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13 Oct 2015, 21:02
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
87% (01:29) correct
13%
(02:13)
wrong
based on 643
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) 3 gallons
(B) 4 gallons
(C) 5 gallons
(D) 10 gallons
(E) 12 gallons
13 Oct 2015, 21:19
Kudos
Bookmarks
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
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
General Discussion
13 Oct 2015, 22:57
Kudos
Bookmarks
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.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
