It is currently 18 Oct 2017, 12:17

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A certain car traveled twice as many miles from Town A

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 17 Jan 2012
Posts: 41

Kudos [?]: 194 [1], given: 16

GMAT 1: 610 Q43 V31
A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

21 Feb 2012, 14:58
1
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:38) correct 37% (01:33) wrong based on 265 sessions

### HideShow timer Statistics

A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?

A. 13
B. 13.5
C. 14
D. 14.5
E. 15

MGMAT 1 Q. 11
The explanation given is unclear to me, why weightage ave is not right to apply here? I want to understand conceptually. Can someone help!
[Reveal] Spoiler: OA

Kudos [?]: 194 [1], given: 16

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128753 [1], given: 12182

Re: A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

21 Feb 2012, 15:15
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
docabuzar wrote:
A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?

A. 13
B. 13.5
C. 14
D. 14.5
E. 15

MGMAT 1 Q. 11
The explanation given is unclear to me, why weightage ave is not right to apply here? I want to understand conceptually. Can someone help!

Average miles per gallon equals to total miles covered/total gallons used (miles/gallons), so if the distance from A to B is $$2x$$ miles and from B to C is $$x$$ miles then we'll have:
$$average \ miles \ per \ gallon=\frac{total \ miles \ covered}{total \ gallons \ used}=\frac{2x+x}{\frac{2x}{12}+\frac{x}{18}}=\frac{3x}{\frac{2x}{9}}=13.5$$.

P.S. As you can see weighted average concept is exactly what we used here.

Hope it's clear.
_________________

Kudos [?]: 128753 [1], given: 12182

Manager
Joined: 10 Jan 2010
Posts: 182

Kudos [?]: 31 [3], given: 7

Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GPA: 3
WE: Consulting (Telecommunications)
Re: A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

21 Feb 2012, 15:40
3
KUDOS
Lets pick numbers:

Distance A to B: 36 miles (2x) --> 3 gallons
Distance B to C: 18 miles (x) --> 1 gallon

Average: $$\frac{(36+18)}{4}$$ = 13.5

Hence, B

Kudos [?]: 31 [3], given: 7

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17349 [2], given: 232

Location: Pune, India
Re: A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

21 Feb 2012, 21:58
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
docabuzar wrote:
A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?

A. 13
B. 13.5
C. 14
D. 14.5
E. 15

MGMAT 1 Q. 11
The explanation given is unclear to me, why weightage ave is not right to apply here? I want to understand conceptually. Can someone help!

If the concept you do not understand is why (12*2 + 18*1)/3 doesn't work, here you go:

'Distances traveled' (i.e. ratio of 2:1) cannot be the weights here to find the average mileage. The weights have to be 'number of gallons'.

If we change the question and make it:
A certain car used [highlight]twice as many gallons[/highlight] from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?

Now you can use (12*2 + 18 *1)/3

Why?

Whenever you are confused what the weights should be (e.g. here should the weights be the distance traveled or should they be gallons of fuel used...), look at the units.

Average required is $$\frac{miles}{gallon}$$. So you are trying to find the weighted average of two quantities whose units must be $$\frac{miles}{gallon}$$.

$$C_{avg} = \frac{C_1*W_1 + C_2*W_2}{{W_1 + W_2}}$$

$$C_{avg}, C_1, C_2 - \frac{miles}{gallon}$$

So $$W_1$$ and $$W_2$$ should be in gallon to get:

$$\frac{miles}{gallon} = (\frac{miles}{gallon}*gallon + \frac{miles}{gallon}*gallon)/(gallon + gallon)$$

Only if weights are in gallons, do we get 'Total miles' in the numerator and 'Total gallons' in the denominator.

We know that Average miles/gallon = Total miles/Total gallons

[highlight]Takeaway: The weights have to be the denominator units of the average.[/highlight]

So what do we do in this question?

What is the distance travelled (i.e.total miles)?
"traveled twice as many miles from Town A to Town B as it did from Town B to Town C"
We know that the ratio of the two distances must be 2:1 or we can say the distances must be 2d and d. Total distance must be (2d + d)

What is the total gallons used?
Fuel used to go from A to B = 2d/12
Fuel used to go from B to C = d/18

So Average miles/gallon = (2d + d)/(2d/12 + d/18)

