0

Director
Joined: 26 Feb 2006
Posts: 900

Kudos [?]: 157 [0], given: 0

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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.

Kudos [?]: 157 [0], given: 0

Intern
Joined: 16 May 2007
Posts: 18

Kudos [?]: 1 [0], given: 0

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29 May 2007, 12:06
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

Kudos [?]: 1 [0], given: 0

Manager
Joined: 22 May 2007
Posts: 121

Kudos [?]: 5 [0], given: 0

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29 May 2007, 12:21
6 it is! Same logic. Bag A ratio - 2-6-9 , bag B 1-4

Kudos [?]: 5 [0], given: 0

Intern
Joined: 07 Apr 2007
Posts: 9

Kudos [?]: 13 [0], given: 0

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29 May 2007, 19:55
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

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

Kudos [?]: 13 [0], given: 0

Director
Joined: 03 Sep 2006
Posts: 865

Kudos [?]: 1072 [0], given: 33

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29 May 2007, 21:28
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

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

BAG A

2:6:9

Bag B

1:4

after that it's easy

Kudos [?]: 1072 [0], given: 33

29 May 2007, 21:28
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