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# D01-28

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Math Expert
Joined: 02 Sep 2009
Posts: 51263

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15 Sep 2014, 23:12
1
13
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:13) correct 34% (02:57) wrong based on 156 sessions

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Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of $$x$$?

A. $$1$$
B. $$1.25$$
C. $$2$$
D. $$2.5$$
E. $$4$$

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Joined: 02 Sep 2009
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15 Sep 2014, 23:12
1
2
Official Solution:

Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of $$x$$?

A. $$1$$
B. $$1.25$$
C. $$2$$
D. $$2.5$$
E. $$4$$

After 2 hours $$2*\frac{1}{10}=\frac{1}{5}$$ of the taks will be done (as only A works);

After 4 hours $$\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}$$ of the task will be done and $$\frac{1}{5}$$ will be left to be done;

We are told that 1/5th of the task is done in 15 minutes (1/4th of an hour) by all three workers: $$\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}$$. From which we can find that $$x=2$$ hours.

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Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
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WE: General Management (Transportation)

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31 Oct 2015, 20:04
2
A works alone for 2 hours,
0.2x(work) completed

joins B
0.2x completed by worker A
1/5 => 2/5 completed or 0.4x completed by worker B

after 4 hours we have 0.8x completed
joins C and everything is finished in 15 minutes
or 0.2x (work) is completed in 0.25 hours

now we can set an equation
1/10 + 1/5+ 1/x = 2/10 * 4/1 simplify 1/5 or 4/5
multiply everyting by 10
1+2+10/x = 8
10/x = 5
x = 2.
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Joined: 21 Mar 2017
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22 Mar 2017, 07:35
not clear why 1/4 has been multiplied at end
Board of Directors
Joined: 17 Jul 2014
Posts: 2617
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
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22 Mar 2017, 07:48
johncath wrote:
not clear why 1/4 has been multiplied at end

1 hour is 1.
15 minutes is 1/4
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04 Jul 2017, 05:01
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
Math Expert
Joined: 02 Sep 2009
Posts: 51263

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04 Jul 2017, 05:05
Sangeeta2018 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

My friend, you should be more specific when asking a question. Which part is unclear? What to elaborate?
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Joined: 06 Oct 2017
Posts: 2
GMAT 1: 690 Q48 V36

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25 Oct 2017, 03:53
The last calculation is not clear. How we are multiplying with with 1/4 and equalizing it to 1/5. I want to know the mathematical formula. Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 51263

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25 Oct 2017, 04:10
1
Kamran23Z wrote:
The last calculation is not clear. How we are multiplying with with 1/4 and equalizing it to 1/5. I want to know the mathematical formula. Thanks

$$\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}$$.

(time)(combined rate) = (job done).
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Joined: 25 Oct 2017
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25 Oct 2017, 21:50
Consider the total work as 10, and A can do 1 work in 1hr, B can do 2 work in 1 hr. A starts work for 2 hrs. So 2 work completed(1×2=2), then B joins for 2 hrs, so B does 4 work (2×2=4), now total work = A's 4+B's 4 work = 8. Balance work is 2. C joins and complete the work in 15 mins. That is A do .25 work and B do .5 work in15 mins., total .75 work(.25+.5=.75).Balace 1.25 work is done by C in 15 mins. So C can do 5 work in 1 hr. It means C takes 2hrs to complete the total work.
Ans : opt.c, 2hrs

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Intern
Joined: 26 Aug 2016
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GMAT 1: 670 Q49 V32
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03 Nov 2017, 05:44
10 A = 5 B =Cx= k = since work remain same that each does

10A = since work remains the same

10 A = A*2 + (A+B)2 + (A+B+C) *1/4

=> K = K/10 *2 + (K/10+K/5)2 + (K/10 + K/5 +k/x) *1/4

solving for above equation

=> 1/2 = 1/x

x =2 hours for C
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Joined: 20 Feb 2017
Posts: 164
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Concentration: Operations, Strategy
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30 Aug 2018, 21:15
A - 10 hours to complete the work
B- 5 hours to complete the work
C- X hours to complete the work
Take the LCM of 10,5,x = 10x (total work)
Hence A rate of work = 10x/10 = X units/hour
B rate of work = 10x/5 = 2x units/hour
C rate of work = 10x/x = 10 units/hour
therefore
X*2 +(2x+x)*2+(2x+x+10)*1/4 =10x
this gives X =2 (quick and easy)
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Joined: 19 Nov 2012
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10 Sep 2018, 19:08
Hi Bunuel: Question M28-19 and D01-28 are the same. Just in case if it was not known earlier.
Intern
Joined: 17 Jul 2018
Posts: 19

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22 Sep 2018, 19:34
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please show how to solve for "X" once the last equation is setup. Thank you
Math Expert
Joined: 02 Sep 2009
Posts: 51263

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23 Sep 2018, 02:50
leonsandcastle332 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please show how to solve for "X" once the last equation is setup. Thank you

Why is the question of poor quality? That's not right. Both the question and the solution are correct and detailed enough.

After you get $$\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}$$, only simple algebraic manipulations are left to be done:

$$\frac{1}{10}+\frac{1}{5}+\frac{1}{x}=\frac{4}{5}$$

$$\frac{1}{x}=\frac{4}{5}-(\frac{1}{10}+\frac{1}{5})$$

$$\frac{1}{x}=\frac{5}{10}$$

$$x = 2$$.

Hope it's clear.
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Joined: 17 Jul 2018
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23 Sep 2018, 05:50
Bunuel wrote:
leonsandcastle332 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please show how to solve for "X" once the last equation is setup. Thank you

Why is the question of poor quality? That's not right. Both the question and the solution are correct and detailed enough.

After you get $$\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}$$, only simple algebraic manipulations are left to be done:

$$\frac{1}{10}+\frac{1}{5}+\frac{1}{x}=\frac{4}{5}$$

$$\frac{1}{x}=\frac{4}{5}-(\frac{1}{10}+\frac{1}{5})$$

$$\frac{1}{x}=\frac{5}{10}$$

$$x = 2$$.

Hope it's clear.

I apologize. I was stuck on something very dumb last night. Is there a way to change my feedback?
Re: D01-28 &nbs [#permalink] 23 Sep 2018, 05:50
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# D01-28

Moderators: chetan2u, Bunuel

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