Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 04 Jul 2010
Posts: 19

A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
11 Aug 2010, 13:17
3
This post received KUDOS
10
This post was BOOKMARKED
Question Stats:
57% (01:53) correct 43% (01:57) wrong based on 623 sessions
HideShow timer Statistics
A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway? A. 28 B. 30 C. 33 D. 36 E. 38
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 30 Mar 2012, 09:36, edited 1 time in total.
Edited the question and added the OA



Math Expert
Joined: 02 Sep 2009
Posts: 43828

Re: More Prep questions [#permalink]
Show Tags
11 Aug 2010, 16:56
6
This post received KUDOS
Expert's post
4
This post was BOOKMARKED
A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway? A. 28 B. 30 C. 33 D. 36 E. 38 Car averages x miles per gallon, means that 1 gallon is enough to drive x miles. We are asked to find average miles per gallon (miles/gallon) > average miles per gallon would be total miles driven divided by total gallons used (miles/gallon). Total miles driven is 10+50=60. As car averages 25 miles per gallon in the city for 10 miles in the city it will use 10/25=0.4 gallons; As car averages 40 miles per gallon on the highway for 50 miles on the highway it will use 50/40=1.25 gallons; So average miles per gallon equals to \(\frac{60}{0.4+1.25}\approx{36}\) Answer: D.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 12 Jul 2010
Posts: 60

Re: More Prep questions [#permalink]
Show Tags
19 Aug 2010, 22:37
Answer D
No of Miles per Gallon = Total no of miles/Total no of Gallons =10+50/(10/25+50/40) ~ 36.3



Current Student
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1914
Concentration: General Management, Nonprofit

Re: GMAT PREP PS [#permalink]
Show Tags
22 Aug 2010, 18:49
1
This post received KUDOS
Average miles per gallon is given by: Total distance traveled/Total gallons used.
Total distance traveled is given to us and is equal to 10+50 = 60 miles
Total gallons used can be determined by reverse working the formula listed above.
Number of gallons in the city = Total distance / Average = \(\frac{10}{25}\)
Number of gallons in the highway = Total distance / Average = \(\frac{50}{40}\)
Total number of gallons = Sum of the above two quantities.
So the average overall
\(\frac{60}{\frac{10}{25} + \frac{5}{4}} = \frac{60}{\frac{2}{5} + \frac{5}{4}} = \frac{60}{\frac{33}{20}} = \frac{1200}{33} = \frac{400}{11}\)
If you solve this you get 36.3636. So the answer is 36.



Manager
Joined: 21 Feb 2010
Posts: 205

Re: GMAT PREP PS [#permalink]
Show Tags
22 Aug 2010, 19:06
i got 36 too using the same method as whiplash2411 did.



Manager
Joined: 27 May 2010
Posts: 197

Re: GMAT PREP PS [#permalink]
Show Tags
22 Aug 2010, 19:22
10/25 => 2/5 gal
50/40 => 5/4 gal
Therefore the car travels 60 miles using 2/5 + 5/4
Calculating it gets 60/(33/20) => 36.36 miles/gal



Manager
Joined: 15 Apr 2010
Posts: 189

Re: Averages [#permalink]
Show Tags
14 Sep 2010, 01:23
D is closest to the correct decimal answer.... the way to solve is to find out total gallons of fuel used and total distance travelled. then divide the total distance 60 miles by X gallons.
to find X: we have 2 steps  10/25 = 0.40 gallons is for city driving; 50/40=1.25 is for highway driving.
hence final answer = 60/1.65 which comes out to be ~36mpg. hope this is clear...



