M27-04

Official Solution:


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?

This is a tricky question.

(1) Of the astronauts who do NOT listen to Bach, 56% are male.

If we denote the number of astronauts who do NOT listen to Bach as \(x\), then the number of male astronauts who do NOT listen to Bach can be represented as \(0.56x\). It is important to note that \(0.56x\) can be expressed as \(\frac{14}{25}x\), and it needs to be an integer. Consequently, \(x\) must be a multiple of 25, such as 25, 50, 75, and so on. Additionally, since \(x\) cannot exceed the total number of astronauts, which is 35, the only feasible value for \(x\) is 25. Therefore, the number of astronauts who do listen to Bach is given by subtracting \(x\) from the total number of astronauts: \(35 - 25 = 10\). Sufficient..

(2) Of the astronauts who listen to Bach, 70% are female.

Applying the same logic as before, let's denote the number of astronauts who listen to Bach as \(y\). In this case, the number of female astronauts who listen to Bach can be expressed as \(0.7y\), which is equivalent to \(\frac{7}{10}y\). To ensure this value is an integer, \(y\) must be a multiple of 10. However, unlike the previous scenario, there are multiple possible values that satisfy this condition: 10, 20, and 30. Therefore, this statement alone is not sufficient to determine the exact number of astronauts who listen to Bach.


Answer: A
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Excellent Question.

I think this is a high-quality question and I agree with explanation. Very good question

For this question, I believe it is helpful to draw a "grid", sort of like this:

Bach NotBach Total

Male

Female

Total >=1 35

And then fill in with the informations from statements 1 and 2. That's how I figured that the 0.56*x and 0.7*x had to be integers.

How to quickly convert the decimal to fraction such as these?
0.56X = [14][/25]X
Please help.

0.56 = 56/100 --> reduce by 4: to get 14/25.

Check for more here: math-number-theory-88376.html

Hope it helps.
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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.

x (25) in the solution denotes the number of astronauts who do not listen to Bach, x is NOT the number of male astronauts who listen to Bach.
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Wonderfulllll! This is such an awesome question. Love the explanation as well. The important point to note here is that we are dealing with people, so we have to take care that we are dealing with integers. First sight at the option choices indicate that the answer is E. but once you drill deeper, you realize that answer is A. Excellent question.
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This question popped up as very first question in GMAT Club tests and had me stumped. I answered E and it was wrong. After the explanation from bunuel, i understood A is the answer. Excellent Question
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One of the best questions on GMAT Club.

Great Question! My friend gave gmat exam last week. He scored q50. He told me that he was majorly tested more on Arithmetic. He got very few and easy questions of inequalities, numbers, geometry, pnc and probability. Exam comprised of percentages and profit loss questions and general arithmetic.

I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

Great question requires actual critical reasoning skills!!

Used the 2x2 matrix to solve (couldn't solve in under 3 mins)

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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