You need to know what the weights are going to be. Here, weights have to be the amount of fuel used i.e. in gallons because you are looking for average miles per gallon.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17349 [2], given: 232 Intern Joined: 17 Jan 2012 Posts: 41 Kudos [?]: 194 [0], given: 16 GMAT 1: 610 Q43 V31 Re: A certain car traveled twice as many miles from Town A [#permalink] ### Show Tags 22 Feb 2012, 04:10 Many Thanks. Just to make myself clearer, we can also say that: Case 1. Car moves A to B @ 12mph and covers 2 miles B to C @ 18 mph and covers 1 mile We want to know the total ave speed, we cant use Weighted averages : (12x2 + 18x1)/3 = 14 mph because the 2 quaintities i.e. Speed units denominator (i.e. hours) does not match with Distance denominator (i.e. nothing). Case 2. Car moves A to B @ 12mph for 2 hrs B to C @ 18 mph for 1 hr We want to know the total ave speed, we can use Weighted averages : (12x2 + 18x1)/3 = 14 mph But in case 2 the units denominators donot match, speed is mph & time is h? What I m missing here! Kudos [?]: 194 [0], given: 16 Math Expert Joined: 02 Sep 2009 Posts: 41886 Kudos [?]: 128753 [0], given: 12182 Re: A certain car traveled twice as many miles from Town A [#permalink] ### Show Tags 22 Feb 2012, 04:50 docabuzar wrote: Many Thanks. Just to make myself clearer, we can also say that: Case 1. Car moves A to B @ 12mph and covers 2 miles B to C @ 18 mph and covers 1 mile We want to know the total ave speed, we cant use Weighted averages : (12x2 + 18x1)/3 = 14 mph because the 2 quaintities i.e. Speed units denominator (i.e. hours) does not match with Distance denominator (i.e. nothing). Case 2. Car moves A to B @ 12mph for 2 hrs B to C @ 18 mph for 1 hr We want to know the total ave speed, we can use Weighted averages : (12x2 + 18x1)/3 = 14 mph But in case 2 the units denominators donot match, speed is mph & time is h? What I m missing here! I think that the issue was over complicated above: {average rate}={total distance}/{total time}; {average salary}={total salary}/{total # of employees}; {average miles per gallon}={total miles}/{total gallons}; ... Keep it simple. _________________ Kudos [?]: 128753 [0], given: 12182 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7674 Kudos [?]: 17349 [0], given: 232 Location: Pune, India Re: A certain car traveled twice as many miles from Town A [#permalink] ### Show Tags 22 Feb 2012, 05:30 docabuzar wrote: Many Thanks. Just to make myself clearer, we can also say that: Case 1. Car moves A to B @ 12mph and covers 2 miles B to C @ 18 mph and covers 1 mile We want to know the total ave speed, we cant use Weighted averages : (12x2 + 18x1)/3 = 14 mph because the 2 quaintities i.e. Speed units denominator (i.e. hours) does not match with Distance denominator (i.e. nothing). Case 2. Car moves A to B @ 12mph for 2 hrs B to C @ 18 mph for 1 hr We want to know the total ave speed, we can use Weighted averages : (12x2 + 18x1)/3 = 14 mph But in case 2 the units denominators donot match, speed is mph & time is h? What I m missing here! You are right. Case 1 doesn't work but case 2 does. What is the unit of the denominator in average speed? Average speed = miles/hour. So you can use weighted averages when the weights are time (i.e. in hours). That is the reason your case 2 works. (By the way, you yourself said speed is miles/hour and time is in hours. Why do you think the units don't match?) When you want to find weighted average speed, distance cannot be the weights, it has to be time. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 17349 [0], given: 232

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128753 [0], given: 12182

Re: A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

26 May 2013, 05:47
Bumping for review and further discussion.
_________________

Kudos [?]: 128753 [0], given: 12182

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16702

Kudos [?]: 273 [0], given: 0

Re: A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

25 Jul 2014, 08:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

BSchool Forum Moderator
Status: I Declare War!!!
Joined: 02 Apr 2014
Posts: 258

Kudos [?]: 96 [0], given: 546

Location: United States
Concentration: Finance, Economics
GMAT Date: 03-18-2015
WE: Asset Management (Investment Banking)
Re: A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

15 Feb 2015, 15:43
Hello Experts!
I am quiet fascinated with The Bunuel approach... of using algebraic expression.
Kindly assess my approach which I will try next time onward to got a shortcut way
step 1) took LCM of 12 and 18.. came as 36. just multiplied by 10...(to make easy calculation)
step 2) 360 distance between B to C... do 360/18 hence 20 gallons used
step 3) twice distance.. hence 360*2= 720... do as above.. 720/12= 60 gallons used
step 4) total gallons.. 20+60= 80 gallons
step ) total miles= 360+720= 1080 miles
hence.. average of whole journey = 1080/80 which comes to 13.5
Thanks
Celestial

Kudos if it makes sense...

Kudos [?]: 96 [0], given: 546

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16702

Kudos [?]: 273 [0], given: 0

Re: A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

06 May 2016, 14:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

BSchool Forum Moderator
Status: I Declare War!!!
Joined: 02 Apr 2014
Posts: 258

Kudos [?]: 96 [0], given: 546

Location: United States
Concentration: Finance, Economics
GMAT Date: 03-18-2015
WE: Asset Management (Investment Banking)
Re: A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

12 Aug 2016, 17:13
Hi!
Kindly share your views on my above approach plz..
experts...
thanks

Kudos [?]: 96 [0], given: 546

Intern
Joined: 06 Jan 2015
Posts: 12

Kudos [?]: 1 [0], given: 4

Re: A certain car traveled twice as many miles from Town A [#permalink]

### Show Tags

15 Aug 2016, 00:57
Celestial09 wrote:
Hello Experts!
I am quiet fascinated with The Bunuel approach... of using algebraic expression.
Kindly assess my approach which I will try next time onward to got a shortcut way
step 1) took LCM of 12 and 18.. came as 36. just multiplied by 10...(to make easy calculation)
step 2) 360 distance between B to C... do 360/18 hence 20 gallons used
step 3) twice distance.. hence 360*2= 720... do as above.. 720/12= 60 gallons used
step 4) total gallons.. 20+60= 80 gallons
step ) total miles= 360+720= 1080 miles
hence.. average of whole journey = 1080/80 which comes to 13.5
Thanks
Celestial

Kudos if it makes sense...

While you approach is not wrong, you have made lots of double and tedious calculations which is quite time consuming. You can do it without multiplying by 10

You got LCM 36. so we will considered total miles traveled under 18 Miles/gallon to be 36. Hence it took 2 gallons
Now, the distance traveled under 12M/ Gallon will be 72 and total gallons used will be 6.

therefore no. of gallons used traveling both route = 2+6 -= 8 and
total miles traveled is 36+72 = 108.

average = 108/8= 13.5 M/Gallon

its much more easier than you steps, which include unnecessary multiplication and double division. Its quite time consuming in GMAT.

Kudos [?]: 1 [0], given: 4

Re: A certain car traveled twice as many miles from Town A   [#permalink] 15 Aug 2016, 00:57
Display posts from previous: Sort by

# A certain car traveled twice as many miles from Town A

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.