MGMAT..please guide

nqhussain 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

19 is the answer.

thx

A percentage question without real numbers - let's pick 100 as the number of interns.

If there are 100 interns, that means we have 80 with fewer than 6 hours of sleep and 20 with 6 or more hour of sleep.

Of the 80 who receive less than 6 hours, 75 are tired (that's the 75% at the beginning), which means that 5 aren't tired.

Of the remaining 20, 70% aren't tired. 70% of 20 is 14.

So, we have 5 + 14 = 19 untired interns (clearly they should be working harder): choose (c).

80% of the interns get less than 6 hrs of sleep.Of which 75 get tired and the rest 5 do not get tired .

20 % of the interns receive more than 6 hrs of sleep .Of which 70 % do not get tired ie 20* 70/100 = 14

so we have 14 ( of 20 % who donot get tired ) + 5 ( of 80% who do not get tired )

= 19

80% of the interns get less than 6 hrs of sleep.Of which 75 get tired and the rest 5 do not get tired .

20 % of the interns receive more than 6 hrs of sleep .Of which 70 % do not get tired ie 20* 70/100 = 14

so we have 14 ( of 20 % who donot get tired ) + 5 ( of 80% who do not get tired )

= 19