Miles and gallons

Expert replies

metallicafan: Master | Next Rank: 500 Posts; Posts: 142; Joined: Sun Jun 12, 2011 7:55 amFollowed by: 3 members; Thanked: 5 times

by metallicafan » Fri Jan 04, 2013 8:44 am

Andrew drove his truck 100 miles, rounded to the nearest 10 miles, and used 10 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Tom's truck got on this vacation trip must have been between

A. 100/10.5 and 100/9.5

B. 95/10.5 and 105/9.5

C. 95/9.5 and 105/10.5

D. 105/10 and 95/9.5

E. 105/10.5 and 95/9.5

OA is B.

In the correct answer, I don't understand why the upper limit for gallons is 10.5. If it is 10.5, that number would be rounded to eleven.
The same with the upper limit for milles. If it is 105, that number would be rounded to 110.

Like this post

Source: Beat The GMAT — Problem Solving | Fri Jan 04, 2013 8:44 am

gander123: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Tue Sep 25, 2012 12:47 amFollowed by: 1 member; Thanked: 3 times

by gander123 » Fri Jan 04, 2013 10:18 am

Hey metalli,

Agree with you, I also boiled down the problem to the following:

x: number of miles driven
y: number of gallons consumed

x/y miles per gallon

95<= X <= 104

9.5<= Y <= 10.4

Thus, 95/10.4 <= x/y <= 104/9.5.

The only plausible solution left would have been B. However, I understand your point.
Let's wait for an expert

.

Brgds,

Tobi

Like this post

GMAT/MBA Expert

Whitney Garner: GMAT Instructor; Posts: 273; Joined: Tue Sep 21, 2010 5:37 amFollowed by: 74 members; Location: Durham, NC; Thanked: 154 times; GMAT Score:770

by Whitney Garner » Fri Jan 04, 2013 11:18 am

metallicafan wrote:In the correct answer, I don't understand why the upper limit for gallons is 10.5. If it is 10.5, that number would be rounded to eleven.
The same with the upper limit for milles. If it is 105, that number would be rounded to 110.

This is a great question metallicafan!

I think the thing you want to think about is the fact that decimals can get smaller and smaller and smaller (and closer and closer and closer to 10.5 without actually getting there). What I mean is the following:

Any number that is even infinitesimally smaller than 10.5 would round down (e.g. 10.49999999999999999999). This means that there are actually an infinite number of numbers that are larger than 10.4 but still smaller than 10.5. So the best way to represent this range is to just say that the highest possible value is infinitely close to 10.5 without actually equaling 10.5 (but how do we write that?? we don't, so we just say that is had to be smaller than 10.5!)

The same would be true for the 105 limit. So the actual ranges would be the following:

x: number of miles driven
y: number of gallons consumed

x/y miles per gallon

95<= X < 104

9.5<= Y < 10.4

Thus, 95/10.5 < x/y < 105/9.5.

Hope this helps!

Whit

Whitney Garner
GMAT/GRE/EA Instructor & Anxiety/Accommodations Coach
www.whitneygarner.com

Contributor to Beat The GMAT!

Math is a lot like love - a simple idea that can easily get complicated

Like this post

sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Fri Jan 04, 2013 11:30 am

10 gallons rounded to the nearest means the lower limit could be 9.5 and the upper limit could be 10.5...10.5+9.5/2 gives 10. If we take 11 and 9.5 as the two quantities the rounded number wont be 10. Similarly 100 miles rounded to nearest mean 95 or 105....95+105/2 = 100 miles..

Work hard in Silence, Let Success make the noise.

If you found my Post really helpful, then don't forget to click the Thank/follow me button.

Like this post

gander123: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Tue Sep 25, 2012 12:47 amFollowed by: 1 member; Thanked: 3 times

by gander123 » Sat Jan 05, 2013 3:22 am

Hey Whit,

Any number that is even infinitesimally smaller than 10.5 would round down (e.g. 10.49999999999999999999). This means that there are actually an infinite number of numbers that are larger than 10.4 but still smaller than 10.5. So the best way to represent this range is to just say that the highest possible value is infinitely close to 10.5 without actually equaling 10.5 (but how do we write that?? we don't, so we just say that is had to be smaller than 10.5!)

Great background knowledge. But dont we go far beyond what is introduced in the Math Section of the official guide?

Brgds,

Tobi

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Jan 05, 2013 5:01 am

gander123 wrote:Hey Whit,

Any number that is even infinitesimally smaller than 10.5 would round down (e.g. 10.49999999999999999999). This means that there are actually an infinite number of numbers that are larger than 10.4 but still smaller than 10.5. So the best way to represent this range is to just say that the highest possible value is infinitely close to 10.5 without actually equaling 10.5 (but how do we write that?? we don't, so we just say that is had to be smaller than 10.5!)
Great background knowledge. But dont we go far beyond what is introduced in the Math Section of the official guide?

Brgds,

Tobi

The problem posted above tests the same concept as does PS142 in the OG13 (PS129 in the OG12). Check my post here:

https://www.beatthegmat.com/og-129-round ... 86849.html

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review