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

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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
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carcass wrote:
hamm0 wrote:
carcass 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?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1

Cool question - a lot going on here.

I'm going to take a shortcut based on some logic: The only way for the 2 houses to get done in under 7 weeks is if they work together. If Mike works alone - it would take him 12 weeks to build 2 houses. If Emily works alone, it would take 16 weeks. The check for this is below.

Together, they have a rate of $$\frac{6*8}{6+8}$$ per house. Knowing that they'll need 2, we get $$2*(\frac{6*8}{6+8})=6 \frac{6}{7}$$

Knowing this - the only way to complete in under 7 weeks is to work together - we can move on to the probability. This is very simple: 2 sides of the dice (a 5 or a 6) out of 6 possible outcomes is 2/6, which reduces to 1/3.. The Answer is B.

Hi hamm thanks for explanation

maybe I do not catch one thing: the question is after 7 weeks, or is misleading ??' this implied after completely 7 weeks (49 days )

Thanks

When the question asks if the houses will be completed "after 7 weeks", it isn't asking if it will take greater than 7 weeks to complete the houses. "After 7 weeks" means "as soon as seven weeks have passed." or at the end of day 49.
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
Rate of Mike=$$\frac{1}{6}==>$$Building two houses would take 12 weeks
Rate of Emily=$$\frac{1}{8}==>$$ Building two houses would take 16 weeks
Rate together to build two houses=$$\frac{6+8}{(6*8)}(t)=2==>t=6\frac{6}{7}weeks$$or$$7weeks$$

Probability of getting 5 or 6 = $$\frac{2}{6}=\frac{1}{3}$$
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
carcass 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?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1

Clearly probability for each case
a) mike to work alone, b) emily to work alone or c) them to work together is 1/3.

Since they take 6 and 8 weeks for 1 house each - in any case they cant build 2 houses in 7 weeks.
So only option A and B remain. We just need to figure out if they can together complete house in 7 weeks.

Again logically- one is completing in 6 week and other in 8 week. average time for completion would be 7 week. So they can complete it in 7 weeks.
probability is 1/3

Ans B it is.
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
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Hi All,
Isnt 1/3 the probability of getting the work done under 7 weeks?
Whereas the question is asking for "What is the probability both houses will be completed after 7 weeks?"
so should not the probability be 1 - 1/3 = 2/3
Answer: D

Second way:
I need to find the probability when the work will take more than 7 weeks. Which means
probability of getting 1 2 3 4
4/6 = 2/3

Please let me know your thoughts. Or have I seriously missed something in the question since I see many people here agree with answer B and not D.

Thanks,
Pritish
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
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Expert Reply
pritish2301 wrote:
Hi All,
Isnt 1/3 the probability of getting the work done under 7 weeks?
Whereas the question is asking for "What is the probability both houses will be completed after 7 weeks?"
so should not the probability be 1 - 1/3 = 2/3
Answer: D

Second way:
I need to find the probability when the work will take more than 7 weeks. Which means
probability of getting 1 2 3 4
4/6 = 2/3

Please let me know your thoughts. Or have I seriously missed something in the question since I see many people here agree with answer B and not D.

Thanks,
Pritish

"both houses will be completed after 7 weeks?" means that both houses should be completed in less than 7 weeks.
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
The question is very easy if you calculate it only with three options, however the questions states THE BUILDING. So if you take into account the possibilities of one huis being build by e.g. Emily and the other together you get very different probabilities. So to my extent the question is a little bit messy.
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
I also misunderstood this question, i considered "after 7 weeks" all cases in which they took more than 7 weeks.
In GMAT every word impacts on process of solution, or may be I am extra cautiously reading after 7 weeks means anything after 7 weeks, my englishhh...
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
carcass 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?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1

After : Lower than in order .
So after 7 weeks means "inside one to six weeks" .....

Alone each of them exceeds 7 weeks. So no need to count the probability of 1 or 2 and 3 or 4 .

Together, to build One house , 1/6 + 1/8 = 1/T or , T = 24/7
So, time to build two houses = 2 * 24/7 = 48/7 < 7 weeks

Finally we have to calculate the probability of 5 or 6 and its 1/6 + 1/6 = 2/6 = 1/3 (Answer B)
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
carcass 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?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1

What does it mean when they say together and independently? Are they working together or are they working independently? Cause if they are working together its 1/6 + 1/8 but if they are working independently then it will only be 1/6 cause its faster than 1/8

Would someone please illustrate what this actually means?

Thanks a lot in advance
Cheers!
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
I think I also misunderstood the wording "together and independently". Sounds for me like they both build their house but they do not help each other. Would mean Mike builds his hous and Emily builds her house -> Both houses are not completed within 7 weeks, because Emily needs 8 weeks...

Strange wording to me, but I'm not a native...
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
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poorly written question IMO. "after 7 weeks" could mean either "after 7 weeks have passed" or "at a time after 7 weeks" depending on one's interpretation.
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
a lot of confusing words, yet very simple to calculate. two houses will be completed in 7 days only if they work together. the rate of both is 7/24 or one house is completed in 3 and 3/7 weeks. thus, two houses will be completed in 6 and 6/7 weeks. the probability that they will work together is 1/6 + 1/6 or 1/3
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
Very poor choice of words tbh, official questions usually do not get you confused

Within or in under 7 weeks would be much clearer
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
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carcass 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?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1

Ambiguous question - best to ignore.

"both houses will be completed after 7 weeks" - technically means that they will be completed after 7 weeks are over so say in the 8th week.
"both houses will be complete by the end of 7 weeks" - means they both will be done before or at the end of 7 weeks.

"they will work together and independently" - work together is fine but does independently mean on each house independently? Most likely no but still a point of confusion since there are two 2 separate independent works given here.
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
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Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
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