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Re M2704 [#permalink]
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16 Sep 2014, 00:26
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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 \(3525=10\). 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
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Re: M2704 [#permalink]
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11 Aug 2016, 20:51
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Re M2704 [#permalink]
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17 Aug 2016, 03:33
I think this is a highquality question and I agree with explanation. Very good question



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Re: M2704 [#permalink]
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29 Oct 2016, 08:28
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.



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Re: M2704 [#permalink]
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31 Oct 2016, 05:00
How to quickly convert the decimal to fraction such as these? 0.56X = [14][/25]X Please help.



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Re: M2704 [#permalink]
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31 Oct 2016, 05:06



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Re M2704 [#permalink]
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01 Nov 2016, 15:18
I think this is a highquality question and the explanation isn't clear enough, please elaborate. "If at least one astronaut does NOT listen to Bach"
1. What would have happened if the question stem did not have these words?? 2. what is the significance of these words? 3. How would it change the answer



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Re: M2704 [#permalink]
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20 Aug 2017, 19:51
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 \(3525=10\). 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 3525=10 " ? Can you please clarify further.



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ran787 wrote: 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 \(3525=10\). 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 3525=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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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: M2704 [#permalink]
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17 Sep 2017, 09:10
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 \(3525=10\). 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 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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