In the following question, select the related letter pair from the given alternatives: AUR is to CXV as which pair is to IHQ?

Introduction / Context:
This analogy involves two three letter groups forming a pair: AUR is related to CXV, and you must choose which given pair shows the same alphabetic transformation. Such problems examine whether you can detect consistent shifts between corresponding letters and then recognise the same pattern in another pair from the options.

Given Data / Assumptions:

• The model pair is AUR on the left and CXV on the right.
• The answer options are four different pairs of three letter groups.
• We need to determine the shift from AUR to CXV and then find which option uses the same pattern between its first and second group.
• Alphabet positions are A = 1, B = 2, ..., Z = 26.
• We assume the transformation is applied position wise, that is, first letter to first letter, second to second, and third to third.

Concept / Approach:
We begin by converting the letters to their numeric positions and then calculating how much each letter in AUR shifts to become the corresponding letter in CXV. If we see a consistent or patterned sequence of shifts such as +2, +3, +4, we then test each option to see which pair uses the same shifts from its first group to its second. Only the pair matching this exact pattern for all three letters is correct.

Step-by-Step Solution:
Step 1: Write the positions of the letters in AUR. A is 1, U is 21, and R is 18. Step 2: Write the positions of the letters in CXV. C is 3, X is 24, and V is 22. Step 3: Compute the shift for each position: from A(1) to C(3) is +2; from U(21) to X(24) is +3; from R(18) to V(22) is +4. Step 4: Note that the shifts are not constant but follow a pattern of +2, +3, and +4. Step 5: Now test each option. Step 6: For GEM to IHQ: G(7) to I(9) is +2; E(5) to H(8) is +3; M(13) to Q(17) is +4. This matches the +2, +3, +4 pattern exactly. Step 7: Briefly check that the other options do not follow this pattern for all three letters, confirming GEM : IHQ as the only correct pair.

Verification / Alternative check:
To verify, we can reverse the transformation for GEM : IHQ using the pattern minus 2, minus 3, and minus 4. Starting from I(9), H(8), and Q(17), subtract 2, 3, and 4 respectively to get G(7), E(5), and M(13), which are exactly the letters of GEM. This confirms that GEM : IHQ uses the same ordered shifts as AUR : CXV. If we try the same test on other options, we will find the differences either do not follow the +2, +3, +4 pattern or are inconsistent across positions.

Why Other Options Are Wrong:
In RFT : SGU, HSO : GRN, and KGA : NIE, the shifts between corresponding letters are not +2, +3, and +4 in order. Some may have constant shifts or mixed patterns, but none replicate the exact incremental sequence discovered from AUR : CXV. Since analogy requires structural repetition, any pair that fails to reproduce this pattern for all three positions cannot be correct.

Common Pitfalls:
One common mistake is to look only for a constant shift and discard a pair because the shift is not the same for each letter. In this question, the shift itself is changing in a systematic way, increasing by one each time. Carefully computing differences for each letter position instead of assuming a constant shift is crucial to avoid incorrect elimination of the correct pair.

Final Answer:
The letter pair that follows the same +2, +3, +4 shift pattern as AUR : CXV is GEM : IHQ.