Interns Falling Asleep

[abcdefg]

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

OA is C .

I understand how to do this via a double matrix. However when I was working on this practice exam, I really got tripped up with thinking the "75%" that was 75% of the 80% interns, not 75% of interns total.

Anyone know how the wording should have been if they were talking about 75% of the 80% interns? Just cant wrap my mind around it. Thanks.

[PussInBoots]

"75% of the interns WHO receive fewer" or "75% of ALL the interns WHO receive fewer"

P.S.: Did you solve the problem this way: <6 hours sleep, not tired + >6 hours sleep, not tired = (80% - 75%) + 70% * (100% - 80%)?

[truplayer256]

x interns in the hospital

.80(x)= Interns who receive fewer than 6 hours of sleep.

.20(x)= Interns who receive 6 or more hours of sleep.

.20(x)*.7=.14(x)= Interns that sleep for 6 or more hours and report no feelings of tiredness during their shifts.

.80(x)-.75(x)=.05(x)= Interns that sleep for less than 6 hours and report no feelings of tiredness during their shifts.

.14(x)+.05(x)/(x)=.19(x)/(x)=.19

.19*100=19% C