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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Tue Sep 15, 2015 2:10 am

It takes 7 high school students, working at identical constant individual rates,
10 hours to paint a certain house. At what time will the house be fully painted
if 7 students start painting at 9AM and one student, working at the same rate,
is added per hour starting at 1PM?
(A) 3:00PM
(B) 4:30PM
(C) 5:00PM
(D) 5:20PM
(E) 6:20PM

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Source: Beat The GMAT — Problem Solving | Tue Sep 15, 2015 2:10 am

prasannakarthik: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Sep 15, 2015 1:49 am

by prasannakarthik » Tue Sep 15, 2015 2:20 am

Choice B. 4:30

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Tue Sep 15, 2015 2:21 am

OA is D - 5:20

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prasannakarthik: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Sep 15, 2015 1:49 am

by prasannakarthik » Tue Sep 15, 2015 2:30 am

Yes...I stand corrected. By 5:00 PM, 66/70 of the work will be completed. It takes 1/3rd of an hour for 12 people to complete 4/70 of the work. Hence 5:20.

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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 » Tue Sep 15, 2015 2:57 am

nikhilgmat31 wrote:It takes 7 high school students, working at identical constant individual rates,
10 hours to paint a certain house. At what time will the house be fully painted
if 7 students start painting at 9AM and one student, working at the same rate,
is added per hour starting at 1PM?
(A) 3:00PM
(B) 4:30PM
(C) 5:00PM
(D) 5:20PM
(E) 6:20PM

Let the rate per student = 1 unit per hour.
Rate for 7 students = 7 units per hour.
Since 7 students can paint the house in 10 hours, the house = rt = 7*10 = 70 units.

9am-1pm: 7 students
Amount of work produced by 7 students in these 4 hours = rt = 7*4 = 28 units.
Remaining work = 70-28 = 42 units.

1pm-2pm: 8 students
Amount of work produced = 8 units.
Remaining work = 42-8 = 34 units.

2pm-3pm: 9 students
Amount of work produced = 9 units.
Remaining work = 34-9 = 25 units.

3pm-4pm: 10 students
Amount of work produced = 10 units.
Remaining work = 25-10 = 15 units.

4pm-5pm: 11 students
Amount of work produced = 11 units.
Remaining work = 15-11 = 4 units.

Since only 4 units remain, it will take less than 1 more hour for the rest of house to be painted.

The correct answer is D.

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Tue Sep 15, 2015 3:36 am

GMATGuruNY wrote:
nikhilgmat31 wrote:It takes 7 high school students, working at identical constant individual rates,
10 hours to paint a certain house. At what time will the house be fully painted
if 7 students start painting at 9AM and one student, working at the same rate,
is added per hour starting at 1PM?
(A) 3:00PM
(B) 4:30PM
(C) 5:00PM
(D) 5:20PM
(E) 6:20PM
Let the rate per student = 1 unit per hour.
Rate for 7 students = 7 units per hour.
Since 7 students can paint the house in 10 hours, the house = rt = 7*10 = 70 units.

9am-1pm: 7 students
Amount of work produced by 7 students in these 4 hours = rt = 7*4 = 28 units.
Remaining work = 70-28 = 42 units.

1pm-2pm: 8 students
Amount of work produced = 8 units.
Remaining work = 42-8 = 34 units.

2pm-3pm: 9 students
Amount of work produced = 9 units.
Remaining work = 34-9 = 25 units.

3pm-4pm: 10 students
Amount of work produced = 10 units.
Remaining work = 25-10 = 15 units.

4pm-5pm: 11 students
Amount of work produced = 11 units.
Remaining work = 15-11 = 4 units.

Since only 4 units remain, it will take less than 1 more hour for the rest of house to be painted.

The correct answer is D.

Thanks Mitch, I solved it with very complex fractions. I will go with your approach of units.

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