• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

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: 4735
Joined: 07 Sep 2017
Followed by:10 members
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

User avatar
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.
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

User avatar
GMAT Instructor
Posts: 5170
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:23 members
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
scott@targettestprep.com

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3007
Joined: 22 Aug 2016
Location: Grand Central / New York
Thanked: 470 times
Followed by:32 members
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.