Tired Interns (CAT 2)

[dixitsandeep]

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
===================

Please note the first line (without a 'who').

At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts.


And also the second line (contains a 'who').

At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness.

First line conveys the meaning that 75% of total interns receive fewer than 6 hours of sleep.

This meaning contrasts the final line..

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

therefore problem is absurd without a 'who' in first line.

The explanation to the question assume that 75% interns mentioned in first are the ones who receive fewer than 6 hours of sleep.

The meaning may be obvious for some, but it confused me during CAT 2. which wasted some of my time, also i did not get this question right.

[tim]

no. take a closer look at what the 75% represents. you can't just stop reading in the middle of a sentence.. :)

[dixitsandeep]

no. take a closer look at what the 75% represents. you can't just stop reading in the middle of a sentence.. :)

Sir,
elaboration of the meaning will help.

[tim]

taking a closer look at this one yourself would help. what does the 75% represent, and what does the 80% represent? you seem to think they represent the same things, which they don't. take a closer look..

[krishnan.anju1987]

Is the answer A for this one? This is how I solved it.

Let the total population of interns be x.

Then, interns who receive less than 6 hours of sleep=.75x.

Interns who receive more than 6 hours of sleep=.25x.

70% of these interns complaint of tiredness.

Now, if 80% of the students receive less than 6 hours of sleep, then .30*.20x=.06X do not complaint.

Am I right in this question. Somehow I don't seem to be using the first part of the question which makes me doubt my answer.

[krishnan.anju1987]

I have read through the question multiple times and the only difference I can find is the second statement involving the quantity 80% has an IF and is thus the hypothetical situation for which we have to calculate data. But if so, the statement mentioning that 75% of the interns receive lesser than 6 hours of sleep is not used.

[allegro2012]

Has anyone found an answer to this question... i cannot seem to understand what the ask is based on the information given.

[krishnan.anju1987]

Yup, I finally got it.

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?

P(people who receive lesser and 6 hours of sleep and are tired)= 0.75*X--------1)

P(people who receive fewer than 6 hours of sleep)=.80*X----2)

Therefore, P(people who receive more than 6 hours of sleep)=0.20*X--------3)

P(receive more than 6 hours of sleep and report no tiredness)=0.70*0.20*x----4)

Now consider the total number of people are 100

Thus the values become

P(people who receive lesser and 6 hours of sleep and are tired)= 75--------1)

P(people who receive fewer than 6 hours of sleep)=80 ----2)

Therefore, P(people who receive more than 6 hours of sleep)=20 --------3)

P(receive more than 6 hours of sleep and report no tiredness)=14----4)

Hence, from 1 and 2) 5 people receive less than 6 hours of sleep and don't complain of tiredness and combining 4 with it answer is 19.

C.

[tim]

sounds good. let us know if there are any further questions on this one..