In this coded letter analogy, “SAP is to WET as ______ is to XVI”. Select the group of letters that, when each letter is shifted forward by the same amount, gives XVI, mirroring the pattern from SAP to WET.

Introduction / Context:
This analogy uses a fixed forward alphabet shift. The example pair “SAP : WET” shows how each letter of the first group becomes a different letter in the second group after shifting. We must find which option, when shifted forward by the same amount, produces the group XVI. This tests your ability to apply and reverse consistent shifts on letter groups.

Given Data / Assumptions:

• Known pair: SAP → WET. • Unknown mapping: ? → XVI. • Options: TRE, SQR, SRQ, PNR. • Alphabet positions: A = 1, B = 2, ..., Z = 26. • We expect a constant shift (e.g. +4) based on SAP to WET.

Concept / Approach:
We first determine the shift used to convert SAP into WET. Once we know the shift value, we reverse it on XVI to find its original letters. Then we match that original group with one of the options. This is often easier than trying to apply forward shifts to every option and checking if the result is XVI.

Step-by-Step Solution:
Step 1: Find the shift from SAP to WET. S = 19, A = 1, P = 16. W = 23, E = 5, T = 20. Compute the differences: 19 → 23: +4; 1 → 5: +4; 16 → 20: +4. Thus, every letter is shifted forward by +4 positions. Step 2: Reverse the shift for XVI. X = 24, V = 22, I = 9. Subtract 4 from each: 24 − 4 = 20 → T. 22 − 4 = 18 → R. 9 − 4 = 5 → E. Step 3: The original group that becomes XVI after a +4 shift is TRE. Step 4: Compare with the options; TRE is given as option A.

Verification / Alternative check:
We can confirm by reapplying the +4 shift to TRE. T (20) + 4 = 24 → X, R (18) + 4 = 22 → V, and E (5) + 4 = 9 → I. This yields X V I (XVI), exactly as required. Testing other options quickly shows that adding 4 to each of their letters does not produce XVI. Therefore, TRE is uniquely correct under the identified rule.

Why Other Options Are Wrong:
• SQR: Shifting S, Q, R by +4 gives W, U, V, which is WUV, not XVI. • SRQ: Shifting by +4 gives W, V, U, again not XVI. • PNR: Shifting by +4 gives T, R, V, which is TRV, not XVI.

Common Pitfalls:
Some candidates try to shift each option forward and compare with XVI, which is fine but slower. Others guess based on visual similarity to XVI without checking the shift. A more systematic approach is to first determine the shift from the example pair and then apply the inverse of that shift to the target group (XVI). This leads directly to TRE and avoids confusion.

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