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# M27-04

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Math Expert
Joined: 02 Sep 2009
Posts: 43787
M27-04 [#permalink]

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16 Sep 2014, 00:26
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Difficulty:

95% (hard)

Question Stats:

38% (00:57) correct 63% (01:23) wrong based on 64 sessions

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If at least one astronaut does NOT listen to Bach at Solaris space station, then how many of 35 astronauts at Solaris space 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.
[Reveal] Spoiler: OA

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Posts: 43787
Re M27-04 [#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 $$35-25=10$$. 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
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Re: M27-04 [#permalink]

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11 Aug 2016, 20:51
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Excellent Question.
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Joined: 29 Jan 2013
Posts: 41
Location: United States
Concentration: Operations, Leadership
Schools: Booth PT '20 (M)
GMAT 1: 650 Q50 V26
WE: Manufacturing and Production (Manufacturing)
Re M27-04 [#permalink]

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17 Aug 2016, 03:33
I think this is a high-quality question and I agree with explanation. Very good question
Intern
Joined: 12 Oct 2016
Posts: 7
Re: M27-04 [#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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Joined: 06 May 2015
Posts: 24
Re: M27-04 [#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.
Math Expert
Joined: 02 Sep 2009
Posts: 43787
Re: M27-04 [#permalink]

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31 Oct 2016, 05:06
reynaldreni wrote:
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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Re M27-04 [#permalink]

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01 Nov 2016, 15:18
I think this is a high-quality 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
Intern
Joined: 23 Aug 2014
Posts: 5
Re: M27-04 [#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 $$35-25=10$$. 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.
Math Expert
Joined: 02 Sep 2009
Posts: 43787
M27-04 [#permalink]

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21 Aug 2017, 02:37
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 $$35-25=10$$. 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.

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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Re: M27-04 [#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 $$35-25=10$$. 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

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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we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Re: M27-04   [#permalink] 17 Sep 2017, 09:10
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# M27-04

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