Solution X, which is 10% alcohol is combined : Data Sufficiency (DS)

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Solution X, which is 10% alcohol is combined

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Solution X, which is 10% alcohol is combined [#permalink]

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30 Sep 2016, 05:44

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Difficulty:

35% (medium)

Question Stats:

64% (01:24) correct

36% (01:23) wrong

based on 384 sessions

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Solution X, which is 10% alcohol is combined with solution Y, which is 18% alcohol to form a new solution that is 12% alcohol. How many liters of solution Y are in the new combined solution?

1. Solution X comprises 3/4 of the combined solution
2. The combined solution is 16 liters.

PS: Please solve this with alligation method.

Spoiler: OA

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Re: Solution X, which is 10% alcohol is combined [#permalink]

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30 Sep 2016, 05:55

X/Y = (18 - 12)/(12 - 10) = 6/2 = 3/1

St1: X = 3/4(X + Y)
4X = 3X + 3Y
X = 3Y --> X/Y = 3/1 --> We know this from the question itself
Not Sufficient

St2: X + Y = 16
3Y + Y = 16 --> Y = 4 and X = 12
Sufficient

Answer: B

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Solution X, which is 10% alcohol is combined [#permalink]

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30 Sep 2016, 10:42

Keats wrote:

1. We don't know about total quantity......not suff....
2. we know total quantity of mixture .
So as derived in below fig. Y=3/4*16=12 lts.....and X=16-12=4lts........sufff....

Ans B

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Joined: 11 May 2018

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Re: Solution X, which is 10% alcohol is combined [#permalink]

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02 Jul 2018, 16:26

From the question prompt, the ratio of Solution X to Solution Y in the combined solution is (18 - 12) : (12 - 10) = 6:2 = 3:1.

1. Solution X comprises 3/4 of the combined solution
This statement provides no extra information than what the question prompt already provides. It's a Tautology!
So statement 1 is insufficient.

2. The combined solution is 16 liters.
Since we know the ratio of Solution X to Solution Y already, we can find the quantity of X or Y in the combined solution if the quantity of the combined solution is given. No need to calculate the answer. Just know that you can calculate the answer!