The average of four consecutive odd numbers is 40. What is the largest of these four odd numbers?

Introduction / Context:
This question is about averages and consecutive odd numbers. It checks how well candidates can link the arithmetic mean with an ordered set of consecutive terms and translate that understanding into a simple algebraic form.

Given Data / Assumptions:
- There are four consecutive odd integers.
- Their average is 40.
- We must identify the largest of these four odd numbers.

Concept / Approach:
For any set of equally spaced numbers such as consecutive odd integers, the average is the same as the middle point of the set. With four consecutive odd numbers, we can represent them in terms of a central value and then use the average to determine that central value. From there, we can easily find the largest number in the group.

Step-by-Step Solution:
Let the four consecutive odd numbers be x − 3, x − 1, x + 1, and x + 3. These are spaced by 2 and centred around x. The average of these four numbers is x, since symmetric deviations cancel out. We are told that the average is 40, so x = 40. Therefore, the four numbers are 37, 39, 41, and 43, and the largest is 43.

Verification / Alternative Check:
We can directly compute the average as follows: (37 + 39 + 41 + 43) ÷ 4. The sum of these four numbers is 160, and 160 ÷ 4 = 40, confirming both the average and the set of numbers. This establishes that 43 is indeed the largest number in the sequence.

Why Other Options Are Wrong:
42 is even and does not fit the pattern of consecutive odd integers around an average of 40.
45 would be the largest number if the average were higher; it does not arise from the correct sequence with mean 40.
44 is even and also unsuitable for a set of odd numbers.
41 is part of the sequence but is not the largest; it is the third term in ascending order.

Common Pitfalls:
Some students forget that consecutive odd numbers differ by 2, not 1, and may incorrectly assume numbers like 39, 40, 41, 42. Others try to guess without using algebra, which can lead to confusion. Remembering that the average equals the central value for symmetric sequences helps solve such questions quickly and accurately.

Final Answer:
The largest of the four consecutive odd numbers is 43.