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

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

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25 Dec 2007, 22:01
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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

Please explain in detail with your answer. I don't know if I can answer this question in 2 to 4 minutes. Is there is a quicker way to get to the answer. I tried the double-matrix table option.

thanks

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CEO
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25 Dec 2007, 22:25
see below
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Manager
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27 Jan 2008, 08:22
i cant view the image..can sum1 plz re-explain the qstn..

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SVP
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27 Jan 2008, 09:21
im not sure what im doing wrong here, but the answer i get isnt one of the choices :-S

I assumed 100 total interns. 80% overall gets less than 6 hrs sleep, so thats 80 people. Of the 80, 75% feel tired ... thats 60 people who are tired, and 20 who arent.

Then we have 20 people who get more than 6 hours of sleep, but 70% of them, i.e. 14 people arent tired ... that leaves 6 people who are tired.

The total # of people who arent tired are the 20 people + 14 people = 34 people, which should be 34% ....

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Director
Joined: 12 Jul 2007
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27 Jan 2008, 09:57
pinal2 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

Please explain in detail with your answer. I don't know if I can answer this question in 2 to 4 minutes. Is there is a quicker way to get to the answer. I tried the double-matrix table option.

thanks

Let's make this super easy guys. We'll say we have 200 interns.

200 interns
150 (75%) get fewer than 6 hours of sleep and report feeling tired
160 (80%) get fewer than 6 hours of sleep
40 (200-160) get more than 6 hours of sleep
28 (70% of 40) get more than 6 hours of sleep and don't report feeling tired

(160-150)+28 = 38 interns don't report feeling tired. (160-150 comes from 160 getting fewer than 6 hours of sleep, but only 150 of that number saying they feel tired. meaning 10 don't feel tired)
38/200 = 19%

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Director
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27 Jan 2008, 10:00
Quote:
I assumed 100 total interns. 80% overall gets less than 6 hrs sleep, so thats 80 people. Of the 80, 75% feel tired ... thats 60 people who are tired, and 20 who arent.

The question is saying 75% of the TOTAL receive fewer than 6 hours of sleep and report feeling tired. Then it says 80% get fewer than 6 hours of sleep, so 80-75 = 5% don't feel tired and get less than 6 hours of sleep.

Then you did the other part correctly and got 14% so 14+5 = 19%

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Manager
Joined: 02 Jan 2008
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27 Jan 2008, 11:15
C is right

75 (st<6, tired: yes)
80 (st<6)

So, not tired with sleep time < 6 = 80 - 75 = 5 people

For Sleep Time>=6
80 (st < 6) so 20 (st >=6). Out of these 20, 70% report no tiredness so 20*70/100=14 people

Adding them, 14+5 = 19 people out of 100

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Director
Joined: 01 May 2007
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27 Jan 2008, 18:17
You use a table to solve this. You want to pay attention to what you are taking percentages of, either the total or another number. If percent questions like this, that do not give a total, just pick a number. I picked 100.
--------------------Less 6 hours----More 6 hours--------------Total
Report Tired---------75%(100)---------blank------------------blank

No Report------------5----------------70%(x)-----------------Solve for

Total---------------80%(100)----------x----------------------100

Solve for the total of no report row. 19% C

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Director
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27 Jan 2008, 19:22
pinal2 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

Please explain in detail with your answer. I don't know if I can answer this question in 2 to 4 minutes. Is there is a quicker way to get to the answer. I tried the double-matrix table option.

thanks

total number of interns = 100

Sleeping < 6 hrs = 75 ( all tired )

Therefore sleeing > 6 hrs = (100-75) = 25

Not tired = 70% of 25

Condition If Sleeping < 6 hrs = 80 ( all tired )

Therefore sleeing > 6 hrs = (100-80) = 20

Not tired = 70% of 20 = "14"

Further you know......

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Re: overlapping sets   [#permalink] 27 Jan 2008, 19:22
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