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m02#7

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m02#7 [#permalink] New post 04 Feb 2011, 02:40
Andy, George and Sally are a team of consultants working on Project Alpha. They have an eight hour deadline to complete the project. The team members work at constant rates throughout the eight hour period. If the team of three has to begin work now and no one else can work on this project, will Project Alpha be completed by the deadline?

1. Sally can finish the project alone in \(4k+7\) hours, where \(k\) is a positive integer with a minimum value of 1 and a maximum value of 5.
2. Working alone, George will take \(2k+1\) hours and Andy will take \(3+2k\) hours, where \(k\) is a positive integer with a minimum value of 1 and a maximum value of 5

(C) 2008 GMAT Club - m02#7

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

i ve a question here.: i got that both George and Andy can complete a Job in 143/24 hour
that is approx . 5.95h not enough to reach 8 h. deadline .

so can anybody advice where my logic went wrong?
thanks
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Re: m02#7 [#permalink] New post 04 Feb 2011, 05:08
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Well, this is how I would solve the problem:

Statement 1:

Sally takes 4k+7 hrs to complete the thing alone.
So time taken by Sally = 11, 15, 19, 23 or 27 hrs.

We know nothing about how fast George and Andy work!

Thus - NOT SUFFICIENT!

Statement 2:
George - 2k+1 hr
Time - 3, 5, 7, 9 or 11

Andy - 3+2k
Time - 5, 7, 9, 11 or 13

Assume the worst case scenario - Only George and Andy are working and they're both taking their own sweet time:

Therefore, time : 13x11/(13+11) = 13x11/24 = 143/24

Quick Math:
24x8 = 192

Thus, 143/24 is less than 8 :D

Which means:
George and Andy can finish the job before the 8hr deadline if they work together (irrespective of how fast or slow they work and independent of Sally's work rate!)

Ans: B
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Re: m02#7 [#permalink] New post 04 Feb 2011, 05:09
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One more thing:

This is not a value Question. It is a 'Yes/No' question. So you don't have to calculate the exact value :)
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Re: m02#7 [#permalink] New post 04 Feb 2011, 05:12
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AmrithS wrote:
Well, this is how I would solve the problem:

Statement 1:

Sally takes 4k+7 hrs to complete the thing alone.
So time taken by Sally = 11, 15, 19, 23 or 27 hrs.

We know nothing about how fast George and Andy work!

Thus - NOT SUFFICIENT!

Statement 2:
George - 2k+1 hr
Time - 3, 5, 7, 9 or 11

Andy - 3+2k
Time - 5, 7, 9, 11 or 13

Assume the worst case scenario - Only George and Andy are working and they're both taking their own sweet time:

Therefore, time : 13x11/(13+11) = 13x11/24 = 143/24

Quick Math:
24x8 = 192

Thus, 143/24 is less than 8 :D

Which means:
George and Andy can finish the job before the 8hr deadline if they work together (irrespective of how fast or slow they work and independent of Sally's work rate!)

Ans: B



OMG !!! very very silly mistake. thanks for opening my eyes :)
+kudo
Re: m02#7   [#permalink] 04 Feb 2011, 05:12
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