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by hey_thr67 » Mon Jul 02, 2012 9:08 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 is D
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by Anurag@Gurome » Mon Jul 02, 2012 9:35 am
hey_thr67 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?
In bag A,
  • R:W = 1:3 = 2:6 and W:B = 2:3 = 6:9 --> R:W:B = 2:6:9
    Say, the numbers of red, white, and blue marbles are 2x, 6x, and 9x
In bag B,
  • R:W = 1:4
    Say, the numbers of red and white marbles are y, and 4y
Hence, (6x + 4y) = 30
As 6x and 4y both have to be positive integers, possible solutions for x and y are (x = 1, y = 6) and (x = 3, y = 3)

Hence, possible number of marbles in bag A is either 2x = 2*1 = 2 or 2x = 2*3 = 6.

The correct answer is D.
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by GMATGuruNY » Mon Jul 02, 2012 9:43 am
hey_thr67 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

OA is D

We can plug in the answers, which represent the number of red marbles in Bag A.
Since R:W = 1:3, the number of white marbles in Bag A is 3 times the number of red marbles in Bag A.
Thus, the answers imply that the number of white marbles in Bag A could be:

3*1 = 3
3*3 = 9
3*4 = 12
3*6 = 18
3*8 = 24.

Since the total number of white marbles between the two bags is 30, the results above imply that the number of white marbles in Bag B could be:

30-3=27
30-9=21
30-12=18
30-18=12
30-24=6.

In Bag B, R:W = 1:4, implying that the number of white marbles in Bag B must be a multiple of 4.
In the list above, only 12 -- the result of answer choice D -- is a multiple of 4.

The correct answer is D.
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