MGMAT CAT Question

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okigbo: Master | Next Rank: 500 Posts; Posts: 177; Joined: Sun Aug 02, 2009 9:39 pm; Thanked: 6 times

MGMAT CAT Question

by okigbo » Sun Oct 04, 2009 5:10 pm

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?
6
14
19
20
81

How can I quickly solve this? Thanks

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Source: Beat The GMAT — Problem Solving | Sun Oct 04, 2009 5:10 pm

ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

by ssmiles08 » Sun Oct 04, 2009 5:44 pm

Let total inters = 100

75 percent of total interns who had less than 6 hours of sleep were tired.

80 percent of total interns had fewer than 6 hours of sleep which means 5 percent of interns who had less than 6 hours of sleep.

if 80 percent of total interns had fewer than 6 hours of sleep, 20 percent of the total interns had more than 6 hours of sleep.

0.7(20) = 14 percent of interns who had more than 6 hours of sleep did not feel tired.

so 14 + 5 = 19% of total interns did not feel tired. IMO C.

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