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# A master builder is building a new house. He gets 3 apprenti

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Manager
Joined: 15 Apr 2010
Posts: 117
A master builder is building a new house. He gets 3 apprenti  [#permalink]

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10 Jun 2010, 11:30
1
15
00:00

Difficulty:

15% (low)

Question Stats:

78% (01:46) correct 22% (02:25) wrong based on 250 sessions

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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???
Math Expert
Joined: 02 Sep 2009
Posts: 50544

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10 Jun 2010, 14:31
1
2
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:

$$\frac{time_{group}}{time_{master}}=\frac{job}{3x}*\frac{x}{job}=\frac{1}{3}$$.

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Manager
Joined: 14 Apr 2010
Posts: 181

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06 Jul 2010, 05:08
1
1
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
Manager
Joined: 06 Jan 2010
Posts: 60

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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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pls kudos if you're satisfied with the reply

Manager
Joined: 14 Apr 2010
Posts: 181

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06 Jul 2010, 05:55
ooopsss .....my bad....now this shows how poor i am in these probs
SVP
Joined: 06 Sep 2013
Posts: 1749
Concentration: Finance
Re: A master builder is building a new house. He gets 3 apprenti  [#permalink]

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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
Manager
Joined: 30 May 2012
Posts: 209
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: A master builder is building a new house. He gets 3 apprenti  [#permalink]

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05 Dec 2014, 09:48

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!
Math Expert
Joined: 02 Sep 2009
Posts: 50544
Re: A master builder is building a new house. He gets 3 apprenti  [#permalink]

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06 Dec 2014, 04:36
Blackbox wrote:

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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Manager
Joined: 30 May 2012
Posts: 209
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: A master builder is building a new house. He gets 3 apprenti  [#permalink]

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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.
VP
Joined: 07 Dec 2014
Posts: 1108
A master builder is building a new house. He gets 3 apprenti  [#permalink]

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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  [#permalink]

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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.

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Re: A master builder is building a new house. He gets 3 apprenti &nbs [#permalink] 14 Jul 2018, 10:06
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