Understand the question:
The question is asking which methods will not show the greatest value of cost of goods sold (COGS) under inflationary conditions.

Understand the methods:
1. FIFO (First-In, First-Out): This method assumes that the goods purchased first are sold first. In other words, the oldest inventory is sold first.
2. LIFO (Last-In, First-Out): This method assumes that the goods purchased last are sold first. In other words, the most recent inventory is sold first.
3. Weighted Average: This method calculates the average cost of all units of inventory available for sale during a period.

Analysis of methods:
In an inflationary environment, the cost of goods tends to increase over time. Let's analyze each method to understand how they would reflect the COGS under inflationary conditions.

1. FIFO:
- Under inflation, FIFO would result in a lower COGS because the oldest and presumably cheaper inventory is sold first. As the cost of goods increases over time, the inventory remaining in stock would have a higher value.
- Therefore, FIFO would not show the greatest value of COGS under inflationary conditions. (Answer: A)

2. LIFO:
- Under inflation, LIFO would result in a higher COGS because the most recent and presumably more expensive inventory is sold first. As the cost of goods increases over time, the remaining inventory would have a lower value.
- LIFO would show the greatest value of COGS under inflationary conditions.

3. Weighted Average:
- The weighted average method calculates the average cost of all units of inventory available for sale. It takes into account both the old and new inventory costs.
- Under inflation, the weighted average method would reflect a higher COGS than FIFO but lower than LIFO. It strikes a balance between the oldest and most recent inventory costs.
- Therefore, the weighted average method would not show the greatest value of COGS under inflationary conditions. (Answer: C)

Conclusion:
Under inflationary conditions, the FIFO and weighted average methods will not show the greatest value of COGS. LIFO would reflect the highest value of COGS.