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# At a certain hospital, 75% of the interns receive fewer than

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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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28 Jul 2014, 01:37
shivdeepmodi wrote:
Bunuel wrote:
gmatpapa 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
Given:
 < 6 hours sleep >= 6 hours sleep TOTAL Tired 75 - - Not Tired - 0.7*X ? TOTAL 80 X 100

Interns who receive < than 6 hours sleep and Not Tired = 80 - 75 = 5;

TOTAL interns who receive >= 6 hours sleep = 100 - 80 = 20, so interns who receive >= 6 hours sleep and are Not Tired = 0.7 * 20 =14;

Interns who are Not Tired = 5 + 14 = 19.

Guys,
As per the solution : interns with LT6 hours of sleep and tired = 75% of total interns(75 assuming a smart number)
However I calculated it as : 0.75x0.80N. i.e. 75% of 80% of internswith LT6 hours of sleep.(which is obviously wrong).
I am not going very far with such mistakes.
Next comes a sillier question: how to avoid such mistakes.
Regards,
shivdeep

Needless to say, Bunuel's method is perfect

There is no need to calculate 75% of 80%

As the answer is expected in percentage, better take the Total interns = 100 so that the %age factor gets computed along
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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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08 Jun 2015, 09:42
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.
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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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11 Jun 2015, 21:36
2
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:

Given
Number 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 $$\frac{a +d}{a + b + c+ d}$$.

Approach
As 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 Out
Let'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 $$\frac{a +d}{a + b + c+ d} = \frac{0.19x}{x} = 19$$%

Hope it's clear

Regards
Harsh
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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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12 Jun 2015, 09:49
EgmatQuantExpert wrote:
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:

Given
Number 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 $$\frac{a +d}{a + b + c+ d}$$.

Approach
As 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 Out
Let'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 $$\frac{a +d}{a + b + c+ d} = \frac{0.19x}{x} = 19$$%

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.
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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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12 Oct 2017, 17:24
gmatpapa 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

100 interns

20(.7)= 14

80 fewer 6 hours ----75 fewer 6 sleepy, 5 fewer 6 not sleepy
20 more 6 hours-----6 more 6 sleepy, 14 more 6 not sleepy

14 + 5= 19

c
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At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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05 Jun 2018, 00:20
Quote:
n(FEW) = 80%
Therefore, n(Not FEW) = 20%

Also since n(FEW and TIRED) = 75%, n(FEW and Not TIRED) = 5%

Could you please tell me why

1. 'Fewer than 6hrs of sleep & Tired' isent 75% of (80% of interns who get less than 6hrs of sleep)
2. 'Fewer than 6hrs of sleep & NOT Tired' isent 25% of (80% of interns who get less than 6hrs of sleep)

Because for 'More than 6hrs of sleep' that's the method that we use right?

"We know that n(Not FEW) = 20%. 70% of these are not tired.
So n(Not TIRED and Not FEW) = 70% of 20% = 14%" ..?
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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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04 Sep 2018, 03:24
gmatpapa 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

We can let the total number of interns surveyed = 100. Thus, 80 interns receive fewer than 6 hours of sleep, and 20 interns receive at least 6 hours of sleep. Furthermore, 75 interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. In other words, 5 interns who receive fewer than 6 hours of sleep report no feelings of tiredness during their shifts. Moreover, 0.7 x 20 = 14 interns who receive at least 6 hours of sleep report no feelings of tiredness during their shifts. Therefore, a total of 5 + 14 = 19 interns, or 19% of all interns, report no feelings of tiredness during their shifts.

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Re: At a certain hospital, 75% of the interns receive fewer than  [#permalink]

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07 Oct 2019, 21:12
Hi. I tried to solve this problem in the manner described in the attachment, and of course it's wrong. But I am not able to figure out where I went wrong. Can you please help? Thanks.
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File comment: Sets_700Q_Problem_2

Sets_700Q_Problem_2.png [ 8.44 KiB | Viewed 86 times ]

Re: At a certain hospital, 75% of the interns receive fewer than   [#permalink] 07 Oct 2019, 21:12

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