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Director  S
Joined: 17 Dec 2012
Posts: 628
Location: India
A, B and C work on a task. To complete the task alone, B  [#permalink]

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13 00:00

Difficulty:   95% (hard)

Question Stats: 45% (03:23) correct 55% (03:05) wrong based on 122 sessions

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A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

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Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Senior Manager  Joined: 13 Jun 2013
Posts: 269
Re: A, B and C work on a task. To complete the task alone, B  [#permalink]

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SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

efficiency of A in doing the work = x
efficiency of B in doing the work = x/2
efficiency of C in doing the work = x/3

now suppose A work for 6 days, then b will work for 3 days and C will work for 2 days

proportion of work completed by B = 3(x/2) / (6x+3(x/2)+2(x/3)
= 9/49
Current Student B
Joined: 23 May 2013
Posts: 183
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45 GPA: 3.5
A, B and C work on a task. To complete the task alone, B  [#permalink]

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1
SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

This is a variable question, so we can just assign arbitrary values to simplify the problem greatly.

To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If it takes 1 day for A to do the project, then it takes 2 days for B and 3 days for C.

If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

Let's say A worked 1 day. Then A completed 1 project. B worked for 1/2 a day, and since it takes him 2 days, he completed $$\frac{1/2}{2} = \frac{1}{4}$$ of a project. C then worked for 1/3 of a day, and completed $$\frac{1/3}{3} = \frac{1}{9}$$ of a project.

Then to find the proportion, we take $$\frac{1/4}{1+1/4+1/9} = \frac{9}{49}$$.

Intern  Joined: 04 Jul 2014
Posts: 45
Schools: Smeal" 20
Re: A, B and C work on a task. To complete the task alone, B  [#permalink]

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SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

The first thing to notice is that A is faster than B and B is faster than C.

Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.

If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.

Therefore total work done = (2*2) + (1*1) + (2/3*2/3) = 49/9

Proportion of work done by B = (1*1) / (49/9) = 9/49

--------------------------------

Kudos please, if this post helps.
Manager  B
Joined: 04 Oct 2017
Posts: 75
Re: A, B and C work on a task. To complete the task alone, B  [#permalink]

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Vetrik wrote:
SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

The first thing to notice is that A is faster than B and B is faster than C.

Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.

If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.

Therefore total work done = (2*2) + (1*1) + (2/3*2/3) = 49/9

Proportion of work done by B = (1*1) / (49/9) = 9/49

--------------------------------

Kudos please, if this post helps.

How did you arrive at ...C does 2/3 of the work??? I did not understand ...B works for 3/2 times the number of days C worked???
Intern  Joined: 23 Feb 2018
Posts: 1
Re: A, B and C work on a task. To complete the task alone, B  [#permalink]

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Kezia9 wrote:
Vetrik wrote:
SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

The first thing to notice is that A is faster than B and B is faster than C.

Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.

If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.

Therefore total work done = (2*2) + (1*1) + (2/3*2/3) = 49/9

Proportion of work done by B = (1*1) / (49/9) = 9/49

--------------------------------

Kudos please, if this post helps.

How did you arrive at ...C does 2/3 of the work??? I did not understand ...B works for 3/2 times the number of days C worked???

We can use ratios to understand it better-
Given that B worked half the number of days that A worked,implies: B= (1/2)*A
Or, A/B = 2/1 (Here it means that when A works for 2 days,B works for a day).

Now, relating B and C: B works 3/2 times C.
Or, B= (3/2)*C
B/C = 3/2.
This can be rewritten as : B/C = 1/(2/3) {In other words, when B works for a day, C works for 2/3 day}

Sent from my iPhone using GMAT Club Forum mobile app Re: A, B and C work on a task. To complete the task alone, B   [#permalink] 23 Feb 2018, 21:23
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# A, B and C work on a task. To complete the task alone, B

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