The average of 4 consecutive odd numbers is 50. What is the greatest number ?

Concept: For a set of evenly spaced (arithmetic) numbers, the average always equals the average of the first and last terms; equivalently, average = first term + (common difference) x (number of terms - 1) / 2. Consecutive odd numbers are evenly spaced with a common difference of 2.

1. Let the four consecutive odd numbers be x, x+2, x+4 and x+6, where x is the smallest of the four.

2. Their sum is x + (x+2) + (x+4) + (x+6) = 4x + 12.

3. The average of the four numbers is (4x + 12) / 4 = x + 3.

4. Since the average is given as 50: x + 3 = 50, so x = 47.

5. The greatest of the four numbers is x + 6 = 47 + 6 = 53.

Cross-check: Listing the four terms gives 47, 49, 51 and 53. Their sum is 200, and 200 / 4 = 50, which matches the given average -- confirming the greatest term found above.