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# At a certain hospital, 75% of the interns receive fewer than

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At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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03 Feb 2011, 08:23
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64% (02:36) correct 36% (02:41) wrong based on 807 sessions

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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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03 Feb 2011, 08:49
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1
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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.

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03 Feb 2011, 09:38
3
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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  [#permalink]

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25 Jul 2011, 21:11
3
the solution is in the table -
Attachments

table.JPG [ 8 KiB | Viewed 37817 times ]

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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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11 Jun 2015, 21:36
2
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:

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 $$\frac{a +d}{a + b + c+ d} = \frac{0.19x}{x} = 19$$%

Hope it's clear

Regards
Harsh
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03 Feb 2011, 09:25
1
2
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.

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  [#permalink]

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25 Jul 2011, 20:38
1
2
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  [#permalink]

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21 Jun 2012, 20:58
1
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  [#permalink]

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16 Feb 2013, 11:39
1
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??

for explanation, Pls go thru the attachment. see if it makes sense.

Regards,

Abhijit
Attachments

Book1.xlsx [10.95 KiB]

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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.
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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% = 80-75
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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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17 Apr 2012, 05:54
Thanks Bunuel for the link to the video
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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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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 ..

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, 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??
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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-------

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Re: Sets problem - Tired  [#permalink]

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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  [#permalink]

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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 %?

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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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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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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.

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 80-75 = 5%.

Rest is well explained in earlier posts.

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Re: Unsettling Sets   [#permalink] 12 Sep 2013, 10:25

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