Math Destroyer 2013 Question

[Incis0r]

Test 4, #37:
"A Survey was taken of 180 people. Each was asked to choose their one favorite type of music. Two thirds of the respondents chose classical music, and one-third of those remaining chose jazz. How many of the people surveyed chose neither classical music nor jazz?"

My answer was A, 15 since 180-15 = 165, which was the only number divisible by three (to match the respondents). All the other numbers (20, 25, 35, 40) did not allow for whole numbers of respondents to choose classical/jazz since 160, 155, 145, and 140 are not divisible by 3.

The answer key, however, says E (40) and explains by saying "Of the 60 people who prefer jazz or pop, two thirds, or 40, prefer pop."

Is this a typo or am I missing something? Help much appreciated!

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[flossboss24]

It says of 180, two thirds chose classical. So 180*2/3 = 120. So 120 chose classical.
Then one third of the remaining chose jazz. So 180 - 120 = 60. So 1/3 of 60 chose jazz, which is 20 people. So 20 people chose jazz.
Lastly, add the people that chose classical and jazz together and subtract from the original amount of respondents to get number of people who chose neither.
120 classical + 20 Jazz = 140 (Classical/Jazz)
180 original respondents - 140 (Classical/Jazz) = 40 respondents who chose neither classical or jazz

Hopefully that helps.

 

[DAT Destroyer]

Test 4, #37:
"A Survey was taken of 180 people. Each was asked to choose their one favorite type of music. Two thirds of the respondents chose classical music, and one-third of those remaining chose jazz. How many of the people surveyed chose neither classical music nor jazz?"

My answer was A, 15 since 180-15 = 165, which was the only number divisible by three (to match the respondents). All the other numbers (20, 25, 35, 40) did not allow for whole numbers of respondents to choose classical/jazz since 160, 155, 145, and 140 are not divisible by 3.

The answer key, however, says E (40) and explains by saying "Of the 60 people who prefer jazz or pop, two thirds, or 40, prefer pop."

Is this a typo or am I missing something? Help much appreciated!

 

[obscurlit]

I did the question the old fashioned way (similar to those posted above):
180 - (2/3)*180 = 60 non-classical
60 - (1/3)*60 = 40 non-classical/non-jazz


For why your method didn't work:

You can't do it the way that you did because first, 1/3 of 60 is 20, so you would be subtracting 20 from 180, and second, 1/3 of 180 didn't choose classical, not 1/3 of 180-20. Basically, the order of your subtracting/dividing matters in this case.

If you wanted to do your way, it would be 180/3 = 60 and then 60/3 = 20 thus 20 and 40 are the possible answers. Since 1/3 of 60 non-classical people (20 people) chose jazz, that means that 2/3 (40 people) did not. Thus, 40 is your answer.


I think for this particular problem, just straight up solving it instead of using techniques or methods is easier. Hope this helps

 

[Incis0r]

It says of 180, two thirds chose classical. So 180*2/3 = 120. So 120 chose classical.
Then one third of the remaining chose jazz. So 180 - 120 = 60. So 1/3 of 60 chose jazz, which is 20 people. So 20 people chose jazz.
Lastly, add the people that chose classical and jazz together and subtract from the original amount of respondents to get number of people who chose neither.
120 classical + 20 Jazz = 140 (Classical/Jazz)
180 original respondents - 140 (Classical/Jazz) = 40 respondents who chose neither classical or jazz

Hopefully that helps.

View attachment 193090 View attachment 193090 View attachment 193090

I did the question the old fashioned way (similar to those posted above):
180 - (2/3)*180 = 60 non-classical
60 - (1/3)*60 = 40 non-classical/non-jazz


For why your method didn't work:

You can't do it the way that you did because first, 1/3 of 60 is 20, so you would be subtracting 20 from 180, and second, 1/3 of 180 didn't choose classical, not 1/3 of 180-20. Basically, the order of your subtracting/dividing matters in this case.

If you wanted to do your way, it would be 180/3 = 60 and then 60/3 = 20 thus 20 and 40 are the possible answers. Since 1/3 of 60 non-classical people (20 people) chose jazz, that means that 2/3 (40 people) did not. Thus, 40 is your answer.


I think for this particular problem, just straight up solving it instead of using techniques or methods is easier. Hope this helps

Thank you all soooo much!!! Really appreciate the effort you all went through to help me understand the problem you're all the reason why SDN is such a great place.

I get it now

 

[DAT Destroyer]

Thank you all soooo much!!! Really appreciate the effort you all went through to help me understand the problem you're all the reason why SDN is such a great place.

I get it now

Always glad to help! Keep up the good work! QR can be tricky indeed..