The average of four consecutive integers A, B, C, and D is 49.5. Find the product B × D.

Introduction / Context:
Consecutive integers form an arithmetic progression with common difference 1. The mean equals the midpoint. Once one term is known, the others follow directly, enabling computation of any requested combination such as a product.

Given Data / Assumptions:

• Four consecutive integers A, B, C, D.
• Average = 49.5.
• Find B × D.

Concept / Approach:
Let A be the smallest; then A, A + 1, A + 2, A + 3 are the four numbers. Their mean is A + 1.5 = 49.5, which gives A immediately. Then B = A + 1, D = A + 3, and compute the product B * D conveniently using the identity (n − 1)(n + 1) = n^2 − 1 when centered around n = A + 2 = 50.

Step-by-Step Solution:

Verification / Alternative check:
Direct multiplication 49 * 51 also yields 2499; both routes agree.

Why Other Options Are Wrong:
2352, 2450, 2550: None matches the exact product; each reflects arithmetic slips or different pairs multiplied.

Common Pitfalls:
Taking 49.5 as a member of the integer set, or pairing B with C instead of D.

Final Answer:
2499