Manager
Joined: 14 Feb 2011
Posts: 181

Re: Tough GMAT prep PS [#permalink]
Show Tags
19 Feb 2011, 10:01
For 10 miles, the fuel expended is 10/25 gallons = 0.4 gallons. Similarly for 50 miles it is 50/40 gallon = 1.25 gallons So for 60 miles total fuel spent is 1.65 gallons and hence average miles per gallon = 60/1.65 = ~36



Manager
Joined: 26 Jan 2012
Posts: 74

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
31 Dec 2012, 10:33
why does weighted average method fail? answer is 37.5 miles/hr. Please explain



Intern
Joined: 21 Mar 2009
Posts: 20

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
31 Dec 2012, 10:45
ketanth wrote: why does weighted average method fail? answer is 37.5 miles/hr. Please explain Your question on weighted avergae is not clear. You need to find out the fractions summing up to 1, thats the basic requirement, which is not applicable here. See my soln, and let me know if you have any question: Km/Gallon Km Gallon neded City 25 10 10/25 = 2/5 Highway 40 50 50/40 = 5/4 Total 60 (8+25)/20 = 33/20 Mileage as asked = Total Km/Total Gallon = 60/(33/20) = 60*20/33 = 400/11 approx 38



Manager
Joined: 26 Jan 2012
Posts: 74

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
31 Dec 2012, 18:34
maibhihun wrote: ketanth wrote: why does weighted average method fail? answer is 37.5 miles/hr. Please explain Your question on weighted avergae is not clear. You need to find out the fractions summing up to 1, thats the basic requirement, which is not applicable here. See my soln, and let me know if you have any question: Km/Gallon Km Gallon neded City 25 10 10/25 = 2/5 Highway 40 50 50/40 = 5/4 Total 60 (8+25)/20 = 33/20 Mileage as asked = Total Km/Total Gallon = 60/(33/20) = 60*20/33 = 400/11 approx 38 Why cant we do the weighted average method: (25X10+40X50)/(50+10) = 37,5 km/gallon I understand your logic. I am trying to understand why weighted average method logic is false.



Current Student
Joined: 14 May 2012
Posts: 75
Location: United States
Concentration: Finance, Strategy
GPA: 3.8
WE: Corporate Finance (Venture Capital)

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
07 Jun 2013, 22:46
Bunnel can you comment on this
Total gallons consumed = 25*10 + 40*50 = 2250 Total miles driven = 50
Avg Mileage in MPG = 2250/50 = 37.5 .. hence close to 38. I picked E pls help me understand



Math Expert
Joined: 02 Sep 2009
Posts: 43828

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
08 Jun 2013, 03:12



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
15 Aug 2013, 11:27
A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
Average miles/gallon = total distance / total fuel consumption Avg = (10+50) / (2/5 + 5/4) Avg = 60 / (8/20 + 25/20) Avg = 60 / (33/20) Avg = 38 miles/gallon
ANSWER: E. 38



Senior Manager
Joined: 10 Jul 2013
Posts: 324

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
15 Aug 2013, 12:21
leafsrule99 wrote: A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
A. 28 B. 30 C. 33 D. 36 E. 38 miles per gallon = 60/(10/25+50/40) = D
_________________
Asif vai.....



Manager
Joined: 10 Feb 2014
Posts: 116

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
09 Apr 2014, 11:59
1
This post received KUDOS
ketanth wrote: maibhihun wrote: ketanth wrote: why does weighted average method fail? answer is 37.5 miles/hr. Please explain Your question on weighted avergae is not clear. You need to find out the fractions summing up to 1, thats the basic requirement, which is not applicable here. See my soln, and let me know if you have any question: Km/Gallon Km Gallon neded City 25 10 10/25 = 2/5 Highway 40 50 50/40 = 5/4 Total 60 (8+25)/20 = 33/20 Mileage as asked = Total Km/Total Gallon = 60/(33/20) = 60*20/33 = 400/11 approx 38 Why cant we do the weighted average method: (25X10+40X50)/(50+10) = 37,5 km/gallon I understand your logic. I am trying to understand why weighted average method logic is false. Weighted average: (n1A1+n2A2+...nxAx)/(n1+n2+...nx) for x terms. Units of n1,n2...nx should be the same as the UNITS W.R.T. which values of A1,A2...Ax are defined as rates. E.G. If Ax represents concentration in a mixture as gm/litre, units of nx should be litre and NOT gms. In the question under consideration, we have rates defined as miles/gallon, so units of nx will be in gallons NOT miles as is give in the question. To illustrate: City journey will consume: 0.4 gallons (as calculated in earlier posts) Highway journey will consume: 1.25 gallons (''"""") Hence by weighted average formula we have: Average consumption = (0.4*25+1.25*40)/(0.4+1.25)=60/1.65=36.363636....



