Bunuel wrote:

Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 2/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what fraction of its capacity?

(A) 3/4

(B) 5/6

(C) 11/12

(D) 7/6

(E) 11/6

Algebra\(X = \frac{1}{2}Y\)

\(X\) is half full of oil. Its oil amount constitutes:

\(\frac{1}{2}\) of \(\frac{1}{2}Y\)

\(\frac{1}{2} * \frac{1}{2}Y=\frac{1}{4}Y\)

\(Y\) is \(\frac{2}{3}\) full of oil = \(\frac{2}{3}Y\)

Contents of X are poured into Y:

\(\frac{1}{4}Y + \frac{2}{3}Y=\frac{(3 + 8)}{12}=\frac{11}{12}Y\)

Answer C

Pick numbers. For Y, do not go smaller than any denominator in answer choicesLet X's capacity = 6 gallons

Y's capacity = (2 * X) = 12 gallons

X is 1/2 full of oil:

6 * 1/2 = 3 gallons inside

Y is 2/3 full

12 * 2/3 = 8 gallons inside

X's oil is poured into Y:

3 + 8 = 11

\(\frac{FillAmt}{CapacityY} = \frac{11}{12}\)

Answer C

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"