Problem Solving

In a hospital, 75% of the interns receive fewer than 6 hours of sleep and complain for the feelings of fatigue during the shifts. 70% of interns, who receive 6 or more hours of sleep, do not complain for the feelings of fatigue during the shifts. If 80% of interns receive fewer than 6 hours of sleep, then what percent of interns do not complain for the feelings of fatigue during the shifts?
A. 6
B. 14
C. 19
D. 20
E. 81

Lets assume there are 100 interns

80% of them got less than 6 hr sleep
therefore 20% got >= 6 hr sleep

20% of 100 = 20

of these 20, 70% did not complain of fatigue

70% of 20 = 14

so 14 is the number of interns who did not complain of fatigue.

14 is what % of 100 = 14%

(in terms of percentage it will remain the same since we assumed there were 100 interns)


B

let number of interns be 100

if 80 get <6 hrs sleep, 20 get >6 hrs of sleep.

70% of interns, who receive >6 hrs of sleep have no fatigue
=> 70%*20=14 have >6 hrs of sleep and no fatigue


given 75% of interns or 75 get <6 hrs of sleep and have fatigue.
=>80-75=5 get <6 hrs of sleep and have no fatigue

total number of no fatigue people: 14+5=19 or 19% of interns

let number of interns be 100

if 80 get <6 hrs sleep, 20 get >6 hrs of sleep.

70% of interns, who receive >6 hrs of sleep have no fatigue
=> 70%*20=14 have >6 hrs of sleep and no fatigue


given 75% of interns or 75 get <6 hrs of sleep and have fatigue.
=>80-75=5 get <6 hrs of sleep and have no fatigue

75% of 80 = 60, so the number of interns with no fatigue = 80 -60 = 20

total number of no fatigue people: 14+5=19 or 19% of interns

14+20=34 or 34% of interns

BUT when it says 75% compalined of fatigue it does not necessarily mean the rest 25 % did not complain of fatigue. They might have had 'no comments'

Whats the OA?

scoobydooby wrote:let number of interns be 100

if 80 get <6 hrs sleep, 20 get >6 hrs of sleep.

70% of interns, who receive >6 hrs of sleep have no fatigue
=> 70%*20=14 have >6 hrs of sleep and no fatigue


given 75% of interns or 75 get <6 hrs of sleep and have fatigue.
=>80-75=5 get <6 hrs of sleep and have no fatigue

total number of no fatigue people: 14+5=19 or 19% of interns

I arrived at this the same way. C. 19 is what I got

I get 34% (20 +14). Either the Question is wrong or answer choices are wrong.

My final matrix looks like the one in the attachment

The answer has to be 14


@Vittal

Please check the Box of the matrix containing 14.That's what the Question is asking for.


I believe this is a simple unitary method question

If there are 100 interns:

If 80% of interns receive fewer than 6 hours of sleep

And 70% of interns, who receive 6 or more hours of sleep, do not complain for the feelings of fatigue during the shifts.

ie: 70% of 20
=14

So 14% of interns do not complain for the feelings of fatigue during the shifts

gmat740 wrote:The answer has to be 14


@Vittal

Please check the Box of the matrix containing 14.That's what the Question is asking for.


I believe this is a simple unitary method question

If there are 100 interns:

If 80% of interns receive fewer than 6 hours of sleep

And 70% of interns, who receive 6 or more hours of sleep, do not complain for the feelings of fatigue during the shifts.

ie: 70% of 20
=14

So 14% of interns do not complain for the feelings of fatigue during the shifts

"what percent of interns do not complain for the feelings of fatigue during the shifts? "

As I understand we need to know what percent of ppl do not complain feelings for fatigue. This would include both ppl who worked < 6 hrs and >= 6hrs.

Anyway, now that we have discussed, we have understood what number to use when.
Thanks for the discussion.

rgds
-V

Why it's 14, not 34 ?

what percent of interns do not complain for the feelings of fatigue during the shifts?

If it's 14, then the question should be

what percent of interns who receive more than 6 hours to sleep do not complain for the feelings of fatigue during the shifts?

BUT when it says 75% compalined of fatigue it does not necessarily mean the rest 25 % did not complain of fatigue. They might have had 'no comments'

Quite a tricky question. This question should be listed in sentence correction

vittalgmat and sacx,
it says "75% of the interns receive fewer than 6 hours of sleep and complain for the feelings of fatigue during the shifts"

so if we take the total number of interns to be 100, 75% of 100 ie, 75 have <6 hrs of sleep +fatigue

it doesnt say "75% of the interns who receive <6 hrs of sleep have fatigue"
so we do not need to take 75% of 80

so the people with no fatigue
(< 6hrs+no fatigue)+(>6 hrs+fatigue)
=5+14=19

Can we have the OA on this?? This is quite confusing!
Is it 75% or 75% of 80...

Please someone post the solution!!!!!

Instructors please help..

KICKGMATASS123 wrote:Can we have the OA on this?? This is quite confusing!
Is it 75% or 75% of 80...

Please someone post the solution!!!!!

Instructors please help..

If there were 100 interns in the hospital, then 80 of them receive fewer than 6 hours of sleep and the remaining 20 interns receive 6 or more hours of sleep, out of them 20 × 0.7 = 14 report no feelings of fatigue. Since, 75 of the interns receive fewer than 6 hours of sleep and report feelings of fatigue, therefore 80 - 75 = 5 receive fewer than 6 hours of sleep and report no feelings of fatigue.

Hence, the total of interns who report no feelings of fatigue during their shifts (are made bold above) = 14 + 5 = [spoiler]19.


C[/spoiler]