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At a certain hospital, 75% of the interns receive fewer than 6 hours o

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GeminiHeat
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At a certain hospital, 75% of the interns receive fewer than 6 hours o [#permalink] New post   04 Jun 2021, 22:46
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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
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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours o [#permalink] New post   05 Jun 2021, 10:41
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GeminiHeat 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


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At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep.png
At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep.png [ 5.94 KiB | Viewed 6121 times ]


Let the total number of interns who sleep more than 6 hours be \(x\)
Then \(0.7x\) interns sleep more than 6 hours and report not tired

Since, 80% interns sleep for less than 6 hours, then other 20% sleep for over 6 hours i.e. \(x = 20\)

So, \(0.7x = 0.7(20) = 14\)

Therefore, interns reporting not tired during their shifts = \(5 + 14 = 19\)

Hence, option C
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piorachid
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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours o [#permalink] New post   15 Jun 2022, 08:36
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80% of all employees sleep less than 6 hours while 75% of all employees report feeling tired.
Thus, 5% of employees who sleep less than 6 hours do not report fatigue.
100-80=20% of all employees sleep over 6 hours.
70% percent of 20%=14%
5%+14%=19%
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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours o [#permalink] New post   05 Jul 2023, 03:09
Hello from the GRE Prep Club BumpBot!

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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours o [#permalink]
05 Jul 2023, 03:09
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