CAT Quant question

[karenshushang]

Below is a question from one of the CATs and I can't wrap my head around the answer....

Question:

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

Answer key: (c)
Using double-set matrix to organize the information:
Tired Not Tired TOTAL
6 or more hours 6 14 20
Fewer than 6 hours 75 5 80
TOTAL 81 19 100

Here's my understanding of the question:
Given "75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts" and "If 80% of the interns receive fewer than 6 hours of sleep" then the not tired interrns with fewer than 6 hours of sleep would account for 20% (25% of not tired interns among the 80% internss with fewers than 6 hours of sleep) of the entire intern population. I can't figure out how the answer key accounts this group as 5% of the population.

I'm fine with calculating the second part of the question regarding the proportion of interns with more than 6 hours of sleep not feeling tired (20%*70%).

Thanks!

[RonPurewal]

Below is a question from one of the CATs and I can't wrap my head around the answer....

Question:

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

Answer key: (c)
Using double-set matrix to organize the information:
Tired Not Tired TOTAL
6 or more hours 6 14 20
Fewer than 6 hours 75 5 80
TOTAL 81 19 100

Here's my understanding of the question:
Given "75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts" and "If 80% of the interns receive fewer than 6 hours of sleep" then the not tired interrns with fewer than 6 hours of sleep would account for 20% (25% of not tired interns among the 80% internss with fewers than 6 hours of sleep) of the entire intern population. I can't figure out how the answer key accounts this group as 5% of the population.

I'm fine with calculating the second part of the question regarding the proportion of interns with more than 6 hours of sleep not feeling tired (20%*70%).

Thanks!

hi, you're misreading the 75% statement. i can tell that you're misreading it because you're taking percentages of the less-than-6-hours group; unfortunately, that's not what the actual words say you should do.

if that statement were to say...
75% of the interns who get less than 6 hours of sleep/day report feeling tired
... then your interpretation would be correct.

but, that's not what it says.
it says that 75% of ALL the interns have BOTH of these things (<6 hours and tired).
let's say that there are 100 interns total. then, 75 of them have both things.
80 of them get <6 hours of sleep (whether they're tired or not), so 80 - 75 = 5 of them get <6 hours of sleep but aren't tired.

[garima_aries01]

Suppose
L = less sleep
M = More sleep
T = tired
N = not tired

we can have 2x2 = 4 combinations
LT
LN
MT
MN

LT + LN +MT + MN = 100

LT = 75
LT + LN = 80
=> LN = 5
and MT + MN = 20

70% of (MT + MN) = MN
=> MN = 14
MT = 6

Ques asks LN + MN = 5 + 14 =19

[tim]

i would definitely recommend using a double set matrix for this and all other overlapping sets problems with two categories..