To determine which group of letters is not like the other three, we need to identify a consistent pattern or rule that applies to three of the groups and see which one deviates from it. This type of problem often involves analyzing the alphabetical positions of the letters.

Analyzing Letter Positions and Patterns

Let's assign a numerical position to each letter of the English alphabet, where A=1, B=2, and so on, up to Z=26. This will help us identify mathematical relationships between the letters in each group.

Now, let's examine each given group of letters to find a common pattern, specifically looking at the relationship between the first and third letters, and the second and fourth letters:

• H L F J: The first letter is H (8) and the third letter is F (6). The difference is \(\text{H} - 2 = \text{F}\) (8 - 2 = 6). The second letter is L (12) and the fourth letter is J (10). The difference is \(\text{L} - 2 = \text{J}\) (12 - 2 = 10). This group follows a pattern where the third letter is 2 positions before the first letter, and the fourth letter is 2 positions before the second letter.
• W F U D: The first letter is W (23) and the third letter is U (21). The difference is \(\text{W} - 2 = \text{U}\) (23 - 2 = 21). The second letter is F (6) and the fourth letter is D (4). The difference is \(\text{F} - 2 = \text{D}\) (6 - 2 = 4). This group also consistently follows the pattern: (1st letter - 2) = 3rd letter AND (2nd letter - 2) = 4th letter.
• Y D W B: The first letter is Y (25) and the third letter is W (23). The difference is \(\text{Y} - 2 = \text{W}\) (25 - 2 = 23). The second letter is D (4) and the fourth letter is B (2). The difference is \(\text{D} - 2 = \text{B}\) (4 - 2 = 2). This group also follows the same pattern: (1st letter - 2) = 3rd letter AND (2nd letter - 2) = 4th letter.

From the analysis above, we can see that three of the given groups (H L F J, W F U D, and Y D W B) share a common pattern where each of the last two letters is obtained by subtracting 2 from the alphabetical position of its corresponding preceding letter in the pair (1st letter to 3rd, and 2nd letter to 4th).

Identifying the Outlier Group: Q N O M

Now, let's examine the group Q N O M to see if it follows this established pattern:

• Q N O M: The first letter is Q (17) and the third letter is O (15). The difference is \(\text{Q} - 2 = \text{O}\) (17 - 2 = 15). This part matches the pattern observed in the other groups. However, the second letter is N (14) and the fourth letter is M (13). The difference is \(\text{N} - 1 = \text{M}\) (14 - 1 = 13). This relationship is a subtraction of 1, not 2. If it followed the pattern, the fourth letter should have been \(\text{L}\) (12).

Since the relationship between the second and fourth letters in Q N O M (\(\text{N} - 1 = \text{M}\)) is different from the consistent \(-2\) pattern found in the other three groups, Q N O M is the group that does not fit the pattern.

Final Answer Determination

The group Q N O M is the unique group among the options because, unlike the others, the difference between its second and fourth letters is 1, not 2, based on their alphabetical positions. This makes it the odd one out.