Intern
Joined: 10 Apr 2014
Posts: 33

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
10 Apr 2014, 13:29
3
This post received KUDOS
ketanth wrote: maibhihun wrote: ketanth wrote: why does weighted average method fail? answer is 37.5 miles/hr. Please explain Your question on weighted avergae is not clear. You need to find out the fractions summing up to 1, thats the basic requirement, which is not applicable here. See my soln, and let me know if you have any question: Km/Gallon Km Gallon neded City 25 10 10/25 = 2/5 Highway 40 50 50/40 = 5/4 Total 60 (8+25)/20 = 33/20 Mileage as asked = Total Km/Total Gallon = 60/(33/20) = 60*20/33 = 400/11 approx 38 Why cant we do the weighted average method: (25X10+40X50)/(50+10) = 37,5 km/gallon I understand your logic. I am trying to understand why weighted average method logic is false. Weighted average: (n1A1+n2A2+...nxAx)/(n1+n2+...nx) for x terms. Units of n1,n2...nx should be the same as the UNITS W.R.T. which values of A1,A2...Ax are defined as rates. E.G. If Ax represents concentration in a mixture as gm/litre, units of nx should be litre and NOT gms. In the question under consideration, we have rates defined as miles/gallon, so units of nx will be in gallons NOT miles as is give in the question. To illustrate: City journey will consume: 0.4 gallons (as calculated in earlier posts) Highway journey will consume: 1.25 gallons (''"""") Hence by weighted average formula we have: Average consumption = (0.4*25+1.25*40)/(0.4+1.25)=60/1.65=36.363636....[/quote] Agreed. Or in other words, you can say that for weighted average you need to use gallons/mile as the weights are miles so average gallons per mile would be = (10*(1/25)+ 50*(1/40))/(10+50) = (10/25+50/40)/60 To get avg. miles/gallon we need to reverse the equation and we get 60/(10/25+50/40)...same as what you calculated by 1st method.



Manager
Joined: 10 Feb 2014
Posts: 116

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
14 Apr 2014, 01:28
Yes, that's absolutely correct!!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7942
Location: Pune, India

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
05 Feb 2015, 20:30
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Quote: A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
A. 28 B. 30 C. 33 D. 36 E. 38
I do not understand why weighted average method fails here.
Methods don't fail. You might need to manipulate them in particular circumstances. You need to understand that whatever is given cannot be the weight. For example, when trying to find the average profit, the weight must be cost price, not number of items or selling price. Similarly, when calculating average speed, weight must be time, not distance. In the same way, here the weight must be amount of fuel used, not distance traveled. How do you figure out what the weight will be in each case? The units help you in figuring that out. Check: http://www.veritasprep.com/blog/2014/12 ... averages/
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Retired Moderator
Joined: 12 Aug 2015
Posts: 2420
GRE 1: 323 Q169 V154

Re: A certain car averages 25 miles per gallon when driving in [#permalink]
Show Tags
04 Dec 2016, 02:06
Excellent Question. Here is what i did in this one => Given Data => 10 miles in city and 50 miles on highway In the City => Gas => \(\frac{1}{25}*10\)=> 0.4 Gallons On the highway => Gas => \(\frac{1}{40}*50\)=> 1.25Gallons Total Gas => 0.4+1.25=>1.65Gallons Total Distance =>10+50=>60miles
So the Car used 1.65Gallons fro 60Miles Average => \(\frac{60}{1.65}=> 60*\frac{100}{165}\)=>36 Approx Hence C
_________________
Getting into HOLLYWOOD with an MBA Stone Cold's Mock Tests for GMATQuant(700+)




Re: A certain car averages 25 miles per gallon when driving in
[#permalink]
04 Dec 2016, 02:06



Go to page
1 2
Next
[ 23 posts ]



