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

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

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???

Bunuel · Accepted Answer

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.

bibha · Answer

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

janani · Answer

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.

bibha · Answer

ooopsss .....my bad....now this shows how poor i am in these probs :-(

jlgdr · Answer

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

Blackbox · Answer

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!

Bunuel · Answer

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.

Blackbox · Answer

You, sir, are freakin' rad 8-)

! What would GMAT clubbers do without your responses! Thank you. :punk

gracie · Answer

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

JeffTargetTestPrep · Answer

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

Westfolia007 · Answer

Bunuel   chetan2u  Can you please check if my approach is correct?

Let total work be 1 unit and let the rate of master's work be 1 unit/time, so apprentice rate would be 2/3
 Time taken by master = 1/1 = 1 unit time
time taken all together = 1/ ( 1 + 3*2/3) = 1/ ( 1+2) = 1/3 unit time

ratio 1/3 : 1 or 1:3

bumpbot · Answer

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