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Bob and Alice can finish a job together in 3 hours.

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Bob and Alice can finish a job together in 3 hours.

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C

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Bob and Alice can finish a job together in 3 hours. If Bob can do the job by himself in 5 hours, what percent of the job does Alice do?

A. 10
B. 20
C. 40
D. 50
E. 60

The OA is C.

Can I say, 3 hours = Job/ (B + A) and 5hours = Job/B ? Then, I'm not sure

Please, can anyone explain this PS question? I need help. Thanks.

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GMAT/MBA Expert

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Hi swerve,

We're told that Bob and Alice can finish a job together in 3 hours and that Bob can do the job by himself in 5 hours. We're asked for the percent of the job that Alice does. This is an example of a "Work Formula" question - when you have two entities working together on a task, you can use the following formula to determine how long it will take the two entities to complete the task:

(A)(B)/(A+B) = time to complete the task (where A and B are the two times it takes the individuals to complete the task when working alone).

Since Bob can complete the job in 5 hours, we'll set B equal to 5 and solve for A (re: Alice's time)...

(A)(5)/(A+5) = 3
5A = 3A + 15
2A = 15
A = 7.5 hours to complete the job

Thus, each hour...
Bob does 1/5 of the job
Alice does 1/7.5 = 2/15 of the job

The entire job took 3 hours, so Alice completed (3)(2/15) = 6/15 = 2/5 = 40% of the job.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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GMAT/MBA Expert

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swerve wrote:
Bob and Alice can finish a job together in 3 hours. If Bob can do the job by himself in 5 hours, what percent of the job does Alice do?

A. 10
B. 20
C. 40
D. 50
E. 60
Let the job = the LCM of the two times = 15 units.
Since Bob and Alice together take 3 hours to produce the job, their combined rate = w/t = 15/3 = 5 units per hour.
Since Bob on his own takes 5 hours to produce the job, Bob's rate = w/t = 15/5 = 3 units per hour.
Since Bob and Alice together produce 5 units per hour, and Bob on his own produces 3 units per hour, Alice's rate = 5 - 3 = 2 units per hour.
Resulting percentage for Alice = (Alice's hourly work)/(hourly work for Bob and Alice together) = 2/5 = 40%.

The correct answer is C.

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GMAT/MBA Expert

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swerve wrote:
Bob and Alice can finish a job together in 3 hours. If Bob can do the job by himself in 5 hours, what percent of the job does Alice do?

A. 10
B. 20
C. 40
D. 50
E. 60
Since Bob and Alice can complete a job in 3 hours, the combined rate of Bob and Alice = 1/3. Since Bob can do the job by himself in 5 hours, his rate is 1/5.

Thus, the rate of Alice is 1/3 - 1/5 = 5/15 - 3/15 = 2/15.

Since Alice has worked for 3 hours, her work is 3 x 2/15 = 2/5. Furthermore, since we consider the complete job the number 1, the percentage of the job done by Alice is:

(2/5)/1 = 2/5 = 40%

Answer: C

_________________
Jeffrey Miller Head of GMAT Instruction

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