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At a certain hospital, 75% of the interns

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At a certain hospital, 75% of the interns

by melguy » Sat Nov 19, 2016 6:30 pm
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 help me with the problem. I tried setting up matrix but I am really confused with the language of the question!

Thanks
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by GMATGuruNY » Sat Nov 19, 2016 6:45 pm
I posted a solution here:
https://www.beatthegmat.com/tired-vs-not ... 59469.html
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by Brent@GMATPrepNow » Sat Nov 19, 2016 7:07 pm
Here's another approach that uses the Double Matrix Method: https://www.beatthegmat.com/hospitals-t283256.html

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by melguy » Sat Nov 19, 2016 8:57 pm
Thanks to both of you for your input.

It is a very straight forward question but I was very confused with the language of the question.

-> 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts
-> 80% of the interns receive fewer than 6 hours of sleep

I thought it was providing contradictory information so could not fit this information in the matrix. But now i get the difference between the two!
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by Matt@VeritasPrep » Fri Nov 25, 2016 3:13 pm
It might be easier to see the distinction if we label each group.

< 6 hours AND tired = x
> 6 hours AND not tired = y
< 6 hours AND not tired = z
> 6 hours AND tired = w

We're told that:

x = .75 * (x + y + w + z)

y = .7 * (y + w)

x + z = .8 * (x + y + w + z)

From there, the algebra is tedious, but relatively straightforward. (Of course, on test day I wouldn't recommend algebra, but it does make the prompt intelligible.)
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