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# A group of 4 junior lawyers require 5 hours to complete a legal resear

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Math Expert
Joined: 02 Sep 2009
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A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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26 Nov 2014, 07:42
5
5
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:54) correct 19% (02:01) wrong based on 206 sessions

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Tough and Tricky questions: Work/Rate Problems.

A group of 4 junior lawyers require 5 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?

A) 13
B) 10
C) 9
D) 6
E) 5

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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26 Nov 2014, 12:46
5
1
Convert rate of assistant to junior lawyer,
Assistant = 2/3 Jr.lawyer,
so 3 assistants = 2/3 * 3 = 2 junior lawyer.
Now 4 lawyers completed the job in 5hrs so 2 of them will complete in 5*2 = 10hrs
##### General Discussion
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Re: A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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26 Nov 2014, 10:45
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Assuming that all junior lawyers work at the same rate, we can formulate the expression of 4*1/x (representing the 4 lawyers working together) and this equals 1/5 (reciprocal of the time it takes them together). Solving for x yields 20 hours (the time it takes one lawyer working alone). Since the assistants work at 2/3 the rate, it takes each of them 20*3/2=30 hours individually. For 3 of them working together, it takes 3*1/30 = 1/10, which is the reciprocal of 10 hours for them working as a group.

Choice B
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Re: A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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26 Nov 2014, 13:01
1
Bunuel wrote:

Tough and Tricky questions: Work/Rate Problems.

A group of 4 junior lawyers require 5 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?

A) 13
B) 10
C) 9
D) 6
E) 5

Kudos for a correct solution.

Source: Chili Hot GMAT

one hr work of 4 lawyers is 1/5
then one hr work of 1 lawyer will be 1/20
given that assistant works at two-thirds the rate of a junior lawyer
therefore in one hr an assistant will complete 2/3 of 1/20 i.e 1/30 of work
then one hr work of a group of 3 assistants will be 3* 1/30 = 1/10
thus a group of 3 assistant will complete the work in 10 hours
[B]
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Re: A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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26 Nov 2014, 20:03
4

Rate of a Lawyer $$= \frac{1}{5*4} = \frac{1}{20}$$

Rate of a assistant $$= \frac{1}{20} * \frac{2}{3} = \frac{1}{30}$$

Rate of 3 assistants $$= 3 * \frac{1}{30} = \frac{1}{10}$$

Time required by3 assistants = 10
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Re: A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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26 Nov 2014, 21:05
2
Work = worker * time = 4*5 =20
20 = (2/3)*3 * t => t=10

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Re: A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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12 Jan 2015, 12:02
Unless my line of reasoning is not correct, this one was actually extremely easy, if you just notice this:

# of people times the # of hours:
4*5 = 20 --> 4 lawyers do 20 "works" in 5 hours.
3*10/3 = 30/3 = 10 --> 3 assistants do 10 "works" in 10/3 hours (2/3*5= 10/3)

So, since the amount of work the assistants do is half the work the lawyers do, the time will be double, so ANS B
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Re: A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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25 Feb 2016, 16:20
Bunuel wrote:

Tough and Tricky questions: Work/Rate Problems.

A group of 4 junior lawyers require 5 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?

A) 13
B) 10
C) 9
D) 6
E) 5

Kudos for a correct solution.

Source: Chili Hot GMAT

4J.L ---- 5hrs ------ 1/20 (per hr per J.L)

1/10 ------ (per hr per L.A)

Therefore 10 hours in total.
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Re: A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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02 Aug 2017, 00:06
So there are 4 junior lawyers and they work for 5 hours, therefore the total work is of 20 units (number of men *number of hours)
Now the rate of the junior lawyer is total work / total time = 20/5=4 units / hour
Now the rate of the legal assistant is 2/3 of the rate of the junior
Therefore, 2/3 (4)=8/3 is the rate of the legal assistant
Is my method of calculation wrong and also can someone help me know as to where am I going wrong in my concepts. Thanks in advance
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Re: A group of 4 junior lawyers require 5 hours to complete a legal resear  [#permalink]

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20 Jan 2019, 19:15
$$numberofpeople_1 · time_1 · rate_1 = numberofpeople_2 · time_2 · rate_2$$ (use of titles 'lawyer' and 'legal assistant' only help for clarity, they don't change the set up of the equation)
$$4(people)·5(hours)·r= 3(people)·t(hours)·\frac{2r}{3}$$
Can cancel the units and r as they are the same both sides
$$4·5=3·t·2/3$$
$$10=t$$
Re: A group of 4 junior lawyers require 5 hours to complete a legal resear   [#permalink] 20 Jan 2019, 19:15
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