Problem Solving

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

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.