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GMAT Diagnostic Test Question 28

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GMAT Diagnostic Test Question 28 [#permalink]

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29 Sep 2013, 20:26
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GMAT Diagnostic Test Question 28
Field: word problems (work problems)
Difficulty: 700

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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Re: GMAT Diagnostic Test Question 28 [#permalink]

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29 Sep 2013, 20:27
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Explanation:

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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Re: GMAT Diagnostic Test Question 28 [#permalink]

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21 Oct 2013, 10:04
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At the time C joins, A and B have done $$\frac{4}{10} + \frac{2}{5} = \frac{4}{5}$$.
Three of them have finished the last $$\frac{1}{5}$$ is 15 minutes (or 1/4 hour). So we have:
$$\frac{1}{4} ( \frac{1}{10} + \frac{1}{5} + \frac{1}{x}) = \frac{1}{5}$$. Then we have x =2.
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Re: GMAT Diagnostic Test Question 28 [#permalink]

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15 Dec 2013, 18:19
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bb wrote:
Explanation:

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

After 4 minutes $$\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}$$ 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.

sorry fellow, this is my very first time comment here
could you please explain why do you use minutes if in statement said hours. I mean after 2 and after 4 hours.
thanks for helping out
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Re: GMAT Diagnostic Test Question 28 [#permalink]

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16 Dec 2013, 01:12
3111987 wrote:
bb wrote:
Explanation:

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

After 4 minutes $$\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}$$ 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.

sorry fellow, this is my very first time comment here
could you please explain why do you use minutes if in statement said hours. I mean after 2 and after 4 hours.
thanks for helping out

It's a typo. Should be "after 2 hours" and "after 4 hours". Edited. Thank you.
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Re: GMAT Diagnostic Test Question 28 [#permalink]

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17 Dec 2013, 19:51
Can you do the Algebra on that last step to isolate the x:
1/4*(1/10)+(1/5)+(1/x)= 1/5

thanks
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18 Dec 2013, 00:51
Policarpa wrote:
Can you do the Algebra on that last step to isolate the x:
1/4*(1/10)+(1/5)+(1/x)= 1/5

thanks

It should be $$\frac{1}{4}*\frac{1}{10}+\frac{1}{4}*\frac{1}{5}+\frac{1}{4}*\frac{1}{x}=\frac{1}{5}$$.
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Re: GMAT Diagnostic Test Question 28 [#permalink]

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18 Dec 2013, 21:12
Hi,
I'm stumped with the algebra at the end do you subtract 1/x from both sides? I keep getting x= -10/3

Thanks
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Re: GMAT Diagnostic Test Question 28 [#permalink]

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18 Dec 2013, 23:56
Policarpa wrote:
Hi,
I'm stumped with the algebra at the end do you subtract 1/x from both sides? I keep getting x= -10/3

Thanks

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

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

$$\frac{3}{10}+\frac{1}{x}=\frac{4}{5}$$;

$$\frac{1}{x}=\frac{4}{5}-\frac{3}{10}$$;

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

$$x=2$$.

Hope it's clear.
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Re: GMAT Diagnostic Test Question 28   [#permalink] 18 Dec 2013, 23:56
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GMAT Diagnostic Test Question 28

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