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At a certain hospital, 75% of the interns receive fewer than [#permalink]
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03 Feb 2011, 09:23
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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 [#permalink]
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03 Feb 2011, 09:49
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 [#permalink]
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03 Feb 2011, 10:25
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: Tired Interns [#permalink]
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03 Feb 2011, 10:38



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Re: Sets problem  Tired [#permalink]
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25 Jul 2011, 21:38
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: Sets problem  Tired [#permalink]
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25 Jul 2011, 22:11
the solution is in the table 
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Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]
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01 Apr 2012, 00:41
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 [#permalink]
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15 Apr 2012, 15:31
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 [#permalink]
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17 Apr 2012, 06:54
Thanks Bunuel for the link to the video



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At a certain hospital, 75% of the interns receive fewer [#permalink]
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21 Jun 2012, 18:53
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: Tuesday Q2  Interns [#permalink]
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21 Jun 2012, 21:58
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: PS 700 level [#permalink]
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28 Oct 2012, 23:56
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 [#permalink]
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16 Feb 2013, 12:00
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 [#permalink]
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16 Feb 2013, 12:39
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 [#permalink]
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03 Mar 2013, 21:26
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 [#permalink]
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07 Apr 2013, 17:19
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 [#permalink]
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07 Apr 2013, 22:45



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Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]
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Re: Unsettling Sets [#permalink]
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12 Sep 2013, 11:25
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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Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]
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25 Jul 2014, 04:48
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 interns with 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




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