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
At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their
This topic has expert replies

 Moderator
 Posts: 5675
 Joined: 07 Sep 2017
 Followed by:18 members
GMAT/MBA Expert
 Ian Stewart
 GMAT Instructor
 Posts: 2583
 Joined: 02 Jun 2008
 Location: Toronto
 Thanked: 1090 times
 Followed by:355 members
 GMAT Score:780
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.
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.
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 6195
 Joined: 25 Apr 2015
 Location: Los Angeles, CA
 Thanked: 43 times
 Followed by:24 members
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.BTGmoderatorDC wrote: ↑Tue Feb 11, 2020 8:10 pmAt 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
Answer: C
Scott WoodburyStewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 3008
 Joined: 22 Aug 2016
 Location: Grand Central / New York
 Thanked: 470 times
 Followed by:32 members
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.BTGmoderatorDC wrote: ↑Tue Feb 11, 2020 8:10 pmAt 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
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
_________________
Manhattan Review
Locations: Manhattan Review Jayanagar  GMAT Prep Tarnaka  GRE Prep Madhapur  Kukatpally GRE Coaching  and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.