In this letter analogy question, select the group of letters that completes the pattern: ACEG : IKMO :: QSUW : ?

Introduction / Context:
Letter analogy questions test your ability to recognize hidden patterns in the positions of letters in the alphabet. In this item you are given the pair ACEG and IKMO and then asked to extend the same pattern from QSUW to a missing group of letters. Such problems are common in aptitude and reasoning exams because they quickly reveal how comfortable you are with systematic pattern recognition.

Given Data / Assumptions:
- The first pair is ACEG and IKMO, both groups of four letters.
- The second given group is QSUW, and you must find another four letter group that fits the same transformation used in the first pair.
- The alphabet positions used are A=1, B=2, C=3, and so on up to Z=26.
- We assume that the pattern is consistent across all corresponding letters in the pair, and that the transformation is applied cyclically if it crosses Z.

Concept / Approach:
The general approach is to map each letter in the first group to the corresponding letter in the second group and examine the numerical shifts in terms of alphabet positions. If the shift is constant, we can treat it like adding or subtracting a fixed number, possibly with wrap around when we move past Z. After finding this rule for ACEG to IKMO, we apply exactly the same rule to each letter in QSUW to generate the correct answer group. Finally, we compare that result to the options to select the matching sequence.

Step-by-Step Solution:
Step 1: Write down alphabet positions for the first pair: A=1, C=3, E=5, G=7 and I=9, K=11, M=13, O=15.Step 2: Compute the shift for each position: 1 to 9 is +8, 3 to 11 is +8, 5 to 13 is +8, and 7 to 15 is also +8, so the transformation is +8 for every letter.Step 3: Now take QSUW where Q=17, S=19, U=21, and W=23.Step 4: Add 8 to each position, using wrap around beyond 26: Q (17) + 8 = 25 which is Y, S (19) + 8 = 27; subtract 26 to get 1 which is A, U (21) + 8 = 29; subtract 26 to get 3 which is C, and W (23) + 8 = 31; subtract 26 to get 5 which is E.Step 5: The resulting group is YACE, which exactly matches option C, so YACE is the required completion of the analogy.

Verification / Alternative check:
You can verify the answer by reversing the process. Starting from YACE, subtract 8 positions from each letter to see if you return to QSUW. Y (25) minus 8 gives 17 which is Q, A (1) minus 8 means move back eight steps from A and wrap around to reach S, C (3) minus 8 wraps to U, and E (5) minus 8 wraps to W. This reverse check confirms that QSUW and YACE maintain the same +8 mapping that appears in the pair ACEG and IKMO.

Why Other Options Are Wrong:
- YZCE: Only the first letter Y is correct; the second letter Z does not follow the +8 pattern and breaks the consistent transformation.
- YACD: The last letter D is incorrect, because W should map to E, not D, under the +8 shift rule.
- YBCE: The second letter B does not follow the computed position for S, which must map to A, so this group does not preserve the constant shift.

Common Pitfalls:
Candidates sometimes compare only the shapes or partial sequences of letters and try to guess, instead of translating letters into their numerical positions. Another mistake is forgetting that the alphabet is treated cyclically, so after Z you wrap back to A. This wrapping is crucial for correctly mapping letters such as S, U, and W when adding 8. Always compute the exact shift with numbers, apply the same rule consistently, and perform a quick reverse check to reinforce accuracy.

Final Answer:
The correct group of letters that completes the analogy ACEG : IKMO :: QSUW : ? is YACE.