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Two dressmakers, Sue and Anne, sewed costumes for a local

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by AAPL » Sun Aug 11, 2019 6:40 am

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Two dressmakers, Sue and Anne, sewed costumes for a local theater production. Sue sewing alone for 10 hours sewed some of the costumes, Anne sewing for 16 hours finished sewing the remaining costumes. How many hours would it have taken Sue alone to sew all of the costumes?

1) Sue sewed 1 costume every 2 hours.
2) Sue sewed twice as many costumes working in 10 hours as Anne produced in 16 hours.

OA B
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Source: — Data Sufficiency |

by Ian Stewart » Sun Aug 11, 2019 7:19 am
Statement 1 is not sufficient, because we know nothing about what Anne did during her 16 hours -- maybe she only sewed one costume, and Sue would have needed another 2 hours alone to finish the entire job, or maybe Anne sewed one billion costumes, and Sue would have needed an enormous amount of additional time to finish the job alone.

From Statement 2, if in 10 hours Sue sews twice as many costumes as Anne does in 16 hours, then in 5 hours Sue sews exactly as many as Anne does in 16 hours. So if, after Sue works for 10 hours, Anne needed 16 hours to finish the job, Sue would instead have needed 5 hours to finish, and Sue could have done the entire job in 15 hours. The answer is B.

That said, the numbers in the question don't make sense. If you use both Statements together, it turns out the total number of costumes is not an integer.
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