Thank you for using the timer  this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]
Show Tags
28 Jul 2014, 02:37
shivdeepmodi wrote:
Bunuel wrote:
gmatpapa wrote:
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
Given:
< 6 hours sleep
>= 6 hours sleep
TOTAL
Tired
75


Not Tired

0.7*X
?
TOTAL
80
X
100
Interns who receive < than 6 hours sleep and Not Tired = 80  75 = 5;
TOTAL interns who receive >= 6 hours sleep = 100  80 = 20, so interns who receive >= 6 hours sleep and are Not Tired = 0.7 * 20 =14;
Interns who are Not Tired = 5 + 14 = 19.
Answer: C.
Guys, As per the solution : interns with LT6 hours of sleep and tired = 75% of total interns(75 assuming a smart number) However I calculated it as : 0.75x0.80N. i.e. 75% of 80% of internswith LT6 hours of sleep.(which is obviously wrong). I am not going very far with such mistakes. Next comes a sillier question: how to avoid such mistakes. Regards, shivdeep
Needless to say, Bunuel's method is perfect
There is no need to calculate 75% of 80%
As the answer is expected in percentage, better take the Total interns = 100 so that the %age factor gets computed along
_________________
Presenting the Venn diagram approach for the question. Please refer the diagram below:
Given Number of interns who receive fewer than 6 hours of sleep and report feeling tired = \(b\) = 75% of total interns.
Number of interns who receive 6 or more hours of sleep and report no feeling of tiredness = \(d\) = 70% of interns who receive more than 6 hours of sleep
Number of interns who receive less than 6 hours of sleep = \(a + b = 80\)% of total interns
We are asked to find the percent of interns who report no feeling of tiredness.
Number of interns who report no feeling of tiredness = \(a + d\).
Hence we need to find \(\frac{a +d}{a + b + c+ d}\).
Approach As we are not given any info about the number of interns, to find the ratio of of interns who report no feeling of tiredness to the total interns we need to express them in the same terms. With this understanding let's proceed to the working out.
Working Out Let's assume the total number of interns to be \(x\). i.e. \(a + b + c + d = x\)
\(b = 75\)% of total interns \(= 0.75x\)
\(a + b = 80\)% of total interns \(= 0.8x\) which would give us \(a = 0.05x\)
It also tells us that \(c + d = 0.2x\).
\(d = 70\)% of interns who receive more than 6 hours of sleep
Interns who received more than 6 hours of sleep \(= c +d\)
So, we can write \(d = 70\)% of \((c + d) = 70\)% of \(0.2x = 0.14x\)
Hence \(a + d = 0.05x + 0.14x = 0.19x\)
So \(\frac{a +d}{a + b + c+ d} = \frac{0.19x}{x} = 19\)%
Presenting the Venn diagram approach for the question. Please refer the diagram below:
Given Number of interns who receive fewer than 6 hours of sleep and report feeling tired = \(b\) = 75% of total interns.
Number of interns who receive 6 or more hours of sleep and report no feeling of tiredness = \(d\) = 70% of interns who receive more than 6 hours of sleep
Number of interns who receive less than 6 hours of sleep = \(a + b = 80\)% of total interns
We are asked to find the percent of interns who report no feeling of tiredness.
Number of interns who report no feeling of tiredness = \(a + d\).
Hence we need to find \(\frac{a +d}{a + b + c+ d}\).
Approach As we are not given any info about the number of interns, to find the ratio of of interns who report no feeling of tiredness to the total interns we need to express them in the same terms. With this understanding let's proceed to the working out.
Working Out Let's assume the total number of interns to be \(x\). i.e. \(a + b + c + d = x\)
\(b = 75\)% of total interns \(= 0.75x\)
\(a + b = 80\)% of total interns \(= 0.8x\) which would give us \(a = 0.05x\)
It also tells us that \(c + d = 0.2x\).
\(d = 70\)% of interns who receive more than 6 hours of sleep
Interns who received more than 6 hours of sleep \(= c +d\)
So, we can write \(d = 70\)% of \((c + d) = 70\)% of \(0.2x = 0.14x\)
Hence \(a + d = 0.05x + 0.14x = 0.19x\)
So \(\frac{a +d}{a + b + c+ d} = \frac{0.19x}{x} = 19\)%
Answer: Option C
Hope it's clear
Regards Harsh
Thanks Harsh for your prompt response. You have demonstrated how venn diagram can be utilized effectively. Although I could grasp your approach, I wonder how you came up with > 6 hrs of sleep & not tired being shown by the empty spaces.
However, I have tried to to visualize in the following way. can you pl. comment on the same? I would like to move from this three circle format to two. Any suggestions.
Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]
Show Tags
12 Oct 2017, 18:24
gmatpapa wrote:
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
100 interns
20(.7)= 14
80 fewer 6 hours 75 fewer 6 sleepy, 5 fewer 6 not sleepy 20 more 6 hours6 more 6 sleepy, 14 more 6 not sleepy