Stephanie, Regine, and Brian ran a 20 mile race...

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BTGmoderatorLU: Moderator; Posts: 2547; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Thu Dec 14, 2017 11:57 am

Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?

I. Stephanie
II. Regine
III. Brian

A. I only
B. II only
C. III only
D. I or II only
E. I, II, or III

The OA is D.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Dec 14, 2017 11:57 am

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 » Thu Dec 14, 2017 12:58 pm

I posted an explanation here:
https://www.beatthegmat.com/word-problem-t272819.html

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8147; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Sep 23, 2019 5:11 pm

BTGmoderatorLU wrote:Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?

I. Stephanie
II. Regine
III. Brian

A. I only
B. II only
C. III only
D. I or II only
E. I, II, or III

We see that since nobody ran faster than 8 miles per hour, then each of them took more than 20/8 = 2.5 hours to complete the 20-mile race.

If Stephanie took 2.6 hours and Regine took 2.7 hours to complete the race, then Brian took 2.6 + 2.7 - 2 = 3.3 hours to complete the race. In this case Stephanie is the winner of the race.

If we switch Stephanie's time with Regine's, then Regine is the winner of the race.

Finally, if we let Stepanie's time = 2.5 + s and Regine's time = 2.5 + r for some positive numbers s and r, then Brian's time = 2.5 + s + 2.5 + r - 2 = 3 + s + r. We see that Brian took more time than either Stepanie or Regine to complete the race, which means he could never be the winner of the race. So only Stephanie or Regine could be the winner of the race.

Answer: D

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