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Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol. [#permalink]

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13 Oct 2015, 20:19

1

This post received KUDOS

Let A = number of gallons on Mixture A in 15 gallon mixture B = number of gallons on Mixture B in 15 gallon mixture (20/100)A + (50/100)B= (30/100)(A+B) --1 A+B=15 -- 2

On solving equations 1 and 2 , we get A=10 B=5 Answer D 10 gallons

Alternatively , a quicker method to solve this will be weighted average . We are mixing A , which has 20 % alcohol with B which has 50 % alcohol to get resultant mixture with 30 % alcohol

20 --30----50 30 is 10 away from 20 and 20 away from 50 . So the volumes of the mix A and B will be in inverse proportion - 2:1 . V1/V2=(50-30)/(30-20)=2/1
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This question can also be solved by TESTing THE ANSWERS.

We're told that two Mixtures have alcohol contents of 20% and 50% respectively. We're also told that mixing 15 total gallons of the two mixtures gives us a combined mixture that is 30% alcohol content. We're asked how many Gallons of Mixture A (the 20% mixture) are in the 15 Gallon Total.

Since the alcohol content of the final mixture is 30%, and 30% is CLOSER to 20% than it is to 50%, there MUST be MORE of the 20% mixture than the 50% mixture. Since there are 15 total gallons, MORE than 7.5 of those Gallons will be from Mixture A.

With 2 possible Answers (D and E), I'll TEST the easier option first.

Answer D: IF....we have 10 Gallons of the 20% mix, then we have 5 Gallons of the 50% mix....

Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

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Re: Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol. [#permalink]

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16 Dec 2017, 08:02

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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