Working alone, three persons P, Q, and R can do a certain

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Nov 03, 2018 5:43 pm

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Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work?

A. 1:3
B. 1:2
C. 1:1
D. 3:1
E. 15:4

OA E

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Sat Nov 03, 2018 5:43 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sat Nov 03, 2018 7:46 pm

BTGmoderatorDC wrote:Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work?

A. 1:3
B. 1:2
C. 1:1
D. 3:1
E. 15:4

OA E

Source: e-GMAT

Nice question

The work will be completed in maximum time if only one among P, Q and R work; since R is the slowest, it is R who would complete the work in maximum time -- 15 hours.

Now the computation of minimum time is tricky.

The phrase, "at least 1 person must work" means that one, two, or even three persons can work together.

It is obvious that the work will be completed in minimum time if all three work together.

Time taken by P, Q and R, working together = Reciprocal of (1/10 + 1/12 + 1/15) = 180/45 hours

The ratio of the maximum and minimum time taken to complete the job = 15 / (180/45) = 15/4.

The correct answer: E

Hope this helps!

-Jay
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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 » Sun Nov 04, 2018 4:10 am

BTGmoderatorDC wrote:Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work?

A. 1:3
B. 1:2
C. 1:1
D. 3:1
E. 15:4

Let the job = the LCM of the 3 times = 60 widgets.

Maximum time:
The maximum time is yielded when the slowest person -- R -- works alone.
Since R takes 15 hours to complete the 60-widget job, the maximum time = 15 hours.

Minimum time:
The minimum time is yielded when all 3 people work together.
Since P takes 10 hours to complete the 60-widget job, P's rate = 60/10 = 6 widgets per hour.
since Q takes 12 hours to complete the 60-widget job, Q's rate = 60/12 = 5 widgets per hour.
Since R takes 15 hours to complete the 60-widget job, R's rate = 60/15 = 4 widgets per hour.
Since the combined rate for P+Q+R = 6+5+4 = 15 widgets per hour, the time for P+Q+R to complete the 60-widget job = 60/15 = 4 hours.

Resulting ratio:
(max time) : (min time) = 15:4.

The correct answer is E.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8211; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Nov 07, 2018 5:59 pm

BTGmoderatorDC wrote:Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work?

A. 1:3
B. 1:2
C. 1:1
D. 3:1
E. 15:4

The maximum amount of time to complete the job is if R , the slowest worker, works alone, and it will take him 15 hours to complete it.

The minimum amount of time to complete the job is if all three people work together, and it will take them 1/(1/10 + 1/12 + 1/15) = 1/(6/60 + 5/60 + 4/60) = 1/(15/60) = 60/15 = 4 hours to complete it.

Therefore, the ratio is 15:4.

Answer: E

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