GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 30 May 2020, 09:56

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 15 Apr 2010
Posts: 93
A master builder is building a new house. He gets 3 apprenti  [#permalink]

### Show Tags

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

Difficulty:

25% (medium)

Question Stats:

76% (01:46) correct 24% (02:28) wrong based on 262 sessions

### HideShow timer Statistics

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: 64245
Re: A master builder  [#permalink]

### Show Tags

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:

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

_________________
Manager
Joined: 14 Apr 2010
Posts: 124
Re: A master builder  [#permalink]

### Show Tags

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
Intern
Joined: 06 Jan 2010
Posts: 36
Re: A master builder  [#permalink]

### Show Tags

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.
Manager
Joined: 14 Apr 2010
Posts: 124
Re: A master builder  [#permalink]

### Show Tags

06 Jul 2010, 05:55
ooopsss .....my bad....now this shows how poor i am in these probs
VP
Joined: 06 Sep 2013
Posts: 1494
Concentration: Finance
Re: A master builder is building a new house. He gets 3 apprenti  [#permalink]

### Show Tags

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: 194
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]

### Show Tags

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!
Math Expert
Joined: 02 Sep 2009
Posts: 64245
Re: A master builder is building a new house. He gets 3 apprenti  [#permalink]

### Show Tags

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.
_________________
Manager
Joined: 30 May 2012
Posts: 194
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]

### Show Tags

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: 1252
A master builder is building a new house. He gets 3 apprenti  [#permalink]

### Show Tags

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
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: A master builder is building a new house. He gets 3 apprenti  [#permalink]

### Show Tags

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.

_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
214 Reviews

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (PRE-BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne