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Hospitals

by j_shreyans » Tue May 05, 2015 9:00 am
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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by DavidG@VeritasPrep » Tue May 05, 2015 9:21 am
Matrix problem!

Let's say that there are 100 interns. We know that 75 of the interns get less than 6 hours of sleep and report feeling tired. We also know that 80 of the interns get less than 6 hours of sleep, so 20 get 6 or more hours of sleep. We know that 70% of the 20 who get 6 or more hours, report no feelings of tiredness, so we know that number is 20*.7 = 14 To start, our matrix will look like this:

Image


Next, just fill in the remaining cells, to get this:


Image


Answer is C
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by Brent@GMATPrepNow » Tue May 05, 2015 9:54 am
I thought I'd point out that David's Double Matrix approach can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- tired or not tired
- less than 6 hours sleep or more than 6 hours sleep

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

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- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
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Easy Data Sufficiency questions
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Medium Data Sufficiency questions
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Difficult Data Sufficiency questions
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- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
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by jain2016 » Sun Apr 03, 2016 6:37 am
Let's say that there are 100 interns. We know that 75 of the interns get less than 6 hours of sleep and report feeling tired. We also know that 80 of the interns get less than 6 hours of sleep, so 20 get 6 or more hours of sleep. We know that 70% of the 20 who get 6 or more hours, report no feelings of tiredness, so we know that number is 20*.7 = 14 To start, our matrix will look like this:

Hi David ,

Just a quick question , we have 80 of the interns get less than 6 hours of sleep and 75% of the interns get less than 6 hours of sleep and report feeling tired.

So shouldn't be the interns who get less than 6 hours of sleep and feeling tired = 80*75/100 ? If not then why 70% of the 20 who get 6 or more hours, report no feelings of tiredness, so we know that number is 20*.7 = 14

Please explain.

Many thanks in advance.

SJ
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