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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]

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22 Sep 2008, 02:09
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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?

A. 6
B. 14
C. 19
D. 20
E. 81

OPEN DISCUSSION OF THIS QUESTION IS HERE: at-a-certain-hospital-75-of-the-interns-receive-fewer-than-108658.html
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Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]

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22 Sep 2008, 02:17
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: At a certain hospital, 75% of the interns receive fewer than [#permalink]

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22 Sep 2008, 03:19
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..

Thanks
Vishal Shah
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Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]

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22 Sep 2011, 14:49
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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
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Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]

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22 Sep 2011, 20:22
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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: At a certain hospital, 75% of the interns receive fewer than [#permalink]

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22 Sep 2011, 22:55
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: At a certain hospital, 75% of the interns receive fewer than [#permalink]

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22 Sep 2011, 23:14
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: At a certain hospital, 75% of the interns receive fewer than [#permalink]

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05 Oct 2015, 10:49
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Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]

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06 Oct 2015, 04:40
Expert's post
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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?

A. 6
B. 14
C. 19
D. 20
E. 81

Given:

 < 6 hours sleep >= 6 hours sleep TOTAL Tired 75 - - Not Tired - 0.7*X ? TOTAL 80 X 100

Interns who receive < than 6 hours sleep and Not Tired = 80 - 75 = 5;

TOTAL interns who receive >= 6 hours sleep = 100 - 80 = 20, so interns who receive >= 6 hours sleep and are Not Tired = 0.7 * 20 =14;

Interns who are Not Tired = 5 + 14 = 19.

OPEN DISCUSSION OF THIS QUESTION IS HERE: at-a-certain-hospital-75-of-the-interns-receive-fewer-than-108658.html
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Re: At a certain hospital, 75% of the interns receive fewer than   [#permalink] 06 Oct 2015, 04:40
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