Question

A survey was conducted of 100 people whether they have read recent issues of 'Golmal', a monthly magazine. Summarized information is presented below:
Only September: 18
September but not August: 23
September and July: 8
September: 28
July: 48
July and August: 10
None of the three months: 24
What is the number of surveyed people who have read exactly for two consecutive months?

• A. 7
• B. 9
• C. 12
• D. 14

Hint:

Break the three-month data into only-one-month, exactly-two-month and all-three-month regions, then add only the July-August and August-September two-month regions, since July and September are not adjacent.

Answer 1

The Correct Option is B

A second way to reach the same figure is to first solve for every single region of the three-month Venn diagram using the total of 100 people, then simply add up the required regions at the end.

1. From the September data: only-September $= 18$, September total $= 28$, so all overlap regions touching September sum to $28 - 18 = 10$.
2. September but not August $= 23$ means September and August together $= 28 - 23 = 5$.
3. September and July together $= 8$.
4. Solving the three overlap equations for September's regions gives July-September-only $= 5$, August-September-only $= 2$, and all-three $= 3$, the same values found by direct substitution.
5. July total $= 48$, and July-August together $= 10$, so July-August-only $= 10 - 3 = 7$, since all-three $= 3$.
6. Only-July $= 48 - (7 + 5 + 3) = 48 - 15 = 33$.
7. Using the grand total of 100 and none-of-the-three $= 24$: $33 + \text{only-August} + 18 + 7 + 5 + 2 + 3 + 24 = 100$, which gives only-August $= 100 - 92 = 8$.
8. The full breakdown is now known: only-July $=33$, only-August $=8$, only-September $=18$, July-August-only $=7$, July-September-only $=5$, August-September-only $=2$, all-three $=3$, none $=24$. These sum to 100, confirming the breakdown is consistent.
9. People who read exactly two consecutive months are those in July-August-only and August-September-only, since July-September-only is skipped as July and September are not adjacent months: $7 + 2 = 9$.

This full-breakdown cross-check confirms the count of readers of exactly two consecutive months.

\[\boxed{9}\]