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

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

A survey was conducted on 100 people to find out whether they had read recent issues of Playboy magazine. The 3-month readership data is as follows: 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)?

This problem uses set theory and the inclusion-exclusion principle to analyze survey data on magazine readership. Learn how to find the number of people who read exactly two consecutive issues out of three. Suitable for Grades 10-12, with a focus on logical deduction and set analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation