In this letter analogy, “BCD is to YXW as FGH is to ______”. Select the group of letters that completes the analogy by using the same mirror image pattern in the alphabet.

Introduction / Context:
This analogy uses a mirror image pattern in the alphabet, where each letter is paired with another letter such that their positions add up to a constant value. The pair BCD : YXW demonstrates that each letter in BCD is mapped to a letter near the end of the alphabet in a symmetric way. The task is to detect this pattern and then apply it to the sequence FGH in order to select the correct matching group from the options. These questions examine understanding of alphabet symmetry and positional reasoning.

Given Data / Assumptions:

• First mapping: BCD → YXW. • Second mapping: FGH → ? • Options: UTS, RQP, STU, TUS. • Alphabet positions: A = 1, B = 2, ..., Z = 26.

Concept / Approach:
In a mirror alphabet pattern, the first letter pairs with a letter such that the sum of their positions is constant, often 27, since 1 + 26 = 27. We check whether B and Y, C and X, D and W follow this rule. If so, we apply the same mirror mapping to F, G, and H. The result should yield a three letter group among the options. The order of letters is preserved, although the mapping itself inverts positions relative to the alphabet centre.

Step-by-Step Solution:
Step 1: Find positions for BCD and YXW. B = 2, C = 3, D = 4. Y = 25, X = 24, W = 23. Step 2: Add positions for each pair. B (2) + Y (25) = 27. C (3) + X (24) = 27. D (4) + W (23) = 27. Thus, each pair of letters is symmetric about the centre of the alphabet, with sums equal to 27. Step 3: Apply the same mirror rule to FGH. F = 6, G = 7, H = 8. To find the mirror letters, we compute 27 − position. For F: 27 − 6 = 21 → U. For G: 27 − 7 = 20 → T. For H: 27 − 8 = 19 → S. So FGH maps to UTS.

Verification / Alternative check:
We can verify by repeating the process for the original pair. Using the rule 27 − position, B becomes Y, C becomes X, and D becomes W, which matches the given mapping exactly. Applying the same transformation to UTS should bring us back to FGH if we again sum to 27: U (21) gives 27 − 21 = 6 → F, T (20) gives 7 → G, S (19) gives 8 → H. This confirms that UTS is the correct mirror of FGH under the same scheme.

Why Other Options Are Wrong:
• RQP: These letters do not match the computed mirror positions of FGH and follow a different ordering pattern. • STU and TUS: Although composed of similar letters, their order does not match the transformation applied to F, G, and H, and they do not preserve position by position mapping.

Common Pitfalls:
Day to day familiarity with alphabetical order may tempt candidates to choose STU or TUS because they look like simple reversals or near sequences. However, analogies involving mirror images rely on strict correspondences of positions rather than approximate visual shapes. Always convert letters to positions and explicitly check sums or differences to confirm the pattern.

Final Answer:
The letter group that correctly completes the analogy is UTS.