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At a certain hospital, 75% of the interns receive fewer than [#permalink]
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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?
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;
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 _________________
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.
_________________
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.
_________________
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.
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 \(\frac{a +d}{a + b + c+ d} = \frac{0.19x}{x} = 19\)%
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?
_________________
My GMAT debrief: http://gmatclub.com/forum/from620to710mygmatjourney114437.html
Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]
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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.
At a certain hospital, 75% of the interns receive fewer than [#permalink]
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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
_________________
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.
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]
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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
Re: At a certain hospital, 75% of the interns receive fewer than [#permalink]
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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
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.
_________________
Regards, Suyash
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