In the letter series BAZ, DCY, FEX, ?, which group of letters should replace the question mark to continue the pattern?

Introduction / Context:
This is a three-letter alphabet series question where each position in the group follows its own pattern. Such problems are designed to test your ability to track multiple simultaneous patterns across the first, second, and third letters independently and then combine them to find the missing term.

Given Data / Assumptions:
- The given groups are: BAZ, DCY, FEX, ?- Each group has exactly three letters.- We assume that each letter position follows a simple pattern when considered separately.

Concept / Approach:
A standard technique for multi-letter series is to split the sequence into three independent sequences: one formed by the first letters, one by the second letters, and one by the third letters. By mapping each letter to its position in the alphabet and then observing differences, you can usually discover simple arithmetic rules and apply them to find the missing term.

Step-by-Step Solution:
- First letters: B, D, F correspond to 2, 4, 6 in the alphabet.- This is an arithmetic progression with a common difference of +2, so the next first letter is 8, which is H.- Second letters: A, C, E correspond to 1, 3, 5, again forming an arithmetic progression with common difference +2.- The next second letter is 7, which corresponds to G.- Third letters: Z, Y, X correspond to 26, 25, 24, a sequence decreasing by 1 each time.- The next third letter is 23, which is W.- Combining these results, the missing group should be H (first), G (second), W (third), giving HGW.

Verification / Alternative check:
- Check all positions: first letters 2, 4, 6, 8; second letters 1, 3, 5, 7; third letters 26, 25, 24, 23.- Each position clearly follows its own arithmetic pattern, so the combined term HGW is fully consistent.- No other option maintains all three independent patterns at once.

Why Other Options Are Wrong:
- FXW and FEX do not have the correct first and second letters according to the +2 pattern.- FEY introduces a third letter Y which does not continue the -1 progression from Z to Y to X to W.- Only HGW correctly follows +2 for the first letters, +2 for the second letters, and -1 for the third letters.

Common Pitfalls:
Some candidates only look at the first letters and guess based on that partial pattern, ignoring the second and third letters. Others try to treat the three-letter groups as a whole without decomposing them, which makes the pattern difficult to see. The safest approach is to treat each position separately and then recombine the results.

Final Answer:
The correct group of letters that completes the pattern is HGW, so the correct option is HGW.