Math Problem Statement

Tom. 495 left 0/6Qns Submitted

A survey was conducted on 100 people to find out whether they had read recent issues of Playboy magazine. The 3 month readership data look this this -

Only Read the September Issue: 18;

Read September but not August Issue: 23;

Read September and July: 8;

Read September Issue: 28;

Read the July Issue: 48;

Read July and August Issue: 10;

None of the three months: 24.

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?

4

9

12

17

Solution

We are tasked with finding how many people have read exactly two consecutive issues of Playboy magazine (out of July, August, and September) based on the given survey data.

Let's break down the information:

  • Read the July Issue: 48 people
  • Read the September Issue: 28 people
  • Read September but not August Issue: 23 people
  • Read September and July: 8 people
  • Read July and August Issue: 10 people
  • None of the three months: 24 people
  • Only Read the September Issue: 18 people

Now, let's identify how many people read exactly two consecutive issues. There are three consecutive pairs of months we can consider:

  1. July and August
  2. August and September
  3. July and September (Note that these two months are not consecutive, but the problem includes both pairs.)

We are interested in those who read exactly two consecutive issues, so we will only count the pairs without considering those who read all three months.


Step 1: Find the total number of people who read only July and August

  • We know that 10 people read both July and August.
  • However, some of these people might have read all three months, which we need to subtract.

Step 2: Find the total number of people who read only August and September

  • We know that 23 people read September but not August, which gives us the intersection we need for people who read August and September but not July.

Step 3: Read exactly two consecutive

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Math Problem Analysis

Mathematical Concepts

Set Theory
Logical Deduction
Inclusion-Exclusion Principle

Formulas

Inclusion-Exclusion for set intersections

Theorems

Principle of Inclusion-Exclusion

Suitable Grade Level

Grades 10-12