## 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

### At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their

by BTGmoderatorDC » 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

### GMAT/MBA Expert

GMAT Instructor
Posts: 2583
Joined: 02 Jun 2008
Location: Toronto
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

### Re: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their

by Ian Stewart » Wed Feb 12, 2020 5:32 am
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.
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

GMAT Instructor
Posts: 6195
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:24 members

### Re: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their

by [email protected] » Fri Feb 14, 2020 1:29 pm
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

Scott Woodbury-Stewart
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

GMAT Instructor
Posts: 3008
Joined: 22 Aug 2016
Location: Grand Central / New York
Thanked: 470 times
Followed by:32 members

### Re: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their

by [email protected] » Tue Feb 18, 2020 12:18 am
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
_________________
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.

• Page 1 of 1