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

Step 1: Understanding the Question:
We have a three magazine reading survey (Business India, Outlook, India Today) broken into "only one magazine," "exactly two magazines," and "all three magazines" counts, and we need the total number of students surveyed.

Step 2: Key Formula or Approach:
In a three set Venn diagram, every student falls into exactly one of seven non-overlapping regions: only one magazine (three regions), exactly two magazines (three regions), or all three magazines (one region). So the total surveyed is simply the sum of all seven given regions.

Step 3: Detailed Explanation:
Only one magazine: only Business India = 40, only Outlook = 60, only India Today = 110.
\[ \text{Only one} = 40 + 60 + 110 = 210 \]
Exactly two magazines: Business India and India Today only = 20, Business India and Outlook only = 50, Outlook and India Today only = 40.
\[ \text{Exactly two} = 20 + 50 + 40 = 110 \]
All three magazines = 30.
Adding every region gives the total surveyed:
\[ \text{Total} = 210 + 110 + 30 = 350 \]

Step 4: Final Answer:
The total number of students surveyed is 350, which is option (B).
\[ \boxed{350} \]