290 students at Music High School are in the band, the : Integrated Reasoning (IR)
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290 students at Music High School are in the band, the

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07 May 2013, 01:14
290 students at Music High School are in the band, the orchestra, or both. There are 210 students in the band.

In the table, identify the number of students currently enrolled in the orchestra and the number of students currently enrolled in both the band and the orchestra. The two numbers must be consistent with each other and with the constraints above. Make exactly one choice in each column.

The orchestra ---- The band and the orchestra
------------------------------------------------------------ 110
------------------------------------------------------------ 150
------------------------------------------------------------ 170
------------------------------------------------------------ 210
------------------------------------------------------------ 230
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07 May 2013, 09:50
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For this question, one can go for a Vienn Diagram to better visualize the problem.

So, the total number of students = 290
Students playing in a Band = Students just in the band + Students in both band and Orchestra.

The same applies to the Students in Orchestra. Hence Total number of students - Students in a Band = Students in just Orchestra.
=> Students just in orchestra = 80

Now Total students in Orchestra = 80 + x, where x is the number of students in both.

f(x) = 80+x represents the students in the Orchestra. The values in the table:

Quote:

The orchestra ---- The band and the orchestra
------------------------------------------------------------ 110
------------------------------------------------------------ 150
------------------------------------------------------------ 170
------------------------------------------------------------ 210
------------------------------------------------------------ 230

The values 230 and 150 satisfy the above equation. Hence, the total number in bands = 210, total number in Orchestra = 230 and the intersection of them both is 150. Please correct me if I am wrong

Regards,
Arpan
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10 May 2013, 21:46
Hi Bunuel,

I am not very good at Sets & Venn Diagrams.
Please provide me a reference to some good explanation given by you.

Thanks & Regards,
Prateek Sharma
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11 May 2013, 02:41
pratsh123 wrote:
Hi Bunuel,

I am not very good at Sets & Venn Diagrams.
Please provide me a reference to some good explanation given by you.

Thanks & Regards,
Prateek Sharma

Theory:
how-to-draw-a-venn-diagram-for-problems-98036.html
advanced-overlapping-sets-problems-144260.html

DS questions on overlapping sets: search.php?search_id=tag&tag_id=45
PS questions on overlapping sets: search.php?search_id=tag&tag_id=65

Hope it helps.
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Re: 290 students at Music High School are in the band, the   [#permalink] 11 May 2013, 02:41
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