In this coded letter analogy, TEW is related to PAS by a fixed backward shift; using the same pattern, select the group of letters that completes the analogy: TEW : PAS :: IVX : ?

Introduction / Context:
This analogy is from the alphabet coding section. The word TEW is coded as PAS by shifting each letter backward in the alphabet. You must discover the exact shift and apply it to the word IVX to find the coded result. These questions assess your ability to track uniform letter shifts and maintain correct ordering.

Given Data / Assumptions:

• The alphabet is numbered A = 1 through Z = 26.
• TEW is transformed into PAS under a consistent rule.
• IVX must be transformed under the same rule.
• The options are ETR, SQR, ERT and RNP.

Concept / Approach:
To solve this, we convert each letter of TEW and PAS to their numeric positions and examine the differences. If the difference is constant and negative, it implies a backward shift. Once we determine the exact amount of the shift for all letters, we apply this same shift to I, V and X in IVX and compare the result with the options.

Step-by-Step Solution:
Step 1: Write the positions of the letters in TEW: T = 20, E = 5 and W = 23.Step 2: Write the positions of the letters in PAS: P = 16, A = 1 and S = 19.Step 3: Compute the shifts: T (20) to P (16) is minus 4; E (5) to A (1) is minus 4; W (23) to S (19) is minus 4.Step 4: Conclude that the coding rule is to shift every letter 4 positions backward in the alphabet.Step 5: Now write the positions for IVX: I = 9, V = 22 and X = 24.Step 6: Apply the same shift of minus 4: I (9) minus 4 equals 5, which is E; V (22) minus 4 equals 18, which is R; X (24) minus 4 equals 20, which is T.Step 7: Combine these letters to obtain the coded form ERT.Step 8: Compare ERT with the options; it appears as option C.

Verification / Alternative check:
We can verify our rule by rechecking TEW to PAS using the minus 4 shift. T becomes P, E becomes A and W becomes S, exactly as given. Applying the same uniform backward shift to IVX yields ERT, and no other option represents this precise transformation. This consistency across both words confirms that we have the correct pattern.

Why Other Options Are Wrong:
Option A, ETR, uses the same letters as ERT but in a different order, which does not result from a simple position shift. Option B, SQR, introduces letters that cannot be obtained by shifting I, V and X backward by 4 places. Option D, RNP, also does not match the required numerical positions. Because the coding rule is strictly a minus 4 shift applied to each letter in order, only ERT satisfies the analogy.

Common Pitfalls:
Some candidates detect that the letters move backward but miscalculate the amount of the shift or reverse letter order accidentally. Others may look for alternating patterns where a constant shift suffices. Always compute the position differences carefully for each letter in the example pair, confirm the regularity, and then apply the same stepwise rule to the new word without changing order.

Final Answer:
Using the same backward shift pattern, IVX is coded as ERT, so option C is correct.