Problem Solving

Another question:

At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired duringtheir 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?

Thanks

creative1 wrote:Another question:

At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired duringtheir 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?

Thanks

Assume, Total Interns = 100
Sleep less than 6 hours = 80
Sleep less than 6 and Tired = 75/100 * 80
Sleep greater than 6 and No tired = 70/100 * 20 = 14

Sleep less than 6 and not tired = 25/100 * 80 = 20

what percent of the interns report no feelings of tiredness during their shifts?

Sleep greater than 6 and No tired + Sleep less than 6 and not tired = 14 + 20 = 34

=> 34/100 * 100% = 34%

Some clarity on this , I also got [spoiler]34%[/spoiler] ,

basically its 25% of 80% of 100 = 20
and
14%

where assume 100 as the total.

In matrix method , ans will be [spoiler]19%[/spoiler] if you

add : 5% of 80% + 14%

can someone explain matrix form here?

great question. Spend a lot of time doing it, and wasnt getting the right answer, used the double matrix but there was something missing.

Then I realized I was being very stupid and not taking out the percentage of the non tired- it says 70 percent- so its 70% of 20% of 100!

Got 14, and then added to the 5!

Double matrix is the best way to solve sets, ive seen a lot of people use calculations, maybe they are more comfortable with that, but the double matrix really allows you to "fill in the gaps"

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

This is an EITHER/OR group problem.
Every intern EITHER receives fewer than 6 hours of sleep OR does not.
Every intern EITHER is tired OR is not.
To organize the data, use a GROUP GRID:

_______________<6______6plus_______Total

tired:

not tired:

total:

In the grid above, every row has to add up to the total, as does every column.
Looking at the top row, (fewer than 6 hours sleep and tired) + (6 or more hours sleep and tired) = total tired.
Looking at the left-most column, (fewer than 6 hours sleep and tired) + (fewer than 6 hours sleep and not tired) = total with fewer than 6 hours sleep.

Now let's fill in the data step by step.
Whenever we have 2 entries in a row or column, we can determine the remaining entry, since everything has to add up horizontally and vertically.
Let the total = 100:

_______________<6______6plus_______Total

tired:

not tired:

total:_______________________________100



75% of the interns receive fewer than 6 hours of sleep and report feeling tired:

__________________<6______6plus_______Total

tired:________________75

not tired:

total:____________________________________100



80% of the interns receive fewer than 6 hours of sleep:

__________________<6______6plus_______Total

tired:______________75

not tired:___________5

total:______________80_______20________ 100



70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness:

__________________<6______6plus_______Total

tired:______________75_______6__________81

not tired:___________5_______14_________19

total:______________70_______20________ 100



Notice that everything adds up horizontally and vertically.
Total not tired = 19.

The correct answer is C.

creative1 wrote:Another question:

At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired duringtheir 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?

Thanks

The wordings of this question are very deceiving once you get through them, solving this problem is easy. Assuming total no of interns =100

80% of the interns receive fewer than 6hrs of sleep (This sentence implies 80 interns received less than 6hrs while rest i.e 20 interns received more than 6hrs of sleep)

75% of the interns receive fewer than 6hrs of sleep and report tiredness(doesn't imply 25% i.e rest of the students received more than 6hrs of sleep, but 75 students out of 80 students who had less than 6hrs of sleep are tired and remaining 5 of them though less than 6hrs of sleep are not tired)

70% of the interns who received 6 or more hrs of sleep are not tired(This statement implies 70% of 20 are not tired & 30% of 20 are tired)

Use the double matrix method to get to the answer as below

100 Slept>6 Slept <6
Tired 6 75
Not tired 14 5
20 80


Ans 14 + 5 = 19

Consider posting the options as well, any alternate method of solving a question can also be discussed if there is any.
Thank you.