Problem Solving

80% of all interns receive less than 6 hours of sleep. 75% of all interns receive less than 6 hours of sleep and report feeling tired. So, subtracting, 5% of all interns receive less than 6 hours of sleep and do not report feeling tired.

We then also have the remaining 20% of interns who get more than 6 hours of sleep. 70% of them do not report being tired. Multiplying, 20% of 70% is 14%, so we know 14% of all interns get more than 6 hours of sleep and do not report being tired.

Adding the percentages from each group, 5+14 = 19% of all interns do not report feeling tired.

BTGmoderatorDC wrote: ↑

Tue Feb 11, 2020 8:10 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



OA C

Source: Manhattan Prep

We can let the total number of interns surveyed = 100. Thus, 80 interns receive fewer than 6 hours of sleep, and 20 interns receive at least 6 hours of sleep. Furthermore, 75 interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. In other words, 5 interns who receive fewer than 6 hours of sleep report no feelings of tiredness during their shifts. Moreover, 0.7 x 20 = 14 interns who receive at least 6 hours of sleep report no feelings of tiredness during their shifts. Therefore, a total of 5 + 14 = 19 interns, or 19% of all interns, report no feelings of tiredness during their shifts.

Answer: C

BTGmoderatorDC wrote: ↑

Tue Feb 11, 2020 8:10 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

OA C

Source: Manhattan Prep

Since 80% of the interns receive fewer than 6 hours of sleep, it means that 20% of the interns receive 6 or more hours of sleep.

Percent of interns who receive 6 or more hours of sleep and feel tired = (100 – 70)% of 20% = 30% of 20% = 6%;

We already know that 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts.

Thus, percent of the interns report tiredness during their shifts = 6 + 75 = 81%

Thus, percent of the interns report no feeling of tiredness during their shifts = 100 – 81 = 19%

The correct answer: C

Hope this helps!

-Jay
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