Question

The following are the results of a survey conducted on a small cross-section of students from the Symbiosis Group of institutes, to determine the readership of three magazines: Business India, Outlook and India Today. This survey was conducted in December 2006.

Number of students who read only Business India = 40
Number of students who read only Outlook = 60
Number of students who read only India Today = 110
Number of students who read all three magazines = 30
Number of students who read Business India and India Today, but not Outlook = 20
Number of students who read Business India and Outlook, but not India Today = 50
Number of students who read Outlook and India Today, but not Business India = 40

What was the total number of students surveyed?

• A. 210
• B. 350
• C. 390
• D. None of these

Hint:

Add up every distinct Venn diagram region (only one magazine, plus exactly two magazines, plus all three) exactly once.

Answer 1

The Correct Option is B

Think of this as filling in a three circle Venn diagram, one circle each for Business India (BI), Outlook (OL) and India Today (IT). The survey hands you every one of the seven inner regions directly, so finding the total surveyed just means adding every region once.

1. Regions with exactly one magazine: only BI = 40, only OL = 60, only IT = 110. Adding these gives 40 + 60 + 110 = 210 students who read exactly one magazine.
2. Regions with exactly two magazines: BI and IT but not OL = 20, BI and OL but not IT = 50, OL and IT but not BI = 40. Adding these gives 20 + 50 + 40 = 110 students who read exactly two magazines.
3. The region with all three magazines: given directly as 30 students.

Since these three groups (exactly one, exactly two, all three) cover the whole surveyed population without any overlap or gap, add them together: 210 + 110 + 30 = 350.

Let's summarize:

• A three set Venn diagram always has seven non-overlapping inner regions.
• Adding every region once, and only once, gives the grand total.

The total number of students surveyed is 350, so option (B) is correct.