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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.

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.

Question : Is Sally's time < Sanjit's time?

Given: Sally's 1 hour work = 1/(x+2)

Statement 1: (Sally+Sanjit) 1 hour work = 1/(x-2) i.e. Sanjit's 1 Hour work = [1/(x - 2)] - [1/(x + 2)] = 4/(x^2 - 4) i.e. Sanjit's total time to finish work alone = (x^2 - 4)/4 = (x+2)(x-2)/4 But since value of (x-2)/4 is unknown therefore we can't compare time of Sanjit with Sally's time NOT SUFFICIENT

Statement 1: (Sally+Sanjit) 1 hour work = 1/4) But x can't be calculated therefore NOT SUFFICIENT

Combining the two statement

(x-2) = 4 i.e. x=6 Now we can calculate the time of Sally as well as Sanjit therefore SUFFICIENT

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Re: Sally and Sanjit are working together at the same task. By herself, Sa [#permalink]

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17 Feb 2015, 17:25

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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.

Combined, we have 2 variables, and 2 different equations. (1/y) = (1/4) - 1/(x+2) ; we can plug the equations from statement 2 into the equation for statement 1 Sufficient

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.

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.

(1) This tells us that, the two people can complete the task in 4 fewer hours than Sally would take to do it on her own, because there is a 4-hour difference between x + 2 and x - 2. However, because we don't know what x is, we cannot determine whether Sally or Sanjit works faster, or whether they even work at the same rate. Thus, this statement is insufficient.

(2) This tells us that the two working together can complete the task in 4 hours. Again, however, this does not tell us what x is or which person will take less time to complete the task, and the statement is therefore, insufficient.

Together, we know that x - 2 = 4, which means that x = 6. Therefore, Sally can complete the task by herself in 8 hours (6 + 2 = 8), and together it takes them 4 hours. We can conclude that Sanjit by also takes 8 hours to do the task independently, because two people who each take 8 hours to complete the task would take 4 hours working together. Therefore, the answer to the question stem is NO, Sally would not take less time than Sanjit to do the task. The statements together are sufficient, and the answer is C.
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Re: Sally and Sanjit are working together at the same task. By herself, Sa [#permalink]

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20 Oct 2017, 18:57

Bunuel wrote:

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.

(1) This tells us that, the two people can complete the task in 4 fewer hours than Sally would take to do it on her own, because there is a 4-hour difference between x + 2 and x - 2. However, because we don't know what x is, we cannot determine whether Sally or Sanjit works faster, or whether they even work at the same rate. Thus, this statement is insufficient.

(2) This tells us that the two working together can complete the task in 4 hours. Again, however, this does not tell us what x is or which person will take less time to complete the task, and the statement is therefore, insufficient.

Together, we know that x - 2 = 4, which means that x = 6. Therefore, Sally can complete the task by herself in 8 hours (6 + 2 = 8), and together it takes them 4 hours. We can conclude that Sanjit by also takes 8 hours to do the task independently, because two people who each take 8 hours to complete the task would take 4 hours working together. Therefore, the answer to the question stem is NO, Sally would not take less time than Sanjit to do the task. The statements together are sufficient, and the answer is C.

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.

(1) This tells us that, the two people can complete the task in 4 fewer hours than Sally would take to do it on her own, because there is a 4-hour difference between x + 2 and x - 2. However, because we don't know what x is, we cannot determine whether Sally or Sanjit works faster, or whether they even work at the same rate. Thus, this statement is insufficient.

(2) This tells us that the two working together can complete the task in 4 hours. Again, however, this does not tell us what x is or which person will take less time to complete the task, and the statement is therefore, insufficient.

Together, we know that x - 2 = 4, which means that x = 6. Therefore, Sally can complete the task by herself in 8 hours (6 + 2 = 8), and together it takes them 4 hours. We can conclude that Sanjit by also takes 8 hours to do the task independently, because two people who each take 8 hours to complete the task would take 4 hours working together. Therefore, the answer to the question stem is NO, Sally would not take less time than Sanjit to do the task. The statements together are sufficient, and the answer is C.

How did u get x-2 = 4?

Check the highlighted parts above, they both talk about the time the two need to complete the task: x - 2 = 4.
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