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

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

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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.
[Reveal] Spoiler: OA

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

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


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

Answer B.
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New post 13 Jan 2015, 03:01
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Answer = (B) 9/20

Lowest fraction means addition of rates of maximum time taken

\(= \frac{1}{4} + \frac{1}{5} = \frac{9}{20}\)

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

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New post 13 Jan 2015, 07:43
Work done by the slowest of the lot in 1 hr = 1/4 + 1/5 = 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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New post 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).

The answer is B.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 19 Jan 2015, 15:43
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Why does the OA indicate D if even the legend Bunuel says it should be B?

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New post 19 Jan 2015, 19:21
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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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New post 20 Jan 2015, 02:07
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Re: Each of the three people individually can complete a certain job in 3, [#permalink]

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New post 21 Sep 2017, 23:10
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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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Re: Each of the three people individually can complete a certain job in 3,   [#permalink] 21 Sep 2017, 23:10
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