Higher Order Thinking A newspaper has more than 30 pages and fewer than 40 pages. The newspaper is divided into sections, and each section has exactly 8 pages. How many sections does the newspaper have?
The Correct Answer and Explanation is:
To solve the problem, we need to determine how many 8-page sections can make up a newspaper that has more than 30 pages and fewer than 40 pages.
Step-by-Step Solution:
We are told:
- The total number of pages is more than 30 but fewer than 40, so possible total page numbers are:
31, 32, 33, 34, 35, 36, 37, 38, or 39. - Each section of the newspaper contains exactly 8 pages.
- We are looking for a total number of pages that is divisible evenly by 8.
Let’s list the numbers from 31 to 39 and check which one is divisible by 8:
- 31 ÷ 8 = 3.875 ❌
- 32 ÷ 8 = 4 ✅
- 33 ÷ 8 = 4.125 ❌
- 34 ÷ 8 = 4.25 ❌
- 35 ÷ 8 = 4.375 ❌
- 36 ÷ 8 = 4.5 ❌
- 37 ÷ 8 = 4.625 ❌
- 38 ÷ 8 = 4.75 ❌
- 39 ÷ 8 = 4.875 ❌
Only 32 is divisible by 8 and falls within the range of more than 30 but fewer than 40.
Now, divide 32 by 8: 328=4\frac{32}{8} = 4
✅ Final Answer: 4 sections
300-Word Explanation:
This problem involves logical reasoning and basic division skills. You’re given a number range (more than 30 and fewer than 40) and a fixed unit of measurement (each section has 8 pages). The goal is to figure out how many of these equal-sized sections fit perfectly within a total page count that meets the stated conditions.
First, you list all the numbers between 30 and 40. These are 31 to 39. Then, you test each one to see if it is divisible by 8, since each section must contain exactly 8 pages. This is a key constraint: you cannot have a partial section or leftover pages.
When you try dividing each number by 8, only 32 results in a whole number (4). All the others result in fractions, which means they would leave pages unaccounted for—something not allowed in this scenario.
Because 32 pages is the only valid option that fits both conditions (within the range and divisible evenly by 8), it must be the correct total number of pages. And since each section is 8 pages, dividing 32 by 8 gives you 4 full sections.
This kind of problem encourages careful reasoning. Instead of rushing to divide any number, you must consider both conditions: the page range and even division. It highlights how critical thinking and number sense can lead to the right answer in real-world scenarios, such as formatting a newspaper.