For a two-digit number, the sum of its digits is 15 and the difference between the two digits is 3. What is the product of its digits?

Introduction: The pair of digits is determined (up to order) by their sum and difference. Once the digits are found, compute the product; order does not affect the product.

Given Data / Assumptions:

• Let digits be a and b.
• a + b = 15.
• |a − b| = 3.

Concept / Approach: Solve the system twice (difference positive or negative); in either case, the same two digits arise in opposite order, resulting in a unique product.

Step-by-Step Solution:

Verification / Alternative check: Check both orders: {9, 6} and {6, 9}; both satisfy sum and difference, and both yield product 54.

Why Other Options Are Wrong: 72, 56, 63 are products of other pairs not meeting both constraints; “Cannot be determined” is incorrect because the product is uniquely determined.

Common Pitfalls: Assuming order affects product or miscomputing the difference condition.

Final Answer: 54