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Efficiency of the three individuals
a) 0.333 (1/3)
b) 0.25 (1/4)
c) 0.20 (1/5)

Clearly lowest fraction of the job is given by

1/4 + 1/5 = 9/20

option B wins
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Work done by the slowest of the lot in 1 hr = 1/4 + 1/5 = 9/20
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Bunuel
Each of the three people individually can complete a certain job in 3, 4, and 5 hours, respectively. What is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates?

(A) 1/3
(B) 9/20
(C) 8/15
(D) 7/12
(E) 2/3

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OFFICIAL SOLUTION:

B. To solve for the lowest portion of the job that can be done by two people in an hour, you have to choose the two slowest people, who are the two who complete the job in 4 and 5 hours.

The person who takes 5 hours completes 1⁄5 of the job in 1 hour (it takes him 5 hours total, so in 1 hour he completes 1 out of 5 hours, or 1⁄5 of the job). Similarly, the person who works 4 hours to complete the job finishes 1⁄4 of the job in 1 hour. Add 1⁄5 and 1⁄4 and you get 9⁄20 (1⁄5 = 4⁄20; 1⁄4 = 5⁄20; 4⁄20 + 5⁄20 = 9⁄20).

The answer is B.
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Why does the OA indicate D if even the legend Bunuel says it should be B?
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Hi Bunuel

You need to change the answer in the question post. It should be B instead of D.


Shekhar
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Edited the OA. Thank you both.
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Answer = (B) 9/20

Lowest fraction means addition of rates of maximum time taken

=14+15=920=14+15=920

Answer = B
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