ankushbagwale wrote:

How this queston can be done with venn diagram. Can anyone suggest. I have tried the following combinations for the circles:

a. Tired one circle & Few than 6 hrs another circle.

Here How do I represent the balance more or equal to 6 hrs ( by another circle??)

2. Non tired one & more than 6 hrs another circle.

Still not gettign there.

Hi

ankushbagwale,

Presenting the Venn diagram approach for the question. Please refer the diagram below:

GivenNumber of interns who receive fewer than 6 hours of sleep and report feeling tired = \(b\) = 75% of total interns.

Number of interns who receive 6 or more hours of sleep and report no feeling of tiredness = \(d\) = 70% of interns who receive more than 6 hours of sleep

Number of interns who receive less than 6 hours of sleep = \(a + b = 80\)% of total interns

We are asked to find the percent of interns who report no feeling of tiredness.

Number of interns who report no feeling of tiredness = \(a + d\).

Hence we need to find \(\frac{a +d}{a + b + c+ d}\).

ApproachAs we are not given any info about the number of interns, to find the ratio of of interns who report no feeling of tiredness to the total interns we need to express them in the same terms. With this understanding let's proceed to the working out.

Working OutLet's assume the total number of interns to be \(x\). i.e. \(a + b + c + d = x\)

\(b = 75\)% of total interns \(= 0.75x\)

\(a + b = 80\)% of total interns \(= 0.8x\) which would give us \(a = 0.05x\)

It also tells us that \(c + d = 0.2x\).

\(d = 70\)% of interns who receive more than 6 hours of sleep

Interns who received more than 6 hours of sleep \(= c +d\)

So, we can write \(d = 70\)% of \((c + d) = 70\)% of \(0.2x = 0.14x\)

Hence \(a + d = 0.05x + 0.14x = 0.19x\)

So \(\frac{a +d}{a + b + c+ d} = \frac{0.19x}{x} = 19\)%

Answer: Option C

Hope it's clear

Regards

Harsh

Thanks Harsh for your prompt response. You have demonstrated how venn diagram can be utilized effectively. Although I could grasp your approach, I wonder how you came up with > 6 hrs of sleep & not tired being shown by the empty spaces.

However, I have tried to to visualize in the following way. can you pl. comment on the same? I would like to move from this three circle format to two. Any suggestions.

Also, the double matrix method seems quite neat & crystal clear.