Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 Sep 2014, 07:57

### 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

Author Message
TAGS:
Intern
Joined: 26 Jul 2010
Posts: 24
Followers: 0

Kudos [?]: 15 [0], given: 8

A certain car traveled twice as many miles from Town A [#permalink]  27 Jan 2011, 15:35
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

62% (02:22) correct 38% (01:01) wrong based on 82 sessions
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?

13
13.5
14
14.5
15

Can some one help me solve this problem using weighted averages? Why cannot we use gallons as weights? Thanks.

Source: GMAT club problem
[Reveal] Spoiler: OA
 Kaplan Promo Code Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes
Math Expert
Joined: 02 Sep 2009
Posts: 23484
Followers: 3500

Kudos [?]: 26434 [3] , given: 2712

Re: Weighted Averages [#permalink]  27 Jan 2011, 16:28
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
pgmat 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?

13
13.5
14
14.5
15

Can some one help me solve this problem using weighted averages? Why cannot we use gallons as weights? Thanks.

Source: GMAT club problem

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.

Now, weighted \ average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2} and as we are asked to determine average miles per gallon then exactly miles per gallon should be the weights and gallons used for 1st and 2nd parts of the trip should be the values, so in this case the weighted average formula will give the same expression as the one above.

Hope it's clear.

P.S.
 ! Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/No posting of PS/DS questions is allowed in the main Math forum.

_________________
Intern
Joined: 26 Jul 2010
Posts: 24
Followers: 0

Kudos [?]: 15 [0], given: 8

Re: Weighted Averages [#permalink]  27 Jan 2011, 17:07
excellent explanation. Thank you.
Director
Joined: 21 Dec 2010
Posts: 658
Followers: 10

Kudos [?]: 81 [1] , given: 51

Re: Weighted Averages [#permalink]  27 Jan 2011, 23:02
1
KUDOS
yes thats fairly simple. the formula for avg. rate of the two rates r1 and r2 is avg= (2r1*r2)/(r1+r2). apply this to anything, speed , work done, mileage , provided the work done using the two rates is the same.
_________________

What is of supreme importance in war is to attack the enemy's strategy.

Senior Manager
Joined: 08 Nov 2010
Posts: 422
Followers: 7

Kudos [?]: 34 [0], given: 161

Re: Weighted Averages [#permalink]  29 Jan 2011, 09:10
good job. thanks for that. i like these kind of questions.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4777
Location: Pune, India
Followers: 1116

Kudos [?]: 5065 [3] , given: 164

Re: Weighted Averages [#permalink]  29 Jan 2011, 19:58
3
KUDOS
Expert's post
pgmat 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?

13
13.5
14
14.5
15

Can some one help me solve this problem using weighted averages? Why cannot we use gallons as weights? Thanks.

Source: GMAT club problem

Note: Whenever you are confused what the weights should be (e.g. here should the weights be the distance traveled 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)

Food for thought: If I sold 10 apples at a profit of 10% and 15 oranges at a profit of 20%, what was my overall profit%?
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Manager Status: Do till 740 :) Joined: 13 Jun 2011 Posts: 105 Concentration: Strategy, General Management GMAT 1: 460 Q35 V20 GPA: 3.6 WE: Consulting (Computer Software) Followers: 0 Kudos [?]: 6 [0], given: 18 Re: Weighted Averages [#permalink] 15 Jan 2012, 06:29 Karishma, Why is this not working ? 12*(2/3) + 18 *(1/3) /1 14?? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4777 Location: Pune, India Followers: 1116 Kudos [?]: 5065 [0], given: 164 Re: Weighted Averages [#permalink] 15 Jan 2012, 23:59 Expert's post shankar245 wrote: Karishma, Why is this not working ? 12*(2/3) + 18 *(1/3) /1 14?? We need to find the average miles per gallon. Average miles/gallon = Total miles/Total gallons What is the distance travelled (i.e. 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. 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) Go back to my post above. It explains that you have to be mindful of how to use weighted averages. 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. If we change the question and make it: A certain car used twice as many gallons 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*(2/3) + 18 *(1/3)/1 I hope it makes sense now. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Status: Do till 740 :)
Joined: 13 Jun 2011
Posts: 105
Concentration: Strategy, General Management
GMAT 1: 460 Q35 V20
GPA: 3.6
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 6 [0], given: 18

Re: A certain car traveled twice as many miles from Town A [#permalink]  16 Jan 2012, 09:41
Thanks karishma..
Guess to excel in gmat you need pay attention to every single word in the question before jumpin on answer it
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 20 [0], given: 1

Re: A certain car traveled twice as many miles from Town A [#permalink]  17 Jan 2012, 04:24
Ans is B
Given d_ab = 2*d_bc
let d_ab = d and d_bc = x so d=2x

for average miles per gallon = (d+x)/((d/12)+(x/18)) = 13.5 (formula avg speed = total distance/ total time)
Intern
Joined: 06 Apr 2012
Posts: 1
GMAT Date: 09-01-2012
Followers: 0

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

Re: A certain car traveled twice as many miles from Town A [#permalink]  26 Dec 2012, 08:46
How about using a plugin techenique?
since we have the car gas milages (miles/gallon) are 12mpg and 18 mpg
LCM of 12 and 18=36
Let's say distance between B and C is 36 miles
Distance between A and B =72
So for traveling from A to B , the required gallons of gas is =72 miles/(12 miles per gallon)=6 gallons ( note : cancell the miles)
For travelling from B to C, the required gallons of gas is = 36 miles/ ( 18 miles per gallon) = 2 gallons
therefore avg miles per gallon for the total trip is = (total distance)/(total gallons) = (36+72) miles/(8) gallons = 108/8=13.5 miles per gallon.
Re: A certain car traveled twice as many miles from Town A   [#permalink] 26 Dec 2012, 08:46
Similar topics Replies Last post
Similar
Topics:
4 A car travels from Town A to Town B at an average speed 2 05 Jan 2013, 17:08
10 A certain car traveled twice as many miles from Town A 8 21 Feb 2012, 13:58
A car traveled 75% of the way from town A to town B by 2 26 Apr 2007, 06:11
A car travelled 75% of the way from town X to town Y at a 3 04 Jun 2005, 14:57
a car traveled 75% of the way from town A to town B by 2 26 Feb 2005, 08:22
Display posts from previous: Sort by