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At a certain hospital, 75% of the interns receive fewer than
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03 Feb 2011, 08:23
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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
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Re: Tired Interns
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03 Feb 2011, 08:49
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.
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Re: Tired Interns
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03 Feb 2011, 09:38
gmatpapa wrote: Thanks!
Bunuel, this tabular method for solving Venn Diagram problems: is it explained anywhere with other examples? It's not a Venn Diagram problem, it's an overlapping sets problem which can be solved with Venn Diagram as well as with Double Matrix Method (which is often better). You can check overlapping sets tag to see that some of the problems are solved with this method. Also check this link for video explanation: http://www.youtube.com/watch?v=uE_aMa_W0o0
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Re: Sets problem  Tired
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25 Jul 2011, 21:11
the solution is in the table 
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Re: At a certain hospital, 75% of the interns receive fewer than
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11 Jun 2015, 21:36
ankushbagwale wrote: How this queston can be done with venn diagram. Can anyone suggest. I have tried the following combinations for the circles:
a. Tired one circle & Few than 6 hrs another circle.
Here How do I represent the balance more or equal to 6 hrs ( by another circle??)
2. Non tired one & more than 6 hrs another circle.
Still not gettign there. Hi ankushbagwale, Presenting the Venn diagram approach for the question. Please refer the diagram below: GivenNumber 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 \(\frac{a +d}{a + b + c+ d}\). ApproachAs 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 OutLet'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
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Re: Tired Interns
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03 Feb 2011, 09:25
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. Thanks! Bunuel, this tabular method for solving Venn Diagram problems: is it explained anywhere with other examples?
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Re: Sets problem  Tired
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25 Jul 2011, 20:38
vatsas 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
I need to understand the method to solve this problem. I tried the matrix method but failed. Is there any other method?
Thanks Sumeet You can just use logic or a Venn diagram, whatever works for you. I will give the logical solution below. Try to figure out the Venn diagram for it. Get back if it gets tricky. Look at the given data line by line. At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts.n(FEW and TIRED) = 75% At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. .... We will come back... If 80% of the interns receive fewer than 6 hours of sleep, n(FEW) = 80% Therefore, n(Not FEW) = 20% Also since n(FEW and TIRED) = 75%, n(FEW and Not TIRED) = 5% Now we go back to the second sentence. We know that n(Not FEW) = 20%. 70% of these are not tired. So n(Not TIRED and Not FEW) = 70% of 20% = 14% what percent of the interns report no feelings of tiredness during their shifts? n(Not TIRED) = n(FEW and Not TIRED) + n(Not TIRED and Not FEW) = 5% + 14% = 19% The notation is used only to explain it to you. You obviously don't need to do that. Just remember that when you get some data '80% people get less sleep,' it also implies that 20% get enough or more.
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Re: Tuesday Q2  Interns
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21 Jun 2012, 20:58
RichaMidha2012 wrote: 5% of 80 =4 but why you guys took it as 5% am I mistaking something asterixmatrix wrote: 80% receive less than 6 hours of sleep 75% report feeling tired so 5% dont feel tired
20% receive 6 or more hours of sleep out of this 70% report no tiredness so it become 14%
total 5%+14% = 19%...C A very important thing in percentages is to note what is the % of i.e. when I say 5%, it is 5% of what? 5% of total interns or 5% of interns who receive less than 6 hrs of sleep or 5% of interns who report tiredness etc The question says: 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts (75% of total interns) If 80% of the interns receive fewer than 6 hours of sleep (again, 80% of the total interns) So out of 80% of total interns i.e. if total interns are 100, 80 of them receive fewer than 6 hrs of sleep. Out of 100, 75 receive fewer than 6 hrs of sleep and report tiredness. Therefore, 5 receive fewer than 6 hrs of sleep but report no tiredness.
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Re: At a certain hospital, 75% of the interns receive fewer than
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16 Feb 2013, 11:39
thinktank wrote: Guys, I am like SUPER CONFUSED right now .. I used the tabular method to solve the problem but it was just the opposite to the explanations (ie). Tired and not tired in the X axis, Receive < 6 hrs , >6 hours in the Y axis .. I know this would yield the same answer but im confused.. If someone could explain by drawing the grid the way i did.. id be really really grateful. And also, how do u choose which attribute to go where.. does that really matter?? Thanks in advance for explanation, Pls go thru the attachment. see if it makes sense. Regards, Abhijit
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Re: At a certain hospital, 75% of the interns receive fewer than
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31 Mar 2012, 23:41
Let's assume total number of students are 1000. 80% of 1000 students gets <6 hrs of sleep = 800 (both tired and not tired) 75% of 1000 students gets <6 hrs and tired = 750 Therefore, students who get <6 hrs and not tired = 50..........(1)
20% of 1000 students gets >= 6 hrs of sleep = 200 (both tired and not tired) 70% of 200 students gets >=6 and not tired = 140.......(2)
(1) + (2) = 190 or 19% of total students. Hence C.



