Bunuel

If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?
A) 5
B) 9
C) 12
D) 23
E) 46
Since a bit more than 10% of the 37 marbles in P are blue, the number of blue marbles in P = a bit more than 3.7 = 4.
Since 1/2 of the 32 marbles in R are blue, the number of blue marbles in R = 16.
We can PLUG IN THE ANSWERS, which represent the total number of marbles in Q.
Rule:
MULTIPLE OF X + MULTIPLE OF X = MULTIPLE OF X
MULTIPLE OF X + NONMULTIPLE OF X = NONMULTIPLE OF X
Since 1/3 of all the marbles are blue, the total number of marbles must be a MULTIPLE OF 3.
Number of marbles in P and R combined = 37+32 = 69
Since 69 is a multiple of 3, the rule above indicates that the number of marbles in Q must also be a multiple of 3.
Eliminate A, D and E.
The chart indicates that 2/3 of the marbles in Q are blue.
When the correct answer is plugged in, \(\frac{total-blue}{total-marbles} = \frac{1}{3}\).
B: 9, implying 6 blue marbles in Q\(\frac{total-blue}{total-marbles} = \frac{4+16+6}{37+32+9} = \frac{26}{78} = \frac{1}{3}\)
Success!