When n liters of fuel was added to a tank that was already 1/3 full

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.

Here are a couple of video explanations for this question.

Algebra:



Value Substitution:

What if :
7/9-1-3 = n
=>, 4/9 capacity = n
so full capacity = 9n/4
Ans. D

Also, we can answer it this way,

1/3*c+n=7/9*c
c/3+n=7c/9
n=7c/9-c/3
n=4c/9

The question asked is what is the capacity of the tank, in liters? so here as we have already considered C as the capacity of the tank.
C=9/4*n which is the option D.

N liters added to a tank 1/3 full, equals 7/9 of its capacity, which translates to:

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

To make in terms of n, multiple both sides by 9/4.
c = 9/4n

Answer is D

When you see variables in the answer choices, use smart numbers.

Suppose that the capacity of the tank is 27 liters. (I chose 27 because it's divisible by the other numbers in the problem). In that case, the tank already contained 9 liters, and when we added a certain amount, it was filled to 7/9(27), or 21 liters. That means n = 21-9 = 12.

So, n = 12, and the capacity is 27. Try plugging 12 into the answer choices, and see whether you end up with 27.

(A) 10/9(12) isn't an integer!
(B) 4/3(12) = 16 - too small
(C) 3/2(12) = 18 - too small
(D) 9/4(12) = 27 - perfect!
(E) 7/3(12) = 28 - too big

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, chetan2u, ArvindCrackVerbal, GMATGuruNY, GMATinsight
Can I say the 'numerator' has to be 'factor' or 'multiple' of 9 (if 9 is considered as total capacity of anything) in the correct choices?
Also, in the choices A, B, and C says: the capacity is a bit greater than that we add (n), but in choices D and E says: the capacity is a bit more than double that we add (n). Could you explain a bit what's going on the answer choices?
Thanks__

Asad

I don't find anything wrong with the option choices.

1) No, we can NOT say that numerator has to be a multiple of 9 because question doesn't mention that n is an Integer

2) when n is added to it when it was 1/3rd full confirms that the n is less than 2/3rd the capacity so all that we can conclude here is that n < (2/3) capacity i.e. capacity > 1.5n and using this we can eliminate Options A B and C. But to arrive at correct answer, we need to solve it as needed and that's not difficult in this question.

I hope this help

Hi,
As GMATinsight has also written, you cannot take the numerator to be 9.
Every capacity will have 7/9 of itself, even if it is fraction. This is different from saying 7/9 of an integer gives you another integer. Yes, here n will be multiple of 9.

Having said that, 1/3 should immediately tell you that it looks a bit like 7/9, so convert 1/3 to 3/9.
Now after adding n litres 3/9 goes to 7/9 or a jump of 4/9 of capacity.
That is n=(4/9) of capacity. Capacity=9n/4

Thanks for the feedback.
But, if we let the capacity is 9, then we can think of n+3=7 which says that n=4 (here n is not multiple of 9 ). Can you clarify where I've missed?

'Factor' and 'multiple' mean opposite things. 7 is a 'factor' of 35, while 35 is a 'multiple' of 7. You can't use those words interchangeably.

Yes, in this question, the number in the numerator of the right answer must be a factor of 9 (the above replies aren't correct on that point, or are answering a different question) but you need to solve almost the whole problem to see that, so I'm not sure there's any great advantage to the observation.

I don't understand your question about the answer choices: some answers (A, B and C) suggest n is more than half a tank, some (D and E) suggest n is less than half a tank. If you can see from the fractions in the question that n represents less than half a tank, you can get down to D or E, but seeing that takes about as much time as just solving the problem, and then you don't need to guess at all.

Yes, I am just talking about THIS specific question. My observation could not be correct in all cases, probably.

So far I know that GMAC does not make any any answer options randomly-they definitely have logic how they make answer option.
Choices D (9/4=2.something) and E (7/3=2.something) are more than 2 (apart from the value of n), but in choices A (10/9=1.something), B (4/3=1.something) and C (3/2=1.something). I've just curiosity why three answer options are a bit greater than 1 and the remaining two are greater than 2.


Yes, get it....
appreciating your help...

But why should n be a multiple of 9? You are taking the capacity to be 9, so how can anything less than 9 be a multiple of 9. n will of course be less than total capacity that is 9.

You are mixing up n and the capacity

Hi Asad,

This question can be solved relatively quickly in a couple of different ways, so it's really not necessary to try to think in terms of whether there's a quick, logical 'shortcut' to take advantage of.

We're told that 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. We're asked for the capacity of the tank, in terms of N, in liters. This question can be solved by TESTing VALUES.

Since the tank ends up 7/9 full, it would make sense to choose a value for the FULL TANK that is a multiple of 9. In this case, the easiest value would be 9 (note: this is NOT the value of N). We can now set up an equation and solve for N...

N + (1/3)(9) = (7/9)(9)
N + 3 = 7
N = 4

Thus, we're looking for an answer that equals 9 when N=4. There's only one answer that matches...

You might also approach this question Arithmatically. Since 1/3 = 3/9... and we know that adding N liters of fuel increases the tank from "3/9 full" to "7/9 full", those N liters represent an increase of 4/9 of a tank. So how many of those "Ns" would it take to completely fill an empty tank?

(9/9) / (4/9) = 9/4

GMAT assassins aren't born, they're made,
Rich

Hi,
Thanks for the explanation. I just wonder in what type of questions we can imagine a number like 9 you used here?
I feel afraid to use such numbers thinking that it might lead me to incorrect answers.

and how do I know that which is the best number to use. Like here may be I could use 3 or 10. How can I be sure that 9 will be the best?

Hi nazmulhasandu,

TESTing VALUES can be used to answer a variety of Quant questions on the GMAT (and can even be used on some rare CR prompts and in IR as well). When you say that you are 'afraid' to try that approach, can you go into more detail about what you mean? DID you actually try it on this question (and if you did, then what answer did you end up with).

When using this Tactic, you should think in terms of the information that the prompt gives you; in this question, we're told that the tank is "filled to 7/9 of its capacity".... so using a multiple of 9 for that total capacity would make sense. The simplest multiple of 9 is 9, but you don't have to use that number to correctly answer the question.

GMAT assassins aren't born, they're made,
Rich