Rate and average Problem

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Kaunteya: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Mon Jan 28, 2008 4:12 pm; Location: Montreal, Canada; Thanked: 2 times

Rate and average Problem

by Kaunteya » Mon Mar 03, 2008 11:47 am

A car averages 25 mpg in the city and 40 mpg on the highway. According to these rates which of the following is the closest to the number of mpg that the car averages when it drives 10 miles in the city and 50 miles on the highway.

a. 28
b. 30
c. 33
d. 36
e. 38

In the city the car used 10/25 gallons of gas (2/5) and on the highway it used 5/4 gallons. Added together you get 8/5 gallons used over the total 60 miles journey. Then to figure out the mpq divide the total miles driven (60) by the total gas consumed (8/5). Now you get 300/8. This is equal to 37.5. Why then is the answer 36 and not 38. Why was the 37.5 mpg not rounded up to 38 but down 1.5 mpg to 36? Are you not to round up?? I don't know, help please.

Kaunteya

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Source: Beat The GMAT — Problem Solving | Mon Mar 03, 2008 11:47 am

rajmirra: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Tue Jan 08, 2008 10:40 am; Location: Canada; Thanked: 4 times

Re: Rate and average Problem

by rajmirra » Mon Mar 03, 2008 12:02 pm

Kaunteya wrote:A car averages 25 mpg in the city and 40 mpg on the highway. According to these rates which of the following is the closest to the number of mpg that the car averages when it drives 10 miles in the city and 50 miles on the highway.

a. 28
b. 30
c. 33
d. 36
e. 38

In the city the car used 10/25 gallons of gas (2/5) and on the highway it used 5/4 gallons. Added together you get 8/5 gallons used over the total 60 miles journey. Then to figure out the mpq divide the total miles driven (60) by the total gas consumed (8/5). Now you get 300/8. This is equal to 37.5. Why then is the answer 36 and not 38. Why was the 37.5 mpg not rounded up to 38 but down 1.5 mpg to 36? Are you not to round up?? I don't know, help please.

Kaunteya

The Car's mileage within the city is 25 Miles/Gallon and on HWY is 40 Miles/Gallon.

The car was driven 10 miles within the city. So the gas required is 1/25 * 10 = 0.4 gallon ( i.e To drive 25 miles 1 gallon is required, so to drive 10 miles 0.4 gallon is required)

Similarly to drive 50 miles on the Hwy at the rate of 40 Miles/gallon 1.25 gallons of gas is required.

Average Mileage is Total distance travelled/ Total gas used

This implies 10 + 50/ 0.4+1.25 = 60/1.65 = 36.33. If you approximate it is 36MPG.

Last edited by rajmirra on Mon Mar 03, 2008 12:18 pm, edited 1 time in total.

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Kaunteya: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Mon Jan 28, 2008 4:12 pm; Location: Montreal, Canada; Thanked: 2 times

by Kaunteya » Mon Mar 03, 2008 12:09 pm

I am a retard. 8 + 25 is 33 not 32. AHHHHHH.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: Rate and average Problem

by Stuart@KaplanGMAT » Mon Mar 03, 2008 12:14 pm

Kaunteya wrote:A car averages 25 mpg in the city and 40 mpg on the highway. According to these rates which of the following is the closest to the number of mpg that the car averages when it drives 10 miles in the city and 50 miles on the highway.

a. 28
b. 30
c. 33
d. 36
e. 38

In the city the car used 10/25 gallons of gas (2/5) and on the highway it used 5/4 gallons. Added together you get 8/5 gallons used over the total 60 miles journey. Then to figure out the mpq divide the total miles driven (60) by the total gas consumed (8/5). Now you get 300/8. This is equal to 37.5. Why then is the answer 36 and not 38. Why was the 37.5 mpg not rounded up to 38 but down 1.5 mpg to 36? Are you not to round up?? I don't know, help please.

Kaunteya

Rajmirra's approach is 100% correct (with a little typo - the numerator should be 10 + 50, not 10 + 40, but the correct numerator "60" is in the next part).

The problem with your solution is your addition of fractions.

2/5 + 5/4 = (8 + 25)/20 = 33/20 which does not equal 8/5.

60/(33/20) = 60*20/33 = 400/11 = a bit more than 36.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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rajmirra: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Tue Jan 08, 2008 10:40 am; Location: Canada; Thanked: 4 times

by rajmirra » Mon Mar 03, 2008 12:17 pm

Thanks Stuart for pointing the typo. I have corrected it.

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igo8: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Dec 12, 2006 11:58 am

Rounding up....

by igo8 » Wed Mar 12, 2008 3:29 pm

129- On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gas, rounded to the nearest gallon. The actual number of miles per gallon that Cindy’s car got on this trip must have been between

a) 290/12.5 and 290/11.4
b) 295/12 and 284/11.4
c) 284/12 and 295/12
d) 284/12.5 and 295/11.4
e) 295/12.5 and 284/11.4

The answer says it is D, but that doesn't make sense if you actually round up since 12.5 would go to 13 rounded to the nearest mile and 295 would go 300 if rounded to the nearest 10 miles. Are you not to round up in the GMAT when it is 5???

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camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 am; Location: India; Thanked: 34 times; Followed by:5 members

Re: Rounding up....

by camitava » Wed Mar 12, 2008 8:18 pm

igo8 wrote:129- On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gas, rounded to the nearest gallon. The actual number of miles per gallon that Cindy’s car got on this trip must have been between

a) 290/12.5 and 290/11.4
b) 295/12 and 284/11.4
c) 284/12 and 295/12
d) 284/12.5 and 295/11.4
e) 295/12.5 and 284/11.4

The answer says it is D, but that doesn't make sense if you actually round up since 12.5 would go to 13 rounded to the nearest mile and 295 would go 300 if rounded to the nearest 10 miles. Are you not to round up in the GMAT when it is 5???

Refer the post - https://www.beatthegmat.com/question-ps1 ... t%20gallon

Again, igo8 its a request to post different Qs in different post.

Correct me If I am wrong

Regards,

Amitava