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Working together, Machine A and Machine B can produce a

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Working together, Machine A and Machine B can produce a

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Magoosh

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.

OA D.

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AAPL wrote:
Magoosh

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..
Since A+B take 4 hours to produce 200 widgets, the combined rate for A+B = w/t = 200/4 = 50 widgets per hour.

To determine A's time to produce 200 widgets, we need to know A's rate.
Question stem, rephrased:
What is A's rate?

Statement 1:
Since B takes 5 hours to produce 50 widgets, B's rate = w/t = 50/5 = 10 widgets per hour.
Thus, A's rate = (rate for A+B) - (B's rate) = 50-10 = 40 widgets per hour.
SUFFICIENT.

Statement 2:
For every 1 widget produced by B, A produces 4 widgets.
Thus:
Of every 5 widgets produced when A+B work together, A produces 4 widgets, with the result that A produces 4/5 of the hourly number of widgets.
Since the combined rate for A+B = 50 widgets per hour, we get:
A's rate = (4/5)(50) = 40 widgets per hour.
SUFFICIENT.

The correct answer is D.

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AAPL wrote:
Magoosh

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.
$$200\,\,{\rm{widgets}}\,\,\,\left\{ \matrix{
\,A\,\, = \,\,? \hfill \cr
\,B\, \hfill \cr
\,4\,\,\, \to \,\,\,{\rm{together}} \hfill \cr} \right.\,\,\,\,\,\left[ {\rm{h}} \right]$$

$$\left( 1 \right)\,\,B = 4 \cdot 5\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\left( {{1 \over 4} = {1 \over A} + {1 \over {20}}\,\,\,\, \Rightarrow \,\,\,\,A\,\,{\rm{unique}}} \right)$$

$$\left( 2 \right)\,\,B = 4A\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\left( {{1 \over 4} = {1 \over A} + {1 \over {4A}}\,\,\,\, \Rightarrow \,\,\,\,A\,\,{\rm{unique}}} \right)\,\,$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
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