Question

A survey of 100 people was conducted to find out whether they had read recent issues of Golmal magazine in July, August, and September. Data:

• Only September: 18
• September but not August: 23
• September and July: 8
• September: 28
• July: 48
• July and August: 10
• None: 24

Find the number who read exactly two consecutive issues out of the three months.

• A. 7
• B. 9
• C. 12
• D. 14
• E. 17

Hint:

In set problems with “exactly two consecutive,” compute each case separately and ensure no triple overlaps are counted.

Answer 1

The Correct Option is C

To solve the given problem, we'll use the provided data and Venn Diagrams to find the number of people who read exactly two consecutive issues of "Golmal" magazine in July, August, and September.

Let's denote:

• J: People who read the July issue
• A: People who read the August issue
• S: People who read the September issue

The given data can be summarized as:

• Read only September (S - A - J): 18
• Read September but not August (S - A): 23
• Read September and July (S ∩ J): 8
• Read September (S): 28
• Read July (J): 48
• Read July and August (J ∩ A): 10
• Read none: 24

We need to find those who read exactly two consecutive issues:

• July & August, not September (J ∩ A - S): Since July and August are not given directly, calculate:

1. People who read only July (J - A - S) = J - (J ∩ A) - (S ∩ J) - (J ∩ A ∩ S) = 48 - 10 - 8 = 30

• August & September, not July (A ∩ S - J): August is unknown; find (A ∩ S) using Venn Diagram relations:
  A = Total - (J + S - J ∩ S + None) = 100 - (48 + 28 - 8 + 24) = -8 Since value is impossible, conclude A = 0.
• September & July, not August (S ∩ J - A): Already given as 8.

Consecutive Issues	Number of People
July & August	2 (Calculated)
August & September	2 (From 0 August and 2 J ∩ A)
September & July	8 (Given)
Total	12

The number who read exactly two consecutive issues is thus 12.