Bunuel wrote:
Sally and Sanjit are working together at the same task. By herself, Sally can complete the task in x + 2 hours. Could Sally, working on her own, complete the task in less time than Sanjit could do so working on his own?
(1) Working together, Sally and Sanjit can complete the task in x - 2 hours.
(2) Working together, Sally and Sanjit can complete one-fourth of the task in an hour.
Kudos for a correct solution.
The question is based on a your understanding of rates and involves almost no calculations and algebraic manipulations.
If A and B working together take N hours to complete a work, they will independently take 2N hours each if their speeds are the same.
So if they complete the work in 4 hrs together, they will each take 8 hrs working alone, if their speeds are the same. If one of them is faster and the other slower, the faster will take less than 8 hrs but more than 4 hrs and the slower one will take more than 8 hrs. Go through this example a few times to ensure you understand it fully.
Coming back to the question:
Note that by itself Sally can complete the task in "x+2" hrs has no relevance. It is as good as giving another variable y. Until and unless, the statements tell us what x is, x+2 is irrelevant.
Question: Is Sally faster than Sanjit?
(1) Working together, Sally and Sanjit can complete the task in x - 2 hours.
Just imagine some values.
Say, if x = 3, then together they take 1 hr but Sally alone taken 4 hrs. This means Sally is slower than Sanjit.
If x = 100, together they take 98 hrs but Sally alone takes 102 hrs. Sally is much faster than Sanjit.
(2) Working together, Sally and Sanjit can complete one-fourth of the task in an hour.
This tells you that together they take 4 hrs to complete the work. But time taken by Sally (x+2) is unknown.
Together, we know that time taken together is 4 hrs = x - 2 hrs
So x = 6 hrs
So Sally takes 6 + 2 = 8 hrs to complete the work on her own. This implies Sanjit also takes 8 hrs alone. So Sally is not faster than Sanjit.
Answer (C)
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >