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When n liters of fuel was added to a tank that was already [#permalink]
20 Apr 2012, 05:55

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82% (02:05) correct
18% (01:29) wrong based on 99 sessions

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?

Re: When n liters of fuel was added to a tank that was already [#permalink]
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.

Re: When n liters of fuel was added to a tank that was already [#permalink]
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.

Re: When n liters of fuel was added to a tank that was already [#permalink]
20 Apr 2012, 07:19

Expert's post

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. _________________

Re: When n liters of fuel was added to a tank that was already [#permalink]
27 Dec 2014, 08:35

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