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# Four carpenters can individually complete a particular task

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Intern
Joined: 26 May 2012
Posts: 9

Kudos [?]: 6 [0], given: 8

GMAT Date: 07-04-2012

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05 Jun 2012, 10:02
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Difficulty:

25% (medium)

Question Stats:

80% (01:47) correct 20% (03:10) wrong based on 312 sessions

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Four carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if three of the carpenters work together at their respective rates ?

A. 11/15
B. 3/5
C. 11/30
D. 47/80
E. 5/9
[Reveal] Spoiler: OA

Kudos [?]: 6 [0], given: 8

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129148 [1], given: 12194

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05 Jun 2012, 10:21
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Four carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if three of the carpenters work together at their respective rates ?

A. 11/15
B. 3/5
C. 11/30
D. 47/80
E. 5/9

In order three of the carpenters to complete the maximum fraction of the task we should select three fastest carpenters. So, those three who complete the task in 3, 4, and 5 hours.

In 1 hour they will complete $$\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{47}{60}$$th of the task. So, in $$\frac{3}{4}$$ hour (45 minutes) they will complete $$\frac{47}{60}*\frac{3}{4}=\frac{47}{80}$$th of the job.

Hope it's clear.
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Kudos [?]: 129148 [1], given: 12194

Current Student
Joined: 08 Jan 2009
Posts: 323

Kudos [?]: 159 [0], given: 7

GMAT 1: 770 Q50 V46

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05 Jun 2012, 15:33
1/3 + 1/4 + 1/5 = 47/60
47/60 * 3/4 = 47 / 80

D

Kudos [?]: 159 [0], given: 7

Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 131

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Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE: Corporate Finance (Consulting)

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05 Jun 2012, 18:05
Four carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if three of the carpenters work together at their respective rates ?

A. 11/15
B. 3/5
C. 11/30
D. 47/80
E. 5/9

Farmer A, B, C, and D

A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour

By intuition we know that the three fastest farmers are A B and C.

As such

(1/3 + 1/4 + 1/5)*(3/4) = ?

47/80 or (D)
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Kudos [?]: 64 [0], given: 16

Math Expert
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14 Jun 2013, 05:27
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

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07 Aug 2015, 11:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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20 May 2017, 00:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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20 May 2017, 00:54
I sometimes do these by taking total work as number of units which is LCM of individual times.
LCM of 3,4,5,7 = 420.

Let total work be 420 units.
Carpenter A does in 1 hour = 420/3 = 140 units.
Carpenter B does in 1 hour = 420/4 = 105 units.
Carpenter C does in 1 hour = 420/5 = 84 units.
Carpenter D does in 1 hour = 420/7 = 60 units.

Clearly, 3 most efficient carpenters are A, B, C. So if we want to find out Max fraction of work possible by 3 carpenters, we have to take these 3 carpenters only.
They do a total of (140+105+84) = 329 units per hour

Now, 45 minutes = 3/4 hours
Work done in 1 hour = 329 units
Work done in 3/4 hours = 329 * 3/4 = 987/4

Now this is what fraction of total work = (987/4)/420 = 47/80.
Hence D

(This is a time taking solution for this question no doubt. Method given by others is better. But I am just trying to add some value by giving an alternate solution. This kind of method can be applied to such questions though, sometimes making them easier)

Kudos [?]: 131 [0], given: 260

Re: Four carpenters can individually complete a particular task   [#permalink] 20 May 2017, 00:54
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