Tired VS Not tired 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

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________≥6_______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_______≥6_______Total

tired:

not tired:

total:_______________________________100



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

__________________<6_______≥6_______Total

tired:_____________75

not tired:

total:____________________________________100



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

__________________<6_______≥6_______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:
Since .7(20) = 14, we get:

__________________<6_______≥6_______Total

tired:______________75_______6__________81

not tired:___________5_______14_________19

total:______________80_______20________ 100



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

The correct answer is C.

GMATGuruNY 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

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.

NW THTS WT I CALL AN XPLAINATION!!!!!