In the letter pair series NO, QR, UV, ZA, ?, which of the following pairs should come next to continue the pattern?

Introduction / Context:
The pair series NO, QR, UV, ZA, ? looks deceptively simple, but it combines steadily increasing steps in the alphabet with wrap around from Z back to A. You must identify which pair continues the pattern. This question tests your understanding of variable step sizes and modular arithmetic on alphabet positions.

Given Data / Assumptions:

• Pairs: NO, QR, UV, ZA, ?
• Alphabet positions A 1 to Z 26.
• We treat the first letters as one sequence and the second letters as another sequence.

Concept / Approach:
First, separate the first letters N, Q, U, Z, ? and the second letters O, R, V, A, ?. Convert them to numerical positions. Notice that the steps between first letters are not constant but increase by 1 each time. The same pattern occurs for the second letters. Extending this logic gives the next pair.

Step-by-Step Solution:
Step 1: First letters are N, Q, U, Z. Step 2: Positions: N 14, Q 17, U 21, Z 26. Step 3: Differences: 17 minus 14 equals 3, 21 minus 17 equals 4, 26 minus 21 equals 5. The step size increases: plus 3, plus 4, plus 5. Step 4: The next step should be plus 6. Step 5: From 26 Z, add 6: 26 plus 6 equals 32, minus 26 equals 6, which is F. So the next first letter is F. Step 6: Second letters are O, R, V, A. Step 7: Positions: O 15, R 18, V 22, A 1. Differences: 18 minus 15 equals 3, 22 minus 18 equals 4, and going from 22 to 1 is plus 5 modulo 26 (22 plus 5 equals 27, minus 26 equals 1). Step 8: This also follows plus 3, plus 4, plus 5, so the next step should be plus 6 from A. Step 9: Add 6: 1 plus 6 equals 7, which is G. Step 10: Therefore the missing pair is FG.

Verification / Alternative check:
The complete sequence of first letters becomes N, Q, U, Z, F (14,17,21,26,6) with step sizes 3, 4, 5, 6 modulo 26. The second letters O, R, V, A, G (15,18,22,1,7) also follow step sizes 3, 4, 5, 6 modulo 26. This symmetry between the two columns confirms that FG is uniquely correct.

Why Other Options Are Wrong:
EF would give first letter E 5 and second letter F 6, which do not respect the increasing step pattern from Z 26. DE and GH shift both columns incorrectly and destroy the plus 3, plus 4, plus 5, plus 6 pattern. HI is further away and also does not align with the expected steps from ZA.

Common Pitfalls:
A common oversight is to search for a constant step and give up when it is not found, without considering that step sizes may change in a controlled way. Another mistake is to ignore wrap around from Z to A and treat letters beyond Z as invalid. Always check whether the differences themselves form a pattern, as they do here with 3, 4, 5, 6.

Final Answer:
The pair that correctly completes the series is FG.