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phoenix9801: Master | Next Rank: 500 Posts; Posts: 190; Joined: Thu Jan 14, 2010 8:29 pm; Thanked: 2 times

by phoenix9801 » Thu May 31, 2012 4:30 pm

Anne can paint a certain house in 1/2 the time it takes Mary to paint the same house. If they work together at their respective constant rates, how many hours will it take them to paint the house if Anne can paint the house by herself in 3 hours?

A) 0.5
B) 1
C) 1.5
D) 2
E) 3

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Source: Beat The GMAT — Problem Solving | Thu May 31, 2012 4:30 pm

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 May 31, 2012 5:02 pm

phoenix9801 wrote:Anne can paint a certain house in 1/2 the time it takes Mary to paint the same house. If they work together at their respective constant rates, how many hours will it take them to paint the house if Anne can paint the house by herself in 3 hours?

A) 0.5
B) 1
C) 1.5
D) 2
E) 3

Let the house = 6 units.
Since Anne takes 3 hours to paint the house -- 1/2 the time it takes Mary -- Mary takes 6 hours to paint the house.
Rate for Anne alone = w/t = 6/3 = 2 units per hour.
Rate for Mary alone = w/t = 6/6 = 1 unit per hour.
When they work together, their combined rate = 2+1 = 3 units per hour.
Time for A+M to paint the house together = w/r = 6/3 = 2 hours.

The correct answer is D.

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GMAT Kolaveri: Master | Next Rank: 500 Posts; Posts: 287; Joined: Fri Mar 23, 2012 12:33 amFollowed by: 6 members; Location: Pune,India; Thanked: 60 times

by GMAT Kolaveri » Thu May 31, 2012 6:44 pm

Assume the work to be done as an LCM of the time taken and find the individual [work/unit time]

A = 3 hrs
==> M = 6 hrs (since A=1/2*M)

Assume work as LCM or any multiple of 3,6 = Take it as 18

Work/unit time:
A= 18/3= 6W/unit time
M= 18/6= 3W/unit time

Combined rate/unit time = 6+3=9

Total work/combined rate = 18/9 = 2

By this method we can avoid fractions --> avoid silly calc mistakes and save time as well!!

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