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Working independently Sam can complete a certain job in 5 hours and Di

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Bunuel
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Working independently Sam can complete a certain job in 5 hours and Di [#permalink] New post   17 Apr 2017, 01:10
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Question Stats:

94% (00:59) correct 6% (01:43) wrong based on 99 sessions
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Working independently Sam can complete a certain job in 5 hours and Diane can complete the same job in x hours. If working together Sam and Diane can complete the job in 3 hours, what is the value of x?

A. 20
B. 12
C. 8
D. 7.5
E. 4
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D
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quantumliner
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Re: Working independently Sam can complete a certain job in 5 hours and Di [#permalink] New post   17 Apr 2017, 08:32
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(1/5 + 1/x) * 3 = 1

=> 3/5 + 3/x = 1

=> 3/x = 1 - 3/5 = 2/5

=> x = 3 * 5/2 = 7.5

Answer is D. 7.5
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Re: Working independently Sam can complete a certain job in 5 hours and Di [#permalink] New post   17 Apr 2017, 11:13
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My approach

1/5 + 1/x = 1/3
1/x = 1/3 - 1/5
1/x = 2/15

Flip over the fraction 15/2 = 7.5

Answer is D :D
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Re: Working independently Sam can complete a certain job in 5 hours and Di [#permalink] New post   17 Apr 2017, 20:25
Assume that there are 60 units of work.
Sam does the work in 5 hours. Hence, the rate of work is 12 units/hour
If both Sam and Diane do the same work in 3 hours, they would have to do 20 units/hour
We can therefore say that Diane would do 8 units of work in a hour.
Time taken is 60/8 = 7.5(Option D)

P.S try to assume a number which is either the LCM or an extension of that number to solve quickly!
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Re: Working independently Sam can complete a certain job in 5 hours and Di [#permalink] New post   28 Sep 2020, 12:36
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Bunuel wrote:
Working independently Sam can complete a certain job in 5 hours and Diane can complete the same job in x hours. If working together Sam and Diane can complete the job in 3 hours, what is the value of x?

A. 20
B. 12
C. 8
D. 7.5
E. 4

Solution:

We see that Sam’s rate is 1/5 and Diane’s rate is 1/x, and their combined rate is 1/3. Thus, we can create the equation:

1/5 + 1/x = 1/3

1/x = 1/3 - 1/5

1/x = 5/15 - 3/15

1/x = 2/15

x = 15/2 = 7.5

Answer: D
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gmatclubot
Re: Working independently Sam can complete a certain job in 5 hours and Di [#permalink]
28 Sep 2020, 12:36
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