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# M02-07

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General Discussion
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A really easy way to look at this is as follows:

for section (2) put 1 into the equation ( the minimum work value) for George and andy and you get G = 3 and A = 5. This add up to 8 so together they can complete it in 8 hours which is already enough to meet the deadline. therefore it doesn't even matter what Sallys rate is. Not sure if this is the correct rational but it worked for me.
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mpcroaming wrote:
A really easy way to look at this is as follows:

for section (2) put 1 into the equation ( the minimum work value) for George and andy and you get G = 3 and A = 5. This add up to 8 so together they can complete it in 8 hours which is already enough to meet the deadline. therefore it doesn't even matter what Sallys rate is. Not sure if this is the correct rational but it worked for me.

hi,

your method is wrong on two counts..
George will take 2k+1 hours and Andy will take 3+2k hours,
1) firstly by substituting k as 1, you are taking the minimum time they will take.
so G alone can finish in 3 hrs, and he doesn't require anyone to finish before 8 hrs....
SO, you look at the max time they take to be certain that even at the lowest speed they can finish the work in <8 hrs..

2) second fault is if G can do it in 3 hrs and A can do in 5 hrs...
both combined will not do it in 3+5 hrs, but less than 3 hrs..
if some one alone was doing in 3 hrs, and he gets help, he will do it in lesser time..

Hope the concepts have become slightly clearer..
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I think this is a high-quality question and I agree with explanation.
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I'm confused by the question. It says all 3 of them have to work together. How is statement 2 SUFF, if it only has two of the workers?
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jjt0407 wrote:
I'm confused by the question. It says all 3 of them have to work together. How is statement 2 SUFF, if it only has two of the workers?

From (2) it follows that George and Andy can alone finish the work in less than required 8 hours, so no matter what the rate of Sally is we can answer the question: yes, the project will be completed by the deadline.
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Hi Bunuel,

Can you please tell why we are taking k as minimum in statement 1 and max in Statement 2?
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I arrived at the correct answer but I used a slightly different approach, not sure if it's appropriate so I welcome any feedback

ST1: The least amount of time that Sally will need to finish the project is in 11h (1/11) , which is over 8 hours. Insufficient

ST2 :The Max Value (Slowest Rates) for Andy and George is when k = 5. Their respective rates are (1/11) and (1/13)

They have 8 hours to finish the project. Let's test if 8 hours will be sufficient.

8x (1/11 )+ 8x (1/13) = 192/143 > 1 . This means that they A & G alone can complete the entire project within the allocated 8 hours, even at their slowest rates.

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sanchitb23 wrote:
Hi Bunuel,

Can you please tell why we are taking k as minimum in statement 1 and max in Statement 2?

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Can someone please explain why 1/11 + 1/13 being greater than 1/8 means that they can together finish in less than 8 hours? Thank you!

Posted from my mobile device
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pcdr wrote:
Can someone please explain why 1/11 + 1/13 being greater than 1/8 means that they can together finish in less than 8 hours? Thank you!

Posted from my mobile device

The question asks whether the project can be completed in 8 hours, or in other words, whether the combined rate of the team is greater than 1/8. Since the combined rate of just two team members is already greater than 1/8, they can complete the project in under 8 hours by themselves, regardless of Sally's rate.

Hope it helps.
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S: time needed for Sally to finish the project alone
A: time needed for Andy ...
G: time needed for George

Question: Whether $$\frac{1}{S} + \frac{1}{A} + \frac{1}{G} >= \frac{1}{8}$$

­Statement 1: S = 4k+7, k can be from 1 to 5

(i) S = 4k+7, k can be from 1 to 5
=> 11 <= S <= 27
=> $$\frac{1}{27} <= \frac{1}{S} <= \frac{1}{11}$$

Even $$\frac{1}{11} < \frac{1}{8}$$

(ii) We know nothing about A and G

=> Statement 1 is insufficient

Statement 2: G = 2k + 1, A = 3 + 2k, k can be from 1 to 5

3 <= G <= 11
$$\frac{1}{11} <= \frac{1}{G} <= \frac{1}{3}$$

5 <= A < = 13
$$\frac{1}{13} <= \frac{1}{A} <= \frac{1}{5}$$

$$\frac{1}{G} + \frac{1}{A} >= \frac{1}{11} + \frac{1}{13} = 0.09 + 0.07 = 0.16 > 0.125 = \frac{1}{8}$$

=> Statement 2 is sufficient

==> Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

­