If at least one astronaut does NOT listen to Bach at the Solaris space station, then how many of the 35 astronauts at the station listen to Bach? (1) Of the astronauts who do NOT listen to Bach, 56% are male. (2) Of the astronauts who listen to Bach, 70% are female.

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LeoGuareschi

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I like the solution - it’s helpful.

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I don’t quite agree with the solution. The involvement of gender has nothing to do with the quantity that listen to Bach. If the first statement claimed 56% listen, then it would be valid. By claiming they are male, an external variable, it is impossible to know if it would be men or women.

Bunuel

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24 Nov 2025, 15:12

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margauxpm

You are wrong, but it’s a hard question and it’s okay.

The thing that matters is that 56% of the non-listeners must be an integer number of astronauts. That forces the size of that group to be a multiple of 25. Since the total is 35, the only possible size is 25, which means exactly 35 - 25 = 10 listen.

So yes, the statement does determine the number. Gender is irrelevant here. The percentage is what restricts the group size.

Please, review the solution and the whole discussion again, this time invest more time in it and study carefully.

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I like the solution - it’s helpful. Excellent question. Need to think deep

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26 Dec 2025, 00:57

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This is a very high quality question. so many questions in GMAT have a variables where you have to assume whether it is interger or not (like in this case, there is no way an astronot is not interger)

vastbarbecue

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Priyanshu7297

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I did not quite understand the solution. HOW WE ARE ASSUMING THE VALUES IN THIS CASE LIKE HOW IT TELLS US THAT THESE MANY MALE DON'T LISTEN TO BACH

Bunuel

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Priyanshu7297

I did not quite understand the solution. HOW WE ARE ASSUMING THE VALUES IN THIS CASE LIKE HOW IT TELLS US THAT THESE MANY MALE DON'T LISTEN TO BACH

It is not an “assumption” about how many males don’t listen.

(1) says: among the x astronauts who don’t listen, 56% are male. That means the male count in that group equals 0.56x = (14/25)x, and a headcount must be an integer.

So x must be a multiple of 25 to make (14/25)x an integer. With a total of 35 astronauts and at least one does not listen, the only possible multiple of 25 is x = 25. That’s the whole logic.