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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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Math Expert
Joined: 02 Sep 2009
Posts: 44634
Drum X is 1/2 full of oil and drum Y, which has twice the capacity of [#permalink]

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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
[Reveal] Spoiler: OA

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Joined: 26 Sep 2017
Posts: 3
Re: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of [#permalink]

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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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Director
Joined: 18 Aug 2016
Posts: 631
Re: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of [#permalink]

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

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

$$\frac{FillAmt}{CapacityY} = \frac{11}{12}$$

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