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At a certain hospital, 75% of the interns receive fewer than
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15 Apr 2012, 14:31
option c. we figure out at that 20% get more than 6 hours of sleep. then from there we know that 70% of those who get more than 6 hrs of sleep feel tired which is 14% + 5% = 19% 5% = 8075



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Re: At a certain hospital, 75% of the interns receive fewer than
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17 Apr 2012, 05:54
Thanks Bunuel for the link to the video



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At a certain hospital, 75% of the interns receive fewer
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21 Jun 2012, 17:53
5% of 80 =4 but why you guys took it as 5% am I mistaking something hogann wrote: asterixmatrix wrote: 80% receive less than 6 hours of sleep 75% report feeling tired so 5% dont feel tired
20% receive 6 or more hours of sleep out of this 70% report no tiredness so it become 14%
total 5%+14% = 19%...C Great Explanation  OA is 19%



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Re: PS 700 level
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28 Oct 2012, 22:56
AartiPajan 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 interns who receive 6 hours or more of sleep report no feeling of tiredness. If 80% of the interns receive fewer than 6 hrs sleep, what percentage of interns report no feelings of tiredness during their shift?
A. 6 B. 14 C. 19 D. 20 E. 81
Plz help... My solution says D. 20 while correct answer is C. 19 .. Thanks in advance. Creating a two overlapping set grid ____________Less Than 6________6 or more__________________Total Tired__________75________________6______________________81 Not Tired________5_______________14______________________19 Total__________80_______________20_____________________100 Kudos Please... If my post helped.



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Re: At a certain hospital, 75% of the interns receive fewer than
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16 Feb 2013, 11:00
Guys, I am like SUPER CONFUSED right now .. I used the tabular method to solve the problem but it was just the opposite to the explanations (ie). Tired and not tired in the X axis, Receive < 6 hrs , >6 hours in the Y axis .. I know this would yield the same answer but im confused.. If someone could explain by drawing the grid the way i did.. id be really really grateful. And also, how do u choose which attribute to go where.. does that really matter?? Thanks in advance



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Re: At a certain hospital, 75% of the interns receive fewer than
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03 Mar 2013, 20:26
Fewer than 6 / 6 or more not tired .75x. tired .05x. /.14x/.19x Total.80x/.20x/x
Answer: C



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Re: Sets problem  Tired
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07 Apr 2013, 16:19
agdimple333 wrote: the solution is in the table  I'm trying to understand why you had to calculate "70% of 20" but at the same time you left "5" untouched? Why would we take % of a %?



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Re: Sets problem  Tired
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07 Apr 2013, 21:45
gmat978 wrote: agdimple333 wrote: the solution is in the table  I'm trying to understand why you had to calculate "70% of 20" but at the same time you left "5" untouched? Why would we take % of a %? This post might help: atacertainhospital75oftheinternsreceivefewerthan108658.html#p863611
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Re: At a certain hospital, 75% of the interns receive fewer than
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05 Jul 2013, 01:27
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
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Re: Unsettling Sets
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12 Sep 2013, 10:25
sidmohan84 wrote: I am havign difficulty understanding teh below problem:
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
What is the relation between the 75% and the 80% stated. Please explain with solution.
Answer: C Hello, There are two things that you need to understand: One is set of intern which receive less than 6 hours of sleep and at the same time they feel tired. As per the question, the % of such interns is 75%. Second set talks about intern who receive less than 6 hours of sleep, however it does not talk anything about whether this set of intern felt tired or not. As per the question, the % of such intern is 80%. Since it is a overlapping set question, we can figure the % of intern who slept of less than 6 Hrs, but didn't felt tired. Hence the % comes out to be 8075 = 5%. Rest is well explained in earlier posts. Hope it answers your question.
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