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

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol.  [#permalink]

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13 Oct 2015, 20:02
2
5
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:28) correct 16% (01:51) wrong based on 184 sessions

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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?

(A) 3 gallons
(B) 4 gallons
(C) 5 gallons
(D) 10 gallons
(E) 12 gallons

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

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13 Oct 2015, 20:19
1
1
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

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

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13 Oct 2015, 21:57
2
1
HI All,

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....

[10(.2) + 5(.5)]/15 =
[2 + 2.5]/15 =
4.5/15 =
9/30 =
3/10 =
30%

This is an exact MATCH for what we were told, so this MUST be the answer.

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

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14 Oct 2015, 03:32
-10x+20(15-x)=0 -> 30x=300, x=10
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Re: Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol.  [#permalink]

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14 Oct 2015, 04:21
Bunuel wrote:
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?

(A) 3 gallons
(B) 4 gallons
(C) 5 gallons
(D) 10 gallons
(E) 12 gallons

(20/100)A + (50/100)B = (30/100)(A+B)

i.e. 10A = 20 B

i.e. A/B = 2/1

A+B=15 Gallon

i.e. A = (2/3)*15 = 10
and B = (1/3)*15 = 5

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

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14 Oct 2015, 11:38
Rich's solution uses an IMPORTANT weighted averages concept to quickly ELIMINATE A, B and C.
Here's a free video that explains this concept in greater detail: http://www.gmatprepnow.com/module/gmat- ... /video/805

Cheers,
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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!

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Re: Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol.   [#permalink] 16 Dec 2017, 08:02
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