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When n liters of fuel was added to a tank that was already

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When n liters of fuel was added to a tank that was already [#permalink] New post 20 Apr 2012, 05:55
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When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?

A. 10/9 n
B. 4/3 n
C. 3/2 n
D. 9/4 n
E. 7/3n
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Re: Fractions [#permalink] New post 20 Apr 2012, 06:06
D is the answer.

To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.

Given
- tank was already 1/3 full.
- When n ltr added, it became 7/9

So 1/3 + n = 7/9
n = 7/9 - 3/9
n = 4/9

capacity of the tank is full fraction . i.e. 1 i.e. 9/9

so the question is 9/9 is how much times n
= 9/9 = 1 = xn

so x = 9/4

and total = 9/4n
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Re: When n liters of fuel was added to a tank that was already [#permalink] New post 20 Apr 2012, 07:03
Expert's post
naveenhv wrote:
When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?

A. 10/9 n
B. 4/3 n
C. 3/2 n
D. 9/4 n
E. 7/3n


Say the capacity of the tank is 9 liters;

So, there are already 3 liters (1/3*9=3) of fuel and after adding n liters there are 7 liters (7/9*9=7) --> 3+n=7 --> n=4 --> capacity=9=n*9/4.

Or just plug n=4 in the answer choices to see which option yields 9, answer choice D fits: 9/4*4=9.

Answer: D.
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Re: When n liters of fuel was added to a tank that was already [#permalink] New post 20 Apr 2012, 07:15
Or you can also solve it another way, check for the integer, which is divisible by both the fractions, here we can take 18 liters as the capacity of the tank.

Then 1/3 of fuel is 6 liters, and 7/9 capacity will be 14 liters. From this we can get the n value as n = 14-6 = 8.
Try to substitute this value in the below options and only option 'D' get the value of 18 as the total capacity.
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Re: When n liters of fuel was added to a tank that was already [#permalink] New post 20 Apr 2012, 07:19
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mission2009 wrote:
Or you can also solve it another way, check for the integer, which is divisible by both the fractions, here we can take 18 liters as the capacity of the tank.

Then 1/3 of fuel is 6 liters, and 7/9 capacity will be 14 liters. From this we can get the n value as n = 14-6 = 8.
Try to substitute this value in the below options and only option 'D' get the value of 18 as the total capacity.


The lowest value for the capacity for which 1/3*capacity and 7/9*capacity are integers is 9 (LCM of 3 and 9). Refer to the solution above.
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Re: When n liters of fuel was added to a tank that was already   [#permalink] 20 Apr 2012, 07:19
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