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At a certain hospital, 75% of the interns receive fewer than

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At a certain hospital, 75% of the interns receive fewer than [#permalink] New post 22 Sep 2008, 01:09
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At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?

6
14
19
20
81
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Re: Zumit PS 024 [#permalink] New post 22 Sep 2008, 01:17
14%.

If x is the number of interns then 0.2x receive 6 or more number of hours of sleep and 70% of 0.2x = 0.14x receive good sleep and do not feel tired.
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Re: Zumit PS 024 [#permalink] New post 22 Sep 2008, 02:19
100 = 80% (< 6 hours of sleep ) + 20% (>=6 hours of sleep)

Now from 80% only 75% (60) reports feeling tired , so 20 from this group do not feel tired .........1

Now from 20% only 30% (6) reports feeling tired , so 14 from this groupd do not feel tired.........2

So we have total 34 people who do not feel tired..

y its not in answer..

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Re: Zumit PS 024 [#permalink] New post 22 Sep 2011, 13:49
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I think the answer is "c"
0.8 of total interns receive less than 6 rest. among them, 0.75 feel tired. so 0.05 have no feelings of tiredness.

on the other hand, o.2 of total interns receive 6 or more than 6 hours rest. 0.70 of them (that is 0.2*0.7=0.14) have no feelings of tiredness.

the total is 0.05+0.14=0.19
Answer "c"
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Re: Zumit PS 024 [#permalink] New post 22 Sep 2011, 19:22
dancinggeometry wrote:
At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?

6
14
19
20
81


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Re: Zumit PS 024 [#permalink] New post 22 Sep 2011, 21:55
How did you get 75 for the people who are tired and sleep less than 6 hrs..
Its 75% and so so 75% of 80 is 60 and not 75.
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Re: Zumit PS 024 [#permalink] New post 22 Sep 2011, 22:14
vishal4584 wrote:
How did you get 75 for the people who are tired and sleep less than 6 hrs..
Its 75% and so so 75% of 80 is 60 and not 75.


Actually, the question says "75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts", this is different from "80% of the interns receive fewer than 6 hours of sleep".

The first statement says the interns are both tired & sleep less whereas the second statement says they only sleep less.

Does this make sense?
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Re: Zumit PS 024   [#permalink] 22 Sep 2011, 22:14
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