GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 04 Aug 2020, 03:59 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # When n liters of fuel was added to a tank that was already 1/3 full

Author Message
TAGS:

### Hide Tags

Manager  Joined: 14 Dec 2010
Posts: 104
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 680 Q44 V39

### Show Tags

3
44 00:00

Difficulty:   5% (low)

Question Stats: 90% (01:24) correct 10% (02:05) wrong based on 1761 sessions

### HideShow timer Statistics

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. $$\frac{10}{9} n$$

B. $$\frac{4}{3} n$$

C. $$\frac{3}{2} n$$

D. $$\frac{9}{4} n$$

E. $$\frac{7}{3}n$$
Math Expert V
Joined: 02 Sep 2009
Posts: 65785
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

7
3
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.

_________________
Senior Manager  Joined: 28 Jun 2009
Posts: 339
Location: United States (MA)
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

9
3

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
##### General Discussion
Manager  Joined: 27 May 2008
Posts: 97
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

1
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.
Math Expert V
Joined: 02 Sep 2009
Posts: 65785
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

1
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.
_________________
Manager  B
Joined: 25 Jun 2016
Posts: 60
GMAT 1: 780 Q51 V46
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

7
1
Here are a couple of video explanations for this question.

Algebra:

Value Substitution:

VP  D
Joined: 07 Dec 2014
Posts: 1260
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

1
let capacity=9/9
9/9-3/9-2/9=4/9=n
(9/9)/(4/9)=9/4
capacity=9/4 n
Senior Manager  S
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 381
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

1
Top Contributor
1
What if :
7/9-1-3 = n
=>, 4/9 capacity = n
so full capacity = 9n/4
Ans. D
_________________
Intern  B
Joined: 20 Apr 2015
Posts: 20
GPA: 3.9
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

1
2
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.
Manager  S
Joined: 19 Jan 2018
Posts: 101
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

1
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

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

Manhattan Prep Instructor G
Joined: 04 Dec 2015
Posts: 948
GMAT 1: 790 Q51 V49 GRE 1: Q170 V170
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

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

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
_________________ Chelsey Cooley | Manhattan Prep | Online tutoring and curriculum

My latest GMAT blog posts | My latest GRE blog posts | Suggestions for blog articles are always welcome!
SVP  V
Joined: 23 Feb 2015
Posts: 2005
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

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

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__
GMAT Club Legend  V
Status: GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator l A learner forever :)
Joined: 08 Jul 2010
Posts: 4512
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

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

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__

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
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Math Expert V
Joined: 02 Aug 2009
Posts: 8792
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

1
1
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

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__

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
_________________
SVP  V
Joined: 23 Feb 2015
Posts: 2005
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

chetan2u wrote:
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

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__

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?
GMAT Tutor P
Joined: 24 Jun 2008
Posts: 2393
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

1
1
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?

'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.
_________________
GMAT Tutor in Montreal

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
SVP  V
Joined: 23 Feb 2015
Posts: 2005
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

IanStewart wrote:
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.

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

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.

IanStewart wrote:
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, get it....
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 6505
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

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

let total capacity of tank be 27
so when n liters was added tank was already 1/3rd full ; ie 9 liters
and tank was filled to 7/9 * 27 ; 21 liters
so value of n is 21-9 ; 12 liters
with option D we get ; 9/4 * 12 = 27 ( total capacity of tank)
Math Expert V
Joined: 02 Aug 2009
Posts: 8792
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

chetan2u wrote:
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

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__

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?

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
_________________
SVP  V
Joined: 23 Feb 2015
Posts: 2005
Re: When n liters of fuel was added to a tank that was already 1/3 full  [#permalink]

### Show Tags

chetan2u wrote:
chetan2u wrote:

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?

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

Actually i raised this question for the highlighted part. You said Yes, here n will be multiple of 9.. I don't know why did you say Yes, here n will be multiple of 9. It gets me confused Thanks chetan2u Re: When n liters of fuel was added to a tank that was already 1/3 full   [#permalink] 08 May 2020, 06:04

Go to page    1   2    Next  [ 22 posts ]

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