At a certain hospital, 75% of the interns receive fewer than : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 23:00

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 541
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Followers: 21

Kudos [?]: 410 [6] , given: 75

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

### Show Tags

03 Feb 2011, 08:23
6
KUDOS
23
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

60% (02:41) correct 40% (01:29) wrong based on 821 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92940 [8] , given: 10528

### Show Tags

03 Feb 2011, 08:49
8
KUDOS
Expert's post
4
This post was
BOOKMARKED
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.

_________________
Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 541
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Followers: 21

Kudos [?]: 410 [0], given: 75

### Show Tags

03 Feb 2011, 09:25
1
This post was
BOOKMARKED
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?
_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92940 [2] , given: 10528

### Show Tags

03 Feb 2011, 09:38
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7119
Location: Pune, India
Followers: 2129

Kudos [?]: 13625 [1] , given: 222

Re: Sets problem - Tired [#permalink]

### Show Tags

25 Jul 2011, 20:38
1
KUDOS
Expert's post
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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 24 Mar 2011 Posts: 457 Location: Texas Followers: 5 Kudos [?]: 164 [3] , given: 20 Re: Sets problem - Tired [#permalink] ### Show Tags 25 Jul 2011, 21:11 3 This post received KUDOS the solution is in the table - Attachments table.JPG [ 8 KiB | Viewed 17511 times ] Intern Joined: 11 Sep 2011 Posts: 27 Followers: 1 Kudos [?]: 39 [0], given: 0 Re: At a certain hospital, 75% of the interns receive fewer than [#permalink] ### Show Tags 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. Manager Joined: 27 Oct 2011 Posts: 191 Location: United States Concentration: Finance, Strategy GMAT 1: Q V GPA: 3.7 WE: Account Management (Consumer Products) Followers: 5 Kudos [?]: 150 [0], given: 4 At a certain hospital, 75% of the interns receive fewer than [#permalink] ### Show Tags 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 _________________ DETERMINED TO BREAK 700!!! Senior Manager Joined: 30 Jun 2011 Posts: 274 Followers: 0 Kudos [?]: 65 [0], given: 20 Re: At a certain hospital, 75% of the interns receive fewer than [#permalink] ### Show Tags 17 Apr 2012, 05:54 Thanks Bunuel for the link to the video Intern Joined: 24 Oct 2011 Posts: 2 GMAT Date: 07-27-2012 Followers: 1 Kudos [?]: 0 [0], given: 4 At a certain hospital, 75% of the interns receive fewer [#permalink] ### Show Tags 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% Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2129 Kudos [?]: 13625 [1] , given: 222 Re: Tuesday Q2 - Interns [#permalink] ### Show Tags 21 Jun 2012, 20:58 1 This post received KUDOS Expert's post 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Moderator
Joined: 02 Jul 2012
Posts: 1231
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 115

Kudos [?]: 1384 [0], given: 116

### Show Tags

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.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Manager
Joined: 28 Aug 2012
Posts: 52
Concentration: Operations, Marketing
GMAT 1: 510 Q36 V25
GPA: 4
WE: Information Technology (Other)
Followers: 0

Kudos [?]: 123 [0], given: 105

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

### Show Tags

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??
MBA Section Director
Status: On vacation...
Affiliations: GMAT Club
Joined: 21 Feb 2012
Posts: 3937
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
Followers: 391

Kudos [?]: 2873 [1] , given: 2159

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

### Show Tags

16 Feb 2013, 11:39
1
KUDOS
Expert's post
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]

_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 433 [0], given: 11

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

### Show Tags

03 Mar 2013, 20:26
-------------Fewer than 6 / 6 or more
--not tired-- .75x.
--tired------ .05x. /------.14x-------/---.19x----
Total-----------.80x-------/------.20x-------/---x-------

_________________

Impossible is nothing to God.

Intern
Joined: 23 Feb 2013
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 22

Re: Sets problem - Tired [#permalink]

### Show Tags

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 %?
Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92940 [0], given: 10528

Re: Sets problem - Tired [#permalink]

### Show Tags

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 %?

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92940 [0], given: 10528

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

### Show Tags

05 Jul 2013, 01:27
Expert's post
1
This post was
BOOKMARKED
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

_________________
Intern
Joined: 05 Aug 2012
Posts: 42
Concentration: Technology, General Management
GMAT Date: 09-16-2013
GPA: 3.5
WE: Analyst (Consulting)
Followers: 0

Kudos [?]: 28 [0], given: 11

### Show Tags

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.

_________________

Regards,
Suyash

I want to live in a world where emails are short, love letters are brave, and every "Thank you" note is scribbled by hand.
GO GREEN

Intern
Joined: 31 May 2013
Posts: 14
Followers: 0

Kudos [?]: 2 [0], given: 31

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

### Show Tags

25 Jul 2014, 03:48
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.

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
Re: At a certain hospital, 75% of the interns receive fewer than   [#permalink] 25 Jul 2014, 03:48

Go to page    1   2    Next  [ 25 posts ]

Similar topics Replies Last post
Similar
Topics:
2 A certain roller coaster ride has fewer than 110 people waiting in lin 6 02 Nov 2016, 01:58
19 If there are fewer than 8 zeroes between the decimal point and the 8 15 Jun 2016, 00:34
1 Jack and Jill work at a hospital with 4 other workers. For an internal 2 02 Jun 2016, 03:33
12 Of the final grades received by the students in a certain 8 26 Dec 2012, 06:04
6 At a certain hospital, 75% of the interns receive fewer than 8 22 Sep 2008, 01:09
Display posts from previous: Sort by