An empty fuel tank with a capacity of 200 gallons was fill : GMAT Problem Solving (PS)
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# An empty fuel tank with a capacity of 200 gallons was fill

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An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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27 May 2012, 03:59
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Difficulty:

25% (medium)

Question Stats:

75% (02:47) correct 25% (02:04) wrong based on 226 sessions

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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]

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27 May 2012, 04:06
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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.

Hope it's clear.
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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27 May 2012, 04:13
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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, 04:16, edited 1 time in total.
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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27 May 2012, 04:16
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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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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27 May 2012, 04:18
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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, 04:23, edited 2 times in total.
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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27 May 2012, 04:19
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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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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27 May 2012, 04:20
@macjas thats a quick method as well! nice.
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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27 May 2012, 04:24
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]

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27 May 2012, 05:15
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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 3901 times ]

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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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08 Jul 2013, 00:10
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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18 May 2014, 14:14
We can solve this problem using weighted averages method.

First we need to find 30 is what % of 200 => 15%;

12%(A) ------------ 15%Final Mix ------------------ 16%(B)
3 1

w1/w2 = 1/3 ;

gallons of fuel A added = 1/4(200) =50;
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Re: An empty fuel tank with a capacity of 200 gallons was fill [#permalink]

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22 May 2014, 01:16
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Let's take Fuel of type A = A litre

Fuel of type B = B litre

Ethanol in type A = 12% => 0.12A
Ethanol in type B = 16% => 0.16B

Now,
A + B = 200
0.12A + 0.16B = 30

Multiplying first with 0.16 and subtracting second

0.16A - 0.12A = 32-30
0.04A = 2
A = 2/0.04=> A = 50

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Re: An empty fuel tank with a capacity of 200 gallons was fill   [#permalink] 22 May 2014, 01:16
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