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

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At a certain hospital, 75% of the interns receive fewer than 6 hours [#permalink]

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New post 13 Oct 2009, 06:25
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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?

1. 6
2. 14
3. 19
4. 20
5. 81


OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/at-a-certain ... 08658.html
[Reveal] Spoiler: OA
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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours [#permalink]

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New post 13 Oct 2009, 08:57
hogann 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?
1. 6
2. 14
3. 19
4. 20
5. 81


80% receive less than 6 hours of sleep
75% report feeling tired so 5% dont feel tired

20% receive 6 or more hours of sleep
out of this 70% report no tiredness so it become 14%

total 5%+14% = 19%...C
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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours [#permalink]

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New post 13 Oct 2009, 09:03
Lets say there are 100 interns. 80 of them receive <6 hrs of sleep and 75 of the 100 receive <6 hrs and report tiredness. So out of the 80 receiving <6 hrs only 5 do not report tiredness.
Also given that 70% of interns getting >= 6 hrs of sleep report no tiredness. There are 100-80 = 20 interns receiving >= 6 hrs of sleep. So 70%x20 = 14 of them report no tiredness.
So total interns reporting no tiredness = 5+14 = 19.

Is that the OA?
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New post 13 Oct 2009, 10:18
I will go with option C
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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours [#permalink]

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New post 13 Oct 2009, 11:31
asterixmatrix wrote:
80% receive less than 6 hours of sleep
75% report feeling tired so 5% dont feel tired

20% receive 6 or more hours of sleep
out of this 70% report no tiredness so it become 14%

total 5%+14% = 19%...C


Great Explanation - OA is 19%
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New post 03 May 2011, 23:16
5 + 0.7x = 5 + 14 = 19
Hence C
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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours [#permalink]

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New post 05 May 2011, 07:49
Let 100 - Total

80 < 6 hrs of sleep

75 < 6 hrs of sleep and tired

=> 5 < 6 hrs of sleep and not tired

0.7 * 20 >= 6 hrs of sleep and not tired

= 14

So total = 19% not tired

Answer - C
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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours [#permalink]

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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours [#permalink]

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New post 21 Mar 2017, 21:34
hogann 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?

1. 6
2. 14
3. 19
4. 20
5. 81




Given:



< 6 hours sleep>= 6 hours sleepTOTAL
Tired75--
Not Tired-0.7*X?
TOTAL80X100


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.

Answer: C.

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Re: At a certain hospital, 75% of the interns receive fewer than 6 hours   [#permalink] 21 Mar 2017, 21:34
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