enigma123 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?
A) 1
B) 3
C) 4
D) 6
E) 8
Guys - can someone please help by explaining this problem?
Responding to a pm:
We need the relation between number of red, white and total number of marbles.
We don't know what that relation in bag A. Let's find it out first.
Red:White = 1:3 = 2:6
White:Blue = 2:3 = 6:9
Red:White:Blue = 2:6:9
In bag A, if you have 17 marbles, 2 will be Red, 6 will be White and 9 will be Blue.
If you have 34 marbles, 4 will be Red, 12 will be White and 18 will be Blue etc
No of white marbles could be 6/12/18/24... etc
No of red marbles could be 2/4/6/8/... etc
In bag B,
Red:White = 1:4
If you have 5 marbles, 1 will be Red, 4 will be White.
If you have 10 marbles, 2 will be Red, 8 will be White.
etc
No of white marbles could be 4/8/12/16... etc
No of red marbles could be 1/2/3/4... etc
Total number of white marbles = 30
There are two ways in which we could have obtained 30.
White marbles in (Bag A, Bag B) = (6, 24) or (18, 12)
If Bag A has 6 white marbles, it will have 2 red marbles.
If Bag A has 18 white marbles, it will have 6 red marbles.
Answer (D).
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Karishma
Veritas Prep GMAT Instructor
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