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An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
 27 May 2012, 04:59
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Question Stats:
74% (01:00) correct
25% (01:42) wrong based on 31 sessions
An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added? A 160 B 150 C 100 D 80 E 50
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
27 May 2012, 05:06
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macjas wrote: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?
A 160
B 150
C 100
D 80
E 50 Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B. The amount of ethanol in A gallons of fuel A is 0.12A; The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A); Since the total amount of ethanol is 30 gallons then 0.12A+0.16(200-A)=30 --> A=50. Answer: E. Hope it's clear.
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Senior Manager
Affiliations: UWC
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Location: India
GMAT 1: 620 Q42 V33
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
27 May 2012, 05:12
Hi Bunuel, correct answer as usual but please change the correct choice to E! (typo)
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
27 May 2012, 05:13
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marked E. Solved it this way:
total ethanol = 30 lts in 200lts therefore % = 30/200 *100 = 15%
now creating an equation in
Let qty of fuel A= x lts and Fuel b = 200-x lts
there fore 0.12x +0.16(200-x) = 30, solving we get x = 50lts.
Hope its clear.
Last edited by vibhav on 27 May 2012, 05:16, edited 1 time in total.
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Senior Manager
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
27 May 2012, 05:16
additionally as be see the mixture's overall % is closer to 16% ethanol mixture, this should show you that the 16% ethanol mixture's quantity is much higher than 12% mixture.
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Senior Manager
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
27 May 2012, 05:18
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Another way to do it (weighted averages): 30 of 200
12% = 15% 16%
A-------------Mixture--------------B
3 1 So 1 part of B and 3 parts of A make 200 So, A is 25% of the total 200 i.e 50
Last edited by macjas on 27 May 2012, 05:23, edited 2 times in total.
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Senior Manager
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
27 May 2012, 05:19
To solve this problem using mixtures is also possible;
qty of A/qty of b = % of B (16%) - final %(15) / final %(15) - % of A(12%)
i.e. a/b = 1/4 and we know a+B = 200 hence a= 200/4 = 50
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Senior Manager
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
27 May 2012, 05:20
@macjas thats a quick method as well! nice.
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Senior Manager
Affiliations: UWC
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
27 May 2012, 05:24
sorry... was having trouble formatting my post correctly
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]
27 May 2012, 06:15
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Hi, The Allegation method is very useful in this case. The percentage of ethanol in two mixtures = 12% & 16% Final percentage in mixture = 30/200 * 100 = 15% Following is the diagrammatic representation of the method:
Attachments
Allegations.jpg [ 11.3 KiB | Viewed 1109 times ]
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Re: An empty fuel tank with a capacity of 200 gallons was fill
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27 May 2012, 06:15
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