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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Mike and Emily need to build 2 identical houses. Mike . . . tagged by: Vincen ##### This topic has 1 expert reply and 0 member replies ## Mike and Emily need to build 2 identical houses. Mike . . . 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 B is the OA. I am confused here. I don't know how to start. With the probability or the rates. Experts, can you show me how to solve this PS question. I'd really like to see the answer. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Top Reply Vincen wrote: Amy and Emily need to build 2 identical houses. Amy, 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, Amy 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 B is the OA. I am confused here. I don't know how to start. With the probability or the rates. Experts, can you show me how to solve this PS question. I'd really like to see the answer. Executive decision: I'm changing the names here. First, rephrase the question. If Amy can do 1 house in 6 weeks, she can do 2 in 12 weeks. If Emily can do 1 house in 8 weeks, she can do 2 in 16 weeks. Neither alone can do 2 houses in 7 weeks. Together: Amy's rate is 1/6 and Emily's rate is 1/8. Their combined rate is 1/6 + 1/8 = 14/48 = 7/24. Rate and Time have a reciprocal relationship, so the time to do one house together would be 24/7. Thus, the time to do two houses together would be 48/7. This is less than 7. So our rephrased question: what is the probability that Amy and Emily work together? Desired outcomes (work together): Roll a 5 or 6 --> so 2 desired outcomes Total possible outcomes: 6 Desired/Total = 2/6 = 1/3. The answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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