swerve wrote:Yves can paint a certain fence in 1/2 the time it takes Marcel to paint the same fence. If they work together, each at his own constant rate, how many hours will it take them to paint the fence?
1) Yves can paint the fence by himself in 3 hours.
2) Working together, each at his own constant rate, they can paint the fence in 1/3 the time it would take Marcel, working alone, to paint the fence.
Time and rate have a RECIPROCAL RELATIONSHIP.
Since Yves' time is ½ Marcel's time, Y's rate is TWO TIMES Marcel's rate.
Statement 1: Yves can paint the fence by himself in 3 hours.
Case 1: Fence = 6 units.
Since Yves' time for the 6-unit fence = 3 hours, Yves' rate = w/t = 6/3 = 2 units per hour, implying that Marcel's rate = 1 unit per hour and that their combined rate = 2+1 = 3 units per hour.
Since their combined rate = 3 units per hour, the time for Yves and Marcel to paint the 6-unit fence = w/r = 6/3 = 2 hours.
Case 2: Fence = 12 units.
Since Yves' time for the 12-unit fence = 3 hours, Yves' rate = w/t =12/3 = 4 units per hour, implying that Marcel's rate = 2 units per hour and that their combined rate = 4+2 = 6 units per hour.
Since their combined rate = 6 units per hour, the time for Yves and Marcel to paint the 12-unit fence = w/r = 12/6 = 2 hours.
Since the time in each case is THE SAME -- 2 hours -- Statement 1 is SUFFICIENT.
Statement 2: Working together, each at his own constant rate, they can paint the fence in 1/3 the time it would take Marcel, working alone, to paint the fence.
Since the time for Yves and Marcel together is â…“ the time for Marcel alone, the combined rate for Yves and Marcel together is THREE TIMES the rate for Marcel alone.
The rates yielded in Case 1 satisfy this condition:
Yves' and Marcel together = 3 units per hour, Marcel alone = 1 unit per hour.
In Case 1, the time for Yves and Marcel together = 2 hours.
Test these rates for a fence larger than 3 units.
Case 3: Fence = 30 units
Since their combined rate = 3 units per hour, the time for Yves and Marcel to paint a 30-unit fence = w/r = 30/3 = 10 hours.
Since the time in each case is DIFFERENT -- 2 hours in Case 1 but 10 hours in Case 2 -- Statement 2 is INSUFFICIENT.
The correct answer is
A.
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
