Working together without taking breaks, Michael and Donna painted the

Question

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.

This is a  Data Sufficiency Butler Question

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chanhthang1802 · Answer

Let the time it takes for Michael or Donna alone to complete the sidewalk be M and D, respectively. We have 1/M + 1/D = 1/6
Question: M = ?
(1) Michael had left when the job was 1/3 done means that Michael and Donna have worked together for 1/3 of the job.
It takes Donna 8 hours to finish 2/3 of the job --> D = 8*3/2 = 12 hours
--> 1/M + 1/12 = 1/6 --> M = 12 --> sufficient
(2) 2D = 24 --> D = 12 --> Same as (1) --> sufficient
Therefore  (D)  is the answer.

TheBipedalHorse · Answer

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.
Donna finishes 2/3 job in 8 hours. Therefore it takes her 12 hours to finish the job alone and therefore it also takes Michael 12 hours to finish the job, only then can the both of them finish the entire job in 6 hours

Therefore 1 alone is enough

(2) If Donna had to paint 2 identical sidewalks all by herself, it would have taken her 24 hours to finish.
To paint one wall, it would take her 12 hours, and again by the same logic, it takes Michael 12 hours also to finish the job

Therefore 2 alone is enough

Therefore each statement alone is enough

RICHA1189 · Answer

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?

Let work done by Michael be M and Donna be D
GIVEN : 1/M + 1/D = 1/6
If we get the rate of Donna , we will be able to find one unique value M

(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.

This statement implies that DONNA does 2/3rd of the work in 8 hrs
I.E. 1 work in 8*3/2 hrs = 12 hrs
We have got value of D , We can find the value of M . On solving we get the value of M = 12 hrs

Sufficient A/D

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

2 identical sidewalks 24 hrs , I.e. 1 sidewalk in 12 hrs
Equation is same as statement 1 
Sufficient

Answer is D

Working together without taking breaks, Michael and Donna painted the

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GMAT Data Sufficiency (DS) Questions

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