Doubt in Kaplan GMAT Challenge Problem: Combined Work

gmatpapa · **Posted:** Tue Apr 19, 2011 8:28 am

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

Hello,

Thanks for posting the question. But I have a doubt as the question asks:
"What is the probability both houses will be completed after 7 weeks?"

The condition will be satisfied if either Mike or Emily work alone and not both together. So, there are 3 ways in which the houses could be built:
1. Mike alone does it: In which case, the houses will be buillt after 7 weeks
2. Emily alone does it: Same as above
3. Both together do it: In this case, the houses will be built before 7 weeks.

Therefore, number of favorable outcomes= 2
Total number of outcomes= 3

So the probability= 2/3

Am I getting it wrong?

Thanks!

Here's the OE that, it seems to me, answers a different question ie, "What is the probability that both houses are completed in less than 7 weeks?"

Solution:

The first step in solving this problem is to determine how long it would take them to build one house working together. The fastest way to do this is to use the combined work formula, which is AB/(A+B), where A is the time it takes the first person working alone and B is the time it takes the second person working alone. In this problem, the equation gives us (6)(8)/(6+8) = 48/14.

48/14, however, is the amount of time it takes Mike and Emily to build one house together and the problem specifies that they must build two houses. To determine how much time it takes them to build two houses, simply double the time it takes to build one house. Thus, it takes them 2(48/14) = 96/14 weeks to complete both houses. 96/14 expressed as a mixed number is 6 6/7 or 6 weeks and 6 days.

Next, we need to consider the probability component of this problem. We have a 1/3 chance of Mike working alone, a 1/3 chance of Emily working alone and a 1/3 chance of them working together. If Mike works alone, two houses take 12 weeks to build; if Emily works alone, two houses take 16 weeks to build; and if they work together, two houses take 6 weeks, 6 days to build. Therefore, there is a 1/3 chance that both houses are completed in less than 7 weeks, which corresponds to choice (B).

KapTeacherEli · **Posted:** Tue Apr 19, 2011 8:25 pm

Hi gmatpapa,

Your math is dead right--you're just misreading the question! When the question asks if the houses will be completed 'after 7 weeks', it isn't asking if it will take MORE than seven weeks to complete the houses. 'After seven weeks' means 'as soon as seven weeks have passed.' Thus, after 7 weeks, the houses will be complete only if the two builders work together--it will be substantially more than 7 weeks if either builder builds it alone.

Hope this helps!

Eli

gmatpapa · **Posted:** Wed Apr 20, 2011 9:04 pm

Ah Okay! I can see clearly now

Thanks, I misread it..

ashu1983 · **Posted:** Wed Apr 20, 2011 9:53 pm

Very good explanation by Eli...

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Doubt in Kaplan GMAT Challenge Problem: Combined Work

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