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Working together, Machine A and Machine B can produce

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Working together, Machine A and Machine B can produce

by VJesus12 » Sat Jan 05, 2019 6:41 am

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Working together, Machine A and Machine B can produce a total of 200 widgets in 4 hours. How many hours would it take Machine A, working alone, to produce 200 widgets?

(1) Working alone, Machine B takes 5 hours to produce 50 widgets.

(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.

[spoiler]OA=D[/spoiler]

Source: Magoosh
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Jan 07, 2019 10:17 pm

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VJesus12 wrote:Working together, Machine A and Machine B can produce a total of 200 widgets in 4 hours. How many hours would it take Machine A, working alone, to produce 200 widgets?

(1) Working alone, Machine B takes 5 hours to produce 50 widgets.

(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.

[spoiler]OA=D[/spoiler]

Source: Magoosh
Say working alone, Machine A can produce 200 widgets in a hours and Machine B can produce 200 widgets in b hours. Thus, we have

1/a + 1/b = 1/4

We have to get the value of a.

Let's take each statement one by one.

(1) Working alone, Machine B takes 5 hours to produce 50 widgets.

=> Working alone, Machine B takes 5*4 = 20 hours to produce 50*4 = 200 widgets.

=> b = 20

Thus, from 1/a + 1/b = 1/4, we have

1/a + 1/20 = 1/4
1/a = 1/4 - 1/20
1/a = 4/20
a = 5. Sufficient.

(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.

=> b = 4a

Thus, from 1/a + 1/b = 1/4, we have

1/a + 1/4a = 1/4

5/4a = 1/4
a = 5. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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