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On Monday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did it

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On Monday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did it

by BTGmoderatorDC » Sun Aug 23, 2020 2:45 pm

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On Monday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did it completely fill the order that morning?

(1) The machine began filling the order at 9:30 a.m.
(2) The machine had filled 1/2 of the order by 10:30 a.m. and 5/6 of the order by 11:10 a.m.



OA B

Source: Official Guide
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Source: — Data Sufficiency |
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Re: On Monday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did

by deloitte247 » Wed Aug 26, 2020 3:31 am

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Target question => At what time did it completely fill the order?

Statement 1 => The machine began filling the order at 9:30 am
This does not tell us about the total time it took to complete 1 order. Statement 1 is NOT SUFFICIENT

Statement 2 => The machine had filled 1/2 of the order by 10:30 am and 5/6 of the order by 11:10 am
$$Rate=\frac{workdone}{time}$$
$$between\ 10:30am\ and\ 11:10am,\ total\ time\ taken\ =\ 40\ \min utes$$
$$Rate=\frac{\frac{5}{6}-\frac{1}{2}}{40}=>\frac{\frac{10-6}{12}}{40}$$
$$\frac{4}{12}\div40\ =>\ \frac{1}{3}\cdot\frac{1}{40}=\frac{1}{120}$$
$$rate\ of\ the\ machine\ is\ \frac{1}{120}$$
$$the\ remaining\ portion\ of\ the\ order\ =\ \frac{6}{6}-\frac{5}{6\ }=\frac{1}{6}$$
$$time\ taken\ to\ complete\ \frac{1}{6}=\frac{workdone}{rate}$$
$$=\frac{1}{6}\div\frac{1}{120}$$
$$=\frac{1}{6}\cdot\frac{120}{1}=20\ \min utes$$
The machine needs 20 more minutes to complete the remaining 1/6 of the job and will finish it by 11:30 am
Statement 2 alone is SUFFICIENT

Answer = B
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