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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 06 Dec 2008, 06:02
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?
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Re: Tired Interns [#permalink] New post 06 Dec 2008, 07:33
My Guess us 75 %. Here is the explanation. I tried putting the given data in a 3 X 3 table format. First row is % pfeeling tired, second row - Not feeling tired, third row - Total % of people having > or < 6 hrs sleep.

Similarly First column is % of people getting fewer than 6 hrs,of sleep, second column is % of people getting >- 6 hrs of sleep, third column is total % of being tired or not tired. The one black are given in the question. And the one in Blue are derived.

75 10 85
05 70 75
80 80
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Re: Tired Interns [#permalink] New post 06 Dec 2008, 10:20
The answer is actually 19%
Like the last poster I advocate using a 3X3 grid to solve all of these problems.
Since this is hard to do online, I'll give write it out.

To begin, let's say there are 100 interns.
So, now we are looking for the number of interns who report no feelings of tiredness. This means there are two groups we are interested in: 1) Interns with fewer than 6 hours sleep who are not tired and 2) Interns with 6+ hours sleep who are not tired.
We'll handle each case separately.
1) We are told that 80 of the interns receive fewer than 6 hours of sleep, and 75 of the interns receive fewer than 6 hours of sleep and report tiredness. This means that 5 of all interns receive fewer than 6 hours of sleep and aren't tired.

2) If 80 of the interns receive fewer than 6 hours of sleep, then 20 of interns get more than 6 hours of sleep. Of the 20 interns that get more than 6 hours sleep, we are told that 70% of them report no feelings of tiredness. This means that 14 interns get 6+ hours sleep and aren't tired.


In total, we have 19 interns who aren't tired.
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Re: Tired Interns [#permalink] New post 06 Dec 2008, 10:30
yep brent is correct.

5% of interns (80% minus 75%) report no tiredness
14% of interns (70% of 20%) report no tiredness

19%

fairly tricky, I started out confused over 75% of the 80% of interns, but it was 75% of the 100%, had to read a couple times. GMAT is all about tricks.
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Re: Tired Interns [#permalink] New post 06 Dec 2008, 12:32
I agree that the ans is 19%. I miscalculated the values for the interns who got 6 hrs or more sleep. Well need to reread the questions couple of more times I guess. :oops:
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Re: Tired Interns [#permalink] New post 06 Dec 2008, 14:13
good question, ended up with a hurried 75% as well - agree that its 19

thanks all
Re: Tired Interns   [#permalink] 06 Dec 2008, 14:13
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