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# Each of the three people individually can complete a certain job in 3,

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Math Expert
Joined: 02 Sep 2009
Posts: 51218
Each of the three people individually can complete a certain job in 3,  [#permalink]

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12 Jan 2015, 10:03
1
3
00:00

Difficulty:

5% (low)

Question Stats:

83% (00:51) correct 17% (00:49) wrong based on 230 sessions

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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

Kudos for a correct solution.

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Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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12 Jan 2015, 10:26
1
The question asks us about the lowest fraction of the job done in an hour, so we need to combine the two slower people:

$$\frac{1}{R}=\frac{1}{4}+\frac{1}{5}=\frac{9}{20}$$

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Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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13 Jan 2015, 03:01
1

Lowest fraction means addition of rates of maximum time taken

$$= \frac{1}{4} + \frac{1}{5} = \frac{9}{20}$$

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Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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13 Jan 2015, 03:07
1
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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Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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13 Jan 2015, 07:43
Work done by the slowest of the lot in 1 hr = 1/4 + 1/5 = 9/20
Math Expert
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Posts: 51218
Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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19 Jan 2015, 01:22
Bunuel wrote:
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

Kudos for a correct solution.

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).

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Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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19 Jan 2015, 15:43
1
Why does the OA indicate D if even the legend Bunuel says it should be B?
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Joined: 17 Sep 2011
Posts: 12
Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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19 Jan 2015, 19:21
1
Hi Bunuel

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

Shekhar
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Posts: 51218
Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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20 Jan 2015, 02:07
1
Edited the OA. Thank you both.
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Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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21 Sep 2017, 23:10

Lowest fraction means addition of rates of maximum time taken

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

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Re: Each of the three people individually can complete a certain job in 3,  [#permalink]

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01 Dec 2018, 07:07
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Re: Each of the three people individually can complete a certain job in 3, &nbs [#permalink] 01 Dec 2018, 07:07
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