A two letter series is given as AY, CW, EU, ? Based on the English alphabet, which pair of letters should come next to continue this pattern correctly?

Introduction / Context:
This question is a letter pair series: each term consists of two letters, and we have AY, CW, EU, followed by a missing pair. Alphabet test questions like this check whether the candidate can simultaneously track patterns in both the first and the second letters using their numeric positions in the alphabet and a consistent rule for movement.

Given Data / Assumptions:

• Series: AY, CW, EU, ? • Options: GS, HS, GR, HR • Alphabet positions: A 1, C 3, E 5, G 7, Y 25, W 23, U 21, S 19, R 18, H 8. • Assumption: The first letters form one pattern, and the second letters form another pattern, both regular.

Concept / Approach:
We treat the first and second letters of each pair as separate sequences. For each sequence we compute the numeric positions and then the differences between terms. If these differences are constant or follow a predictable structure, we extend them to find the next term. The key idea is to notice that the first letters are moving forward in the alphabet while the second letters move backward with equal step sizes.

Step-by-Step Solution:
Step 1: First letters: A, C, E. Positions are 1, 3, and 5. Step 2: The differences between these are +2 (1 to 3) and +2 (3 to 5). So the first letter is moving forward by 2 positions each time. Step 3: Extend first letter sequence: 5 + 2 = 7, which is G, so the next first letter should be G. Step 4: Second letters: Y, W, U. Positions are 25, 23, and 21. Step 5: Differences are −2 (25 to 23) and −2 (23 to 21). So the second letter is moving backward by 2 positions each time. Step 6: Extend second letter sequence: 21 − 2 = 19, which is S. So the next second letter should be S. Step 7: Combining both predictions, the missing pair is GS.

Verification / Alternative check:
We can check symmetry: while the first letters progress A, C, E, G (positions 1,3,5,7), the second letters regress Y, W, U, S (positions 25,23,21,19). Each time we go to the next term, the first letter advances by two and the second letter retreats by two. Among the options, only GS fits this pattern. Other pairs such as HS, GR, or HR either break the +2 or the −2 rule for one of the positions.

Why Other Options Are Wrong:
HS uses H as the first letter, position 8, which is a jump of +3 from E instead of the required +2. GR uses R as the second letter position 18, which would be a movement of −3 from U instead of −2. HR breaks both column rules and therefore does not align with the observed pattern.

Common Pitfalls:
Students sometimes track only one letter in each pair and ignore the other, leading to choices that partly match but do not satisfy the full pattern. Another pitfall is miscounting backward steps when going from Y to W to U, especially because it involves moving from the tail end of the alphabet. Converting letters into their numeric positions and noting plus or minus steps in a small table helps avoid these mistakes.

Final Answer:
The correct pair that continues the series AY, CW, EU is GS.