Bunuel wrote:
Official Solution:
Tricky question.
(1) Of the astronauts who do NOT listen to Bach, 56% are male. If # of astronauts who do NOT listen to Bach is\(x\) , then\(0.56x\) is # of males who do NOT listen to Bach. Notice that\(0.56x=\frac{14}{25}x\) must be an integer. Hence,\(x\) must be a multiple of 25: 25, 50, 75, ... But\(x\) (# of astronauts who do NOT listen to Bach) must also be less than (or equal to) 35. So\(x\) can only be 25, which makes # of astronauts who do listen to Bach equal to\(35-25=10\)
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