In the letter pair series AG, LR, WC, HN, ?, which of the following pairs should come next to continue the pattern?

Introduction / Context:
This problem presents the series of letter pairs AG, LR, WC, HN, and asks you to select the next pair from the options. Many letter pair questions hide two separate patterns: one for the first letters of each pair and another for the second letters. Here, recognising both progressions is essential to finding the correct answer.

Given Data / Assumptions:

• Given pairs: AG, LR, WC, HN, ?
• First letters form the sequence A, L, W, H, ?
• Second letters form the sequence G, R, C, N, ?
• We work with alphabet positions A 1 to Z 26 and allow wrap around from Z back to A when adding a constant.

Concept / Approach:
We treat the first letters as one numeric series and the second letters as another. In many exam questions, both series follow a constant difference, possibly with wrap around. Once we determine the difference for the first letters and the second letters, we can extend each progression by one step to get the missing pair. Then we select the option that matches this computed pair.

Step-by-Step Solution:
Step 1: Convert first letters to positions: A 1, L 12, W 23, H 8. Step 2: Compute differences: from 1 to 12 is +11, from 12 to 23 is +11, and from 23 to 8 is also +11 if we wrap around (23 + 11 equals 34, and 34 minus 26 equals 8). Step 3: Continue this pattern by adding 11 to 8: 8 + 11 equals 19, which corresponds to S. So the next first letter is S. Step 4: Now convert the second letters G, R, C, N to numbers: G 7, R 18, C 3, N 14. Step 5: Compute the differences: 7 to 18 is +11, 18 to 3 is +11 modulo 26 (18 + 11 equals 29, 29 minus 26 equals 3), and 3 to 14 is again +11. Step 6: Continue with the same rule: 14 + 11 equals 25, which corresponds to Y. Step 7: Therefore, the next pair is S (19) and Y (25), written as SY.

Verification / Alternative check:
We can list the full sequence of pairs with numeric positions: AG (1,7), LR (12,18), WC (23,3), HN (8,14), SY (19,25). In each column, the numbers increase by 11 modulo 26: 1,12,23,8,19 and 7,18,3,14,25. This is a very consistent pattern, and there is no deviation in any step. None of the other options matches the letter pair S and Y at the same time.

Why Other Options Are Wrong:
QY has first letter Q 17, which does not follow the +11 sequence 1,12,23,8,19. RX has second letter X 24, not 25. TZ produces T 20 and Z 26, neither of which fits the continuation of the plus 11 rule for both columns. UX gives U 21 and X 24, again breaking both established progressions.

Common Pitfalls:
Some learners look only at the second letters and attempt to guess based on rough visual patterns, ignoring the first letters. Others do not consider wrap around arithmetic from Z back to A, and so miss the true constant difference. Always convert letters to numbers, check for a consistent difference in both sequences, and remember that adding a constant modulo 26 is allowed.

Final Answer:
The pair that correctly continues the series is SY.