Hospitals

[j_shreyans]

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

[DavidG@VeritasPrep]

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:




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





Answer is C

[Brent@GMATPrepNow]

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:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
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- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

[jain2016]

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