In a hospital, 75% of the interns receive fewer than 6 hours of sleep and complain for the feelings of fatigue during the shifts. 70% of interns, who receive 6 or more hours of sleep, do not complain for the feelings of fatigue during the shifts. If 80% of interns receive fewer than 6 hours of sleep, then what percent of interns do not complain for the feelings of fatigue during the shifts?
A. 6
B. 14
C. 19
D. 20
E. 81
Answer is B (14%).
I think in the 1st line of the question, the word ‘who’ should be inserted between ‘interns’ and ‘receive’ as it is given in later part of the question that 80% of interns receive less than 6 hours of sleep. Hence, 20% of interns receive 6 or more hours of sleep.
Interns complaining of fatigue = 75% of 80% of total interns = 60% of interns
Hence, interns who don’t complain of fatigue = 70% of (balance 20% of total interns) = 14% of interns
Pretty confusing, so you need to analyze the data. 75% of all interns are below 6 and complain. 70% of the interns who are above 6 don’t complain, while 80% of all interns are below 6. The question asks what % of everyone does not complain.
Well, we have 20% of everyone who are above 6, and of them 70% don’t complain. That’s 14%, so right away we can rule out answers A and B. Now, we’re left with finding the % of the workers who are below 6 and complain, and add the two up.
Of all interns, we know 80% are at less than 6 hours of sleep. We also know that, our of everyone, 75% are at less than 6 hours and complain. Therefore, we must have 5% who are below 6 but don’t complain.
All together we get 14% + 5% = 19%. The answer is C.
Yes, this requires a bit of caution especially when one tries to answer questions like these quickly.
If 100 is the total number of people, these people are divided into two categories…
1. People who got fewer than 6 hrs of sleep
2. People who got 6 or more hrs of sleep.
Given that number of people of category 1 = 80
Number of people of category 2 = 20.
Given that 75% of the total i.e 75 people sleep for less than 6 hrs and complain fatigue. So out of the 80 people belonging to category 1, 75 complained of fatigue and hence remaining 5 did not complain of fatigue.
Coming to the category 2, it is given clearly that 70% i.e 70%(20) = 14 did not complain of fatigue.
Thus out of 100 people, 5+14 = 19 people did not complain of fatigue
Hence 19%
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