Two-digit number and its reverse: The difference between a two-digit number and the number obtained by interchanging its digits is 36. What is the difference between the two individual digits of that number?

Introduction / Context:This problem checks your understanding of how two-digit numbers change when their digits are reversed and how to model that change with a simple linear expression. The key is realizing that reversing digits produces a fixed multiple of the difference between the tens and units digits.

Given Data / Assumptions:

• A two-digit number has tens digit a and units digit b.
• The reverse is formed by interchanging digits.
• The difference between the original number and its reverse equals 36.

Concept / Approach:Represent the original number as 10a + b and the reversed number as 10b + a. Their difference factors as 9(a − b) in magnitude. This constant factor 9 is the hallmark of “reverse-digit” problems for two-digit numbers.

Step-by-Step Solution:

Verification / Alternative check:Pick any digits with difference 4, e.g., a = 7, b = 3. Then original = 73, reverse = 37, and difference = 36. This confirms the model works for legitimate digits.

Why Other Options Are Wrong:

• 3, 6, 9: None satisfy 9*(digit difference) = 36.
• Cannot be determined: The digit difference is uniquely determined by the factor-of-9 rule.

Common Pitfalls:Forgetting the factor 9 or assuming the difference 36 is the digit difference directly. Always express two-digit numbers as 10a + b to avoid mistakes.

Final Answer:4