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 \(35-25=10\). Sufficient.
(2) Of the astronauts who listen to Bach, 70% are female. Now, if we apply the same logic here we get that, if # of astronauts who listen to Bach is \(y\), then \(0.7y\) is # of females who listen to Bach: \(0.7y=\frac{7}{10}y\) must be an integer. Hence, it must be a multiple of 10, but in this case it can take more than 1 value: 10, 20, 30. So, this statement is not sufficient.
Answer: A
Hi Bunuel,
I have one doubt. Can you please help to clarify.
Its given in Option 1 that "Of the astronauts who do NOT listen to Bach, 56% are male" & from our calculation, its been found that the no is 25. Now we also need to consider the No of Females who do NOT listen to Bach. Without considering that , how are we arriving at the conclusion that :-
"# of astronauts who do listen to Bach equal to 35-25=10 " ?
Can you please clarify further.