Data Sufficiency

The Economist gives hardly any explanations... can someone please help me figure out the equations I can make from this info? Also, was the verbal part of the Economist supposed to be harder than the other practice tests? I found it to be...

Thank you!

Working together without taking breaks, Michael and Donna painted the sidewalk in 6 hours. How long would it take Michael to paint the sidewalk by himself?

(1) If Michael had left when the job was 1/3 done, it would have taken Donna 8 hours to finish the job by herself.

(2) If Donna had to paint 2 identical sidewalks all by herself, it would have taken her 24 hours to finish.

tpz wrote:The Economist gives hardly any explanations... can someone please help me figure out the equations I can make from this info? Also, was the verbal part of the Economist supposed to be harder than the other practice tests? I found it to be...

Thank you!

Working together without taking breaks, Michael and Donna painted the sidewalk in 6 hours. How long would it take Michael to paint the sidewalk by himself?

(1) If Michael had left when the job was 1/3 done, it would have taken Donna 8 hours to finish the job by herself.

(2) If Donna had to paint 2 identical sidewalks all by herself, it would have taken her 24 hours to finish.

Let one sidewalk = 24 units.
Since Michael and Donna take 6 hours to paint one sidewalk, their combined rate = 24/6 = 4 units per hour.

Statement 1:
1/3 of the sidewalk = (1/3)(24) = 8 units.
Remaining work = 24-8 = 16 units.
Since it takes Donna 8 hours to complete the remaining 16 units, Donna's rate alone = 16/8 = 2 units per hour.
Thus:
Michael's rate alone = (combined rate for Michael and Donna) - (Donna's rate alone) = 4-2 = 2 units per hour.
At a rate of 2 units per hour, the time for Michael to complete one sidewalk = 24/2 = 12 hours.
SUFFICIENT.

Statement 2:
Since Donna can complete 2 sidewalks in 24 hours, her time to complete one sidewalk is 12 hours.
Thus, Donna's rate alone = 24/12 = 2 units per hour.
Same rate as that implied by Statement 1.
Thus, since statement 1 is sufficient, statement 2 is also SUFFICIENT.

The correct answer is D.

tpz wrote: Working together without taking breaks, Michael and Donna painted the sidewalk in 6 hours. How long would it take Michael to paint the sidewalk by himself?

(1) If Michael had left when the job was 1/3 done, it would have taken Donna 8 hours to finish the job by herself.

(2) If Donna had to paint 2 identical sidewalks all by herself, it would have taken her 24 hours to finish.

Question : How long would it take Michael to paint the sidewalk by himself?
First thing is to notice that we need to have the rate at which Michael is painting and we need the area that is to be pained

Given : The rate at which Michael and Donna paint is 6 Hours for Complete Sidewalk

Statement 1) If Michael had left when the job was 1/3 done, it would have taken Donna 8 hours to finish the job by herself.
Relation between the rates of Michael and Donna is Given for the fraction of same area to be painted and we already have one relation given in Question therefore
SUFFICIENT

Statement 2) If Donna had to paint 2 identical sidewalks all by herself, it would have taken her 24 hours to finish.

Rate of Donna is given which can get us the rate at which michael will paint as the combined rate is already given in the question. Therefore,
SUFFICIENT

Answer: Option D