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290 students at Music High School are in the band, the

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290 students at Music High School are in the band, the [#permalink] New post 07 May 2013, 01:14
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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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Re: 290 students at Music High School are in the band, the [#permalink] New post 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 :)

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Re: 290 students at Music High School are in the band, the [#permalink] New post 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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Re: 290 students at Music High School are in the band, the [#permalink] New post 11 May 2013, 02:41
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


What are GMAT Club Tests?
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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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