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Number of Red balls

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Number of Red balls

by Cheese12 » Sun Oct 30, 2011 9:35 am
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?

A) 1
B) 3
C) 4
D) 6
E) 8


OA:D

Hello Beatthegmatters,
Could anyone pls help me with this ques, I am having trouble solving this one..
Thanks !
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by GmatMathPro » Sun Oct 30, 2011 9:58 am
First, express the ratios of the marbles in bag A in one three-way ratio.

Bag A-

Red:white=1:3=2:6
White:Blue=2:3=6:9

Red:white:blue=2:6:9

So the actual number of marbles in bag A has to be some integer multiple of this ratio. That is, the actual number of red, white, and blue marbles is 2x, 6x, and 9x respectively, for some positive integer, x.


Bag B-

Red:White=1:4

So there are y and 4y red and white marbles respectively in bag B, for some positive integer y.

There is a total of 30 white marbles, so:

6x+4y=30
or
3x+2y=15

possible solutions:
x=1, y=6 plugging in to R:W:B=2x:6x:9x=2, 6, 9 red white and blue marbles. 2 is not a choice.
x=3, y=1 plugging in to 2x:6x:9x=6,18, 27, which gives 6 red marbles.

Ans: D
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by GmatKiss » Sun Oct 30, 2011 10:01 am
Substitution will help,

Bag A:

R:W:B
2:6:9
4:12:18
6:18:27

Bag B

R:W
1:4
2:8
3:12
4:16

White sums to 30 in the highlighted substitution, and hence no of red balls will be 6(D)
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