Bunuel wrote:

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 any 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.

Kudos for a correct solution.

Solution:-

Lets look at the information given in the question:-

Sue sewed some costumes for 10 hrs, lets assume Sew sews x costumes per hour, therefore she sew 10x costumes

Anne sewed teh rest of the costumes in 16 hrs, lets assume Anne sews y costumes per hour, therefore she sews 16y costumes .

Total costumes sown by Sue and Anne = 10x + 16y

The question is asking how much time is would take Sue to sew 10x+16y costumes.

Statement 1 - Sue sews 1 costume for every 2 hr. From here we know that Sue must have sown 5 costumes in 10 hrs. However since we dont know the total number of costumes sown by Anne, and neither do we know the rate at which Anne works we cannot find the total amount of costumes sown by Sue and Anne. Hence we can conclude that we cannot find out how much time Sue will take to complete the entire work, therefore statement 1 is insufficient.

Statement 2 - Sue sewed twice as many costumes in 10 hrs as Anne in 16 hrs. We have assumed earlier Sue Sews 10x costumes in 10 hrs, From Statement 2 we know that Sue sewed twice as many costumes than Anne, therefore Anne must have sewed 5x costumes in 16 hrs, and 16y= 5x.

Replacing 5x into 16y we get that the total work done is equal to 10x + 5x = 15x

Now using unitary method we can calculate that if Sue sewed 10x costumes in 10 hrs she would take 15 hrs to sew 15x costumes. Therefore statement 2 is sufficient to answer the question .

Answer - B

Tip - Understand the question and write down the information given and then devise an approach to answer the question. This allows a systematic way to approach the solution.

---------------------------------------------------------------------------------------------------------------------

Kudos for reply