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Tired VS Not tired problem

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by AIM TO CRACK GMAT » Mon Jan 14, 2013 7:05 am
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?

i) 6 ii)14 iii) 19 iv) 20 v)81
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by vkb001 » Mon Jan 14, 2013 4:49 pm
If T is the total number of interns,

Number of interns with less than 6 hours of sleep and feeling tired = 0.75*T (given)
Number of interns with less than 6 hours of sleep = 0.8*T (given)

Therefore, number of interns with less than 6 hours of sleep and NOT feeling tired = (0.8 - 0.75)*T = 0.05*T

Number of interns with 6 or more hours of sleep = T - 0.8*T = 0.2*T
Number of interns with 6 or more hours of sleep and NOT feeling tired = 0.7*(0.2*T) = 0.14*T
Number of interns with 6 or more hours of sleep and feeling tired = 0.2*T - 0.14*T = 0.06*T

Answer: The number of interns that report no tiredness = 0.14*T + 0.05*T = 0.19*T = 19% of the total
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by e-GMAT » Tue Jan 15, 2013 12:16 am
AIM TO CRACK GMAT 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?

i) 6 ii)14 iii) 19 iv) 20 v)81
Hi,

Pl. look at the image. Hope it is self explanatory.

Image

Answer would be 19%.

-Shalabh
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by BTG14 » Thu Jan 17, 2013 3:45 am
iii) 19%. Correct answer.

Nicely explained by e-gmat.
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by AIM TO CRACK GMAT » Thu Jan 17, 2013 6:38 am
e-GMAT wrote:
AIM TO CRACK GMAT 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?

i) 6 ii)14 iii) 19 iv) 20 v)81
Hi,

Pl. look at the image. Hope it is self explanatory.

Image

Answer would be 19%.



Thank u sooo much... this is another easy method or may b easier to undastand since its in a tabular form...thank u sooo much!!! Apreciate it

-Shalabh
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