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Mary and Nancy can each perform a certain task in m and n

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Mary and Nancy can each perform a certain task in m and n  [#permalink]

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New post 15 Aug 2011, 04:04
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Mary and Nancy can each perform a certain task in m and n hours, respectively. Is m<n?

(1) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is greater than m.

(2) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is less than n.
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Re: Advanced RTD problem  [#permalink]

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New post 13 Sep 2011, 21:11
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Saurajm wrote:
Can you let me know how do you get the expression 2mn/(m+n)??
Thanks

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Mary takes m hrs to complete a job and Nancy takes n hrs. Together, how long will they take?

Time taken by Mary = m hrs
Time taken by Nancy = n hrs

Time taken is inverse of Rate of Work which we get from the expression Work = Rate * Time. If work done is 1, Rate = 1/Time. Hence,

Rate of work of Mary = 1/m
Rate of work of Nancy = 1/n
When they are working together, their rate of work = 1/m + 1/n = (m+n)/mn
Time taken by them together = mn/(m+n)

2mn/(m+n) is 'Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates'
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Re: Advanced RTD problem  [#permalink]

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New post 15 Aug 2011, 04:08
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Using statement (1),
2mn/(m+n) > m
As m and n are both positive,
=> 2mn > m^2 + mn
=> mn > m^2
=> n > m
Sufficient.

Using statement (2),
2mn / (m+n) < n
=> 2mn < mn + n^2
=> mn < n^2
=> m < n
Sufficient.

(D) is the answer.
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Re: Advanced RTD problem  [#permalink]

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New post 15 Aug 2011, 09:31
D..
A results in n>m
B results in m<n
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Re: Advanced RTD problem  [#permalink]

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New post 19 Aug 2011, 02:30
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LGOdream wrote:
Mary and Nancy can each perform a certain task in m and n hours, respectively. Is m<n?

(1) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is greater than m.

(2) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is less than n.


You can also solve this logically. Use numbers if it is tougher with variables.

Say, together they take 30 mins to complete the work. If both were working at the same rate, each would have taken 60 mins (so that working together would reduce the time taken by half). If one works faster and the other slower, the faster one will take less than 60 mins and the slower one will take more than 60 mins.

Statement 1 says that m (time taken by Mary) is less than 60 mins. This means rate of work of Mary is more than that of Nancy. So m < n. Sufficient.

Statement 2 says that n (time taken by Nancy) is more than 60 mins. This means rate of work of Nancy is less than that of Mary. So n > m. Sufficient.

Answer D
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Re: Advanced RTD problem  [#permalink]

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New post 13 Sep 2011, 05:51
Can you let me know how do you get the expression 2mn/(m+n)??
Thanks

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Re: Advanced RTD problem  [#permalink]

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New post 13 Sep 2011, 08:21
D is the correct answer.

1- Leads for n>m
2- Leads for m<n

Using either of them the question can be answered
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Re: Advanced RTD problem  [#permalink]

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New post 13 Sep 2011, 23:36
LGOdream wrote:
Mary and Nancy can each perform a certain task in m and n hours, respectively. Is m<n?

(1) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is greater than m.

(2) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is less than n.


D it is.

The basic equation for RTD problems is work = rate X time
Let work be 1, so the rate by which Mary works per hour is 1/m
Similarly, the rate by which Nancy works per hour is 1/n

Statement 1:
With the information given in the question and using the RTD formula, the combined time to complete the same work (say 1) can be calculated as:

1= (1/m+1/n)t (t is the time)
Therefore, t = mn/(m+n)

Now, according to the statement, 2mn/(m+n) > m
Here we need to understand that m can not be negative. So we can divide both sides of the equation by m. By solving the equation we get,
n>m
Hence Sufficient.

Statement 2:
We can prove the statement to be true as Statement 1.
Hence Sufficient

Both statements are sufficient, so the answer is D.
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Re: Mary and Nancy can each perform a certain task in m and n  [#permalink]

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New post 26 Jul 2016, 19:25
Since the question asked " Is m<n?", I see we can get both answers YES and NO for the question . Because we do not have enough information, using all given info in 1 and 2 may result in both m>n and n>m.... think about it
confusing ?
All posted solutions assume that Mary's rate is 1/m (1 over m) and Nancy's rate is 1/n, but what is Mary's rate would be m or 2/m or ... so we may have different answers in these diff. cases, do not we ?
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Re: Mary and Nancy can each perform a certain task in m and n  [#permalink]

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New post 26 Jul 2016, 21:27
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Magdi wrote:
Since the question asked " Is m<n?", I see we can get both answers YES and NO for the question . Because we do not have enough information, using all given info in 1 and 2 may result in both m>n and n>m.... think about it
confusing ?
All posted solutions assume that Mary's rate is 1/m (1 over m) and Nancy's rate is 1/n, but what is Mary's rate would be m or 2/m or ... so we may have different answers in these diff. cases, do not we ?


The question tells you that Mary takes m hours to complete 1 work.

We know

Work = Rate * Time

1 = Rate * m

Rate = 1/m

So the question tells you that Mary's rate is 1/m only.
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Re: Mary and Nancy can each perform a certain task in m and n  [#permalink]

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New post 13 Aug 2017, 15:30
My 2 cents:
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Re: Mary and Nancy can each perform a certain task in m and n &nbs [#permalink] 13 Aug 2017, 15:30
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