In this letter coding analogy, DBCE is coded as QOPR by adding a fixed number to each alphabet position. Using the same rule, what is the correct code for JLKI?

Introduction / Context:
This question is a four letter coding analogy based on uniform shifts in the alphabet. The example DBCE : QOPR shows that each letter of DBCE has been transformed into the corresponding letter in QOPR by adding the same number to its alphabet position. Your task is to discover this numeric shift and apply it to the letters in JLKI to find the correct coded form from the options. This tests accuracy in working with alphabet positions and consistent transformations.

Given Data / Assumptions:

The known mapping is DBCE to QOPR.
We use alphabet positions A = 1, B = 2, ..., Z = 26.
The target word is JLKI, which must be coded using the same shift rule.
Options are YWXU, WYXV, WXYV and WYVX.
We assume the coding is position based and does not rearrange the order of letters.

Concept / Approach:
The concept is a constant Caesar shift. We convert each letter of DBCE to its numeric position and compare it with the position of the corresponding letter in QOPR. If we find that the difference is the same for all positions, then we have identified the shift value. Once the shift is known, we add the same number to the positions of J, L, K and I in JLKI, adjusting for wrap around if necessary, and then convert back to letters to form the code.

Step-by-Step Solution:
Step 1: Write positions for DBCE. D = 4, B = 2, C = 3, E = 5. Step 2: Write positions for QOPR. Q = 17, O = 15, P = 16, R = 18. Step 3: Calculate differences: 17 - 4 = 13, 15 - 2 = 13, 16 - 3 = 13, 18 - 5 = 13. Each letter has been shifted forward by 13 positions. Step 4: Conclude that the rule is “add 13 to each alphabet position”. Step 5: Now find positions for JLKI. J = 10, L = 12, K = 11, I = 9. Step 6: Add 13 to each: 10 + 13 = 23, 12 + 13 = 25, 11 + 13 = 24, 9 + 13 = 22. Step 7: Convert these positions back to letters: 23 is W, 25 is Y, 24 is X and 22 is V. Step 8: Combine them to obtain WYXV as the coded form of JLKI.

Verification / Alternative check:
To check our understanding, we can reverse the process. If we subtract 13 from each letter in QOPR, do we get DBCE back? Q (17) minus 13 is 4 (D), O (15) minus 13 is 2 (B), P (16) minus 13 is 3 (C) and R (18) minus 13 is 5 (E). This confirms that +13 is indeed the correct shift. Similarly, subtracting 13 from W (23), Y (25), X (24) and V (22) returns us to J (10), L (12), K (11) and I (9). This confirms that WYXV is the correct code for JLKI under the same rule.

Why Other Options Are Wrong:
YWXU, WXYV and WYVX all use some of the same letters but in different orders or with slight changes. Any rearrangement breaks the rule because our transformation does not change the order of letters, it only shifts their positions uniformly. For instance, in YWXU, the last letter U has position 21, which does not correspond to 22 (V) that we obtained from 9 + 13. WXYV similarly misassigns the second and third letters. WYVX changes the last two positions, again breaking the exact position mapping. Only WYXV maintains the correct shifted positions for J, L, K and I.

Common Pitfalls:
One common error is to detect that letters have moved roughly halfway around the alphabet but to miscount the exact shift, especially since a shift of 13 is symmetrical in the 26 letter alphabet. Another mistake is to focus only on the first or last letter and then guess an option that looks visually similar without verifying all positions. To avoid such errors, always compute numeric positions and differences for every letter in the example pair, confirm the constant shift and then apply it systematically to the new word.

Final Answer:
Since DBCE is coded to QOPR by adding 13 to each alphabet position, JLKI is coded to WYXV under the same rule. Therefore WYXV is the correct answer.