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# Mike and Emily need to build 2 identical houses. Mike, working alone,

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Joined: 12 May 2017
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Mike and Emily need to build 2 identical houses. Mike, working alone,  [#permalink]

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06 Mar 2018, 15:38
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Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?

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Math Expert
Joined: 02 Aug 2009
Posts: 7212
Mike and Emily need to build 2 identical houses. Mike, working alone,  [#permalink]

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06 Mar 2018, 19:41
1
div10 wrote:
Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?

M does it in 6 weeks and E does it in 8 weeks, so both combined have to do it in less than 6 weeks...
Both will make it in
1/6+1/8=14/48..
So 48/14 days or two houses in 2*48/14 which is <7

So only when E and M work together it can be less than 7 weeks..

Now what is the probability of that ...
A dice has 6 sides and on roll of two sides, E will work alone
So 2/6=1/3

So >7 weeks is 1-1/3=2/3

Please provide the choices and read the rules for posting
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Posts: 52360
Re: Mike and Emily need to build 2 identical houses. Mike, working alone,  [#permalink]

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06 Mar 2018, 19:47
1
div10 wrote:
Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?

Discussed here: mike-and-emily-need-to-build-2-identical-houses-mike-work-142453.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: Mike and Emily need to build 2 identical houses. Mike, working alone, &nbs [#permalink] 06 Mar 2018, 19:47
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# Mike and Emily need to build 2 identical houses. Mike, working alone,

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