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A master builder is building a new house. He gets 3 apprenti
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10 Jun 2010, 11:30
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A master builder is building a new house. He gets 3 apprentices who EACH work 2/3 as fast as he does. If all 4 work on it together, they should finish it in what fraction of the time that it would have taken the master builder working alone? A) 4/7 B) 1/3 C) 2/3 D) 3/4 E) 4/3 My solution:
Rate at which the master builder does work: x Rate at which each apprentice works: (2/3)x For 3 apprentices: 2x
If all 4 work together then: (1/x) + (1/2x) = (3/2x)
Hence the ratio should be (x/(3/2x)) = 2/3
But the OA is 1/3. Any pointers???
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Re: A master builder
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10 Jun 2010, 14:31
tingle15 wrote: Can somebody help me with the following question...
A master builder is building a new house. He gets 3 apprentices who EACH work 2/3 as fast as he does. If all 4 work on it together, they should finish it in what fraction of the time that it would have taken the master builder working alone?
A) 4/7
B) 1/3
C) 2/3
D) 3/4
E) 4/3
My solution:
Rate at which the master builder does work: x Rate at which each apprentice works: (2/3)x For 3 apprentices: 2x
If all 4 work together then: (1/x) + (1/2x) = (3/2x)
Hence the ratio should be (x/(3/2x)) = 2/3
But the OA is 1/3. Any pointers??? Rate of the master  \(x\); Rate of one apprentice would be \(\frac{2}{3}x\), the rate of the 3 apprentices would be \(3*\frac{2}{3}x=2x\). Combined rate of the master and 3 apprentices would be \(x+2x=3x\). The master and 3 apprentices will do the job in \(time_{group}=\frac{job}{rate}=\frac{job}{3x}\); Only the master will do the job in \(time_{master}=\frac{job}{rate}=\frac{job}{x}\). So if the master alone needs 3 hours to do the job then the group will need 1 hour to do the job, which is 1/3 of the time needed by the master: \(\frac{time_{group}}{time_{master}}=\frac{job}{3x}*\frac{x}{job}=\frac{1}{3}\). Answer: B.
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Re: A master builder
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06 Jul 2010, 05:08
Please tell me whether my approach is right or wrong,
Let the time taken by the master builder be 12 hrs Then, time taken by each apprentice will be 8 hrs. (since they're each 2/3rd as fast as the mb) So, total time taken by them to finish the task  12+8(3) = 36 fracn = 12/36 = 1/3



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Re: A master builder
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06 Jul 2010, 05:26
bibha although u got the right answer, the logic is wrong. notice that u have concluded that it takes 4 people 36 hours to get the work done, whereas if only 1 person did it, it takes them only 12 hours. intuitively, when more people work, it should take less time, not more time. bunuel's method is correct and appropriate.
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Re: A master builder
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06 Jul 2010, 05:55
ooopsss .....my bad....now this shows how poor i am in these probs



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Re: A master builder is building a new house. He gets 3 apprenti
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31 Jan 2014, 07:24
Or one can use smart numbers to solve
Say master builder does the job in 6 days, then each apprentice does the job in 9 days, now 3 apprentices will do the job in 3 days. Now together all 4 will do the work together in 2 days, therefore 2/6 = 1/3 (B)
Hope it helps Cheers J



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Re: A master builder is building a new house. He gets 3 apprenti
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05 Dec 2014, 09:48
Could someone please correct me:
Master  12 Days  1 Piece
Each Minion  \(\frac{2}{3}*12 Days\)  1 Piece
Rate of Master = \(\frac{1}{12}\)
Rate of 1 Minion= \(\frac{1}{8}\)
Rate of 3 Minions= 3*\(\frac{1}{8}\)
Rate of all 4s =\(\frac{Total Work}{Total Time}\)
\(\frac{1}{12}\) + \(\frac{3}{8}\) = \(\frac{1}{T}\)
T = \(\frac{24}{11}\) ... and it stops!



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Re: A master builder is building a new house. He gets 3 apprenti
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06 Dec 2014, 04:36
Blackbox wrote: Could someone please correct me:
Master  12 Days  1 Piece
Each Minion  \(\frac{2}{3}*12 Days\)  1 Piece
Rate of Master = \(\frac{1}{12}\)
Rate of 1 Minion= \(\frac{1}{8}\)
Rate of 3 Minions= 3*\(\frac{1}{8}\)
Rate of all 4s =\(\frac{Total Work}{Total Time}\)
\(\frac{1}{12}\) + \(\frac{3}{8}\) = \(\frac{1}{T}\)
T = \(\frac{24}{11}\) ... and it stops! The master works faster but you got that his rate is 1/12 units per day while the rate of each apprentice is 1/8 units per day: 1/12 < 1/8. That's not correct. Each of the 3 apprentices works 2/3 as fast as the master, so the rate of 1 apprentices is 2/3 of the rate of the master. So, if the master makes 1 unit in 12 days, then his rate is 1/12 units per day, and the rate of each apprentices is 2/3*1/12 = 1/18 units per day. Hope it helps.
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Re: A master builder is building a new house. He gets 3 apprenti
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06 Dec 2014, 04:50
Bunuel wrote: The master works faster but you got that his rate is 1/12 units per day while the rate of each apprentice is 1/8 units per day: 1/12 < 1/8. That's not correct You, sir, are freakin' rad ! What would GMAT clubbers do without your responses! Thank you.



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A master builder is building a new house. He gets 3 apprenti
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30 May 2018, 13:38
tingle15 wrote: A master builder is building a new house. He gets 3 apprentices who EACH work 2/3 as fast as he does. If all 4 work on it together, they should finish it in what fraction of the time that it would have taken the master builder working alone?
A) 4/7 B) 1/3 C) 2/3 D) 3/4 E) 4/3 let time for builder alone to finish=3 days builder's rate=1/3 apprentice rate=2/3*1/3=2/9 1/(1/3+6/9)=1 day for builder/apprentices to finish 1 day/3 days=1/3 B



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Re: A master builder is building a new house. He gets 3 apprenti
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14 Jul 2018, 10:06
tingle15 wrote: A master builder is building a new house. He gets 3 apprentices who EACH work 2/3 as fast as he does. If all 4 work on it together, they should finish it in what fraction of the time that it would have taken the master builder working alone?
A) 4/7 B) 1/3 C) 2/3 D) 3/4 E) 4/3 We can let the time the master builder to complete a house = x when he works alone. Thus his rate is 1/x and each of his apprentices has a rate of (2/3)(1/x) = 2/(3x). The four will have a combined rate of 1/x + 3(2/(3x)) = 1/x + 6/(3x) = 1/x + 2/x = 3/x. So the time it takes them to complete a house when they work together is 1/(3/x) = x/3. Since x/3 is 1/3 of x, we see that the time when they work together is 1/3 of the time when the master builder works alone. Answer: B
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