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Drum X is 1/2 full of oil and drum Y, which has twice the capacity of

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Drum X is 1/2 full of oil and drum Y, which has twice the capacity of  [#permalink]

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New post 06 Dec 2017, 23:18
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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

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Re: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of  [#permalink]

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New post 07 Dec 2017, 00:03
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

2/3+1/4 = 11/12

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Re: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of  [#permalink]

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New post 07 Dec 2017, 01:36
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


Assume Drum X capacity to be 300 and Drum Y capacity to be 600
Drum X has 150 lltrs and Drum Y has 400 ltrs
After pouring Drum y will be 550/600 = 11/12
C
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Drum X is 1/2 full of oil and drum Y, which has twice the capacity of  [#permalink]

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New post 07 Dec 2017, 17:54
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 choices

Let 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
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Drum X is 1/2 full of oil and drum Y, which has twice the capacity of &nbs [#permalink] 07 Dec 2017, 17:54
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