The sum of two numbers, when multiplied by each number separately, produces 2418 and 3666 respectively. Find the absolute difference between the two numbers.

Introduction:
Let the numbers be a and b with sum s = a + b. We are given s * a and s * b; this permits solving for s and then |a − b| without finding a and b individually.

Given Data / Assumptions:

• s * a = 2418
• s * b = 3666
• s = a + b

Concept / Approach:
Add the two equations and use s = a + b to solve for s, then use the difference to find |a − b|.

Step-by-Step Solution:
s * a + s * b = 2418 + 3666 = 6084s(a + b) = s * s = s^2 = 6084s = sqrt(6084) = 78Compute |a − b| = |(s * b − s * a)| / s = |3666 − 2418| / 78 = 1248 / 78 = 16

Verification / Alternative check:
One can set a = 2418/78 and b = 3666/78, then verify the difference is 16.

Why Other Options Are Wrong:
21, 19, 23: Do not match the computed difference from the given products.

Common Pitfalls:
Forgetting that s^2 = 6084; making arithmetic slips with 1248/78 simplification.

Final Answer:
16