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

[BTGmoderatorLU]

Source: Princeton Review

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

The OA is B

[Jay@ManhattanReview]

Source: Princeton Review

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

The OA is B

Statement 1 alone is insufficient as it gives us information that Sue sewed 5 consumes in 10 hours. However, we have no information about the rate of Anne. Insufficient.

Statement 2 alone is sufficient. Given that Sue sewed twice as many costumes working in 10 hours as Anne produced in 16 hours, say Anne sewed x costumes in 16 hours; thus, Sue would sew 2x consumes in 10 hours. So, Sue would take 10 + 10/2 = 15 hours working alone to sew all the costumes.

The correct answer: B

Hope this helps!

-Jay
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[deloitte247]

How many hours would it have taken Sue alone to sew all the costumes?
Sue sewing alone for 10 hours? Assuming Sue sews 'x' costume per hour than she will sew 10x in 10 hours.
Anne sewing for 16 hours to finish the remaining costume assuming Anne sews y costume per hour then she will sue 16x in 16hours.
Total costume sewn by the two = 10x + 16y
Question: How many hours would it have taken Sue alone to sew all the costumes? i.e time taken to complete 10x+16o costumes.
Statement 1: Sue sewed 1 costume every 2 hours.
1 costume per 2 hours and
x costume per 1 hour, hence; x=1/2 = 0.5 costume per hour, and in 10 hours that will be 5 costumes but Anne's work rate and workdone are unknown. So, there is no way we can use Sue's work rate to find her time taken to complete the total (unknown) workdone. Hence, statement 1 is NOT SUFFICIENT.

Statement 2: Sue sewed twice as many costumes working in 10 hours as Anne produced in 16 hours.
There if Sue sews 10x in 10 hours, then for the 16 hours of Anne, Anne sew 10x / 2 = 5x
Total workdone = Sue's workdone + Anna's workdone
= 10x + 5x = 15x
If Sue sewed 10x costumes in 10 hours, then, she will sew 15x costumes in 9 hours
$$\frac{a\cdot10x}{10x}=\frac{15x\cdot10}{10x}$$
$$a=15\ hours$$
Statement 2 alone is SUFFICIENT.
Answer = option B