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Of the 200 seniors at Monroe High School, exactly 40 are in

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Of the 200 seniors at Monroe High School, exactly 40 are in [#permalink] New post 23 Jan 2019, 16:14
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Of the 200 seniors at Monroe High School, exactly 40 are in the band, 60 are in the orchestra, and 10 are in both. How many seniors are in neither the band nor the orchestra?

[Reveal] Spoiler: OA
110

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Re: Of the 200 seniors at Monroe High School, exactly 40 are in [#permalink] New post 27 Jan 2019, 07:29
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Solution,

Total number of seniors = 200

Number of seniors that are in band only = 40-10 = 30

Number of seniors that are in orchestra only = 60 - 10 = 50

Number of seniors that are in both = 10

Number of seniors that are in neither the band nor the orchestra = 200 - 30 - 50 - 10

= 200 - 90

= 110
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Re: Of the 200 seniors at Monroe High School, exactly 40 are in [#permalink] New post 12 Jun 2019, 08:08
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200 = 40+60 - 10 +Neither
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Re: Of the 200 seniors at Monroe High School, exactly 40 are in [#permalink] New post 13 Jun 2019, 05:46
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Carcass wrote:
Of the 200 seniors at Monroe High School, exactly 40 are in the band, 60 are in the orchestra, and 10 are in both. How many seniors are in neither the band nor the orchestra?

[Reveal] Spoiler: OA
110


Let's use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..

Here, we have a population of seniors, and the two characteristics are:
- in band or not in band
- in orchestra or not in orchestra

From the given information, we can set up our matrix as follows:
Attachment:
Of the 200 seniors at Monroe High School, exactly 40 are in the band1.png
Of the 200 seniors at Monroe High School, exactly 40 are in the band1.png [ 4.72 KiB | Viewed 1265 times ]




Since there are 200 students in total, we can add some additional values:
Attachment:
Of the 200 seniors at Monroe High School, exactly 40 are in the band2.png
Of the 200 seniors at Monroe High School, exactly 40 are in the band2.png [ 5.49 KiB | Viewed 1265 times ]



Now complete the matrix:
Attachment:
Of the 200 seniors at Monroe High School, exactly 40 are in the band3.png
Of the 200 seniors at Monroe High School, exactly 40 are in the band3.png [ 6.16 KiB | Viewed 1266 times ]


Answer: There are 110 seniors who are in neither the band nor the orchestra

This question type is COMMON on the GRE, so be sure to master the technique.

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Re: Of the 200 seniors at Monroe High School, exactly 40 are in   [#permalink] 13 Jun 2019, 05:46
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