Alphabet Analogy — Fixed Forward Shift by 8 ACEG : IKMO :: QSUW : ?

Difficulty: Easy

Correct Answer: YACE

Explanation:


Introduction / Context:
Another standard letter analogy uses a constant forward shift. Identify the magnitude in the exemplar pair and apply the same to the query pair, wrapping around the alphabet as needed.


Given Data / Assumptions:

  • Mapping: ACEG → IKMO.
  • Target: QSUW → ?
  • Alphabet positions: A=1 … Z=26.


Concept / Approach:
Compute the difference for corresponding letters in the first pair, confirm the difference is consistent, then add that difference to each letter of the second string. When sums exceed 26, wrap around by subtracting 26.


Step-by-Step Solution:

A(1) → I(9): +8.C(3) → K(11): +8.E(5) → M(13): +8.G(7) → O(15): +8.Rule: add 8 to each letter.Apply to QSUW: Q(17)+8=25 → Y; S(19)+8=27 → 27−26=1 → A; U(21)+8=29 → 29−26=3 → C; W(23)+8=31 → 31−26=5 → E.Therefore, QSUW → YACE.


Verification / Alternative check:
Apply −8 to YACE: Y→Q, A→S (wrapping backward), C→U, E→W. We recover QSUW, confirming the mapping.


Why Other Options Are Wrong:

  • YZCE / YBCE / YACD alter one or more letters, not matching the exact +8 rule with wrap-around.
  • None of the above: Incorrect because YACE is present and correct.


Common Pitfalls:
Forgetting wrap-around beyond Z. Always convert positions exceeding 26 by subtracting 26 (or use modular arithmetic).


Final Answer:
YACE

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