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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