Problem Solving

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?
6
14
19
20
81

You've got 80% of the interns receiving fewer than 6h of sleep, but only 75% also report feeling tired. That means that the remaining 5% receive less than 6h of sleep, but don't feel tired.
Since 80% of them report less than 6 h of sleep, that means that 20% get more rest. Of these guys, 70% say they don't feel tired. 70% of 20% means 14% of the total "population" of interns.
So you've got:
- 5% of interns sleep less than 6h and don't feel tired
- 14% of interns sleep 6h or more and don't feel tired.

Adding those up, you get 19% of the total number of interns don't feel tired.

Nice solution DanaJ.

Here is an alternate way to look at it visually as a double set matrix. This helps visualizing the problem very clearly...Please refer to the attached diagram for details.