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At a community center, three separate pumps- A, B, and C

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At a community center, three separate pumps- A, B, and C

by M7MBA » Tue Apr 30, 2019 12:44 am

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At a community center, three separate pumps- A, B, and C- started to fill an empty swimming pool at 8:00 AM, and each pump worked at its own constant rate until the pool was full. Was the pool completely filled at 3:00 PM?

1) Working alone, pump C could fill 3/10 of the pool in 126 minutes.
2) Working together, pumps A and B could fill 1/8 of the pool in 55 minutes.

[spoiler]OA=A[/spoiler]

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Source: — Data Sufficiency |

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by Ian Stewart » Wed May 01, 2019 2:37 am

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If C alone fills 3/10 of the pool in 126 minutes, it fills the whole pool in (10/3)(126) = 1260/3 = 420 minutes, or 7 hours. So C alone would fill the pool at 3pm, even with no help from A or B, and Statement 1 is sufficient.

If A+B together fill 1/8 of the pool in 55 minutes, they fill the whole pool in (8)(55) = 440 minutes, or 7 hours and 20 minutes. So without any help from C, pumps A and B would fill the pool at 3:20pm, but that's not quite sufficient to answer the question -- we need to know how much help pump C provides. So the answer is A.
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