In a certain coding scheme, the word RATION is written as OXQFLK by shifting each letter in the alphabet. Using the same pattern, how should the word LUMBER be coded?

Introduction / Context:
This problem is a classic letter shifting or Caesar cipher question in the coding and decoding section of verbal reasoning. The aim is to understand how each letter of a given word is replaced by another letter based on a consistent shift in the alphabet, and then apply the same shift to a new word to obtain its coded form.

Given Data / Assumptions:

• RATION is coded as OXQFLK.
• The code is consistent for all letters of the word.
• We must find the code for LUMBER using the same rule.
• The English alphabet positions are used implicitly: A = 1, B = 2, up to Z = 26.
• Shifts are applied cyclically, meaning that if we move back from A, we wrap around to the end of the alphabet.

Concept / Approach:
We compare each letter in the original word RATION with the corresponding letter in the coded word OXQFLK to detect a consistent shift. If the difference between positions is the same for all letters, that shift defines the coding rule. Then we apply the same shift to each letter of LUMBER and construct the final coded word from the shifted letters.

Step-by-Step Solution:
Step 1: Write the letter positions for RATION: R = 18, A = 1, T = 20, I = 9, O = 15, N = 14.Step 2: Write the letter positions for the code OXQFLK: O = 15, X = 24, Q = 17, F = 6, L = 12, K = 11.Step 3: Find the shift for each pair. For R to O, 18 to 15 is a shift of minus 3. For A to X, 1 to 24 is also equivalent to minus 3 with wrap around. Similarly, T to Q (20 to 17), I to F (9 to 6), O to L (15 to 12) and N to K (14 to 11) are all shifts of minus 3.Step 4: Therefore, the coding rule is: each letter is replaced by the letter that is 3 positions earlier in the alphabet.Step 5: Apply this rule to LUMBER. L = 12 shifts to I = 9, U = 21 shifts to R = 18, M = 13 shifts to J = 10, B = 2 shifts to Y = 25, E = 5 shifts to B = 2 and R = 18 shifts to O = 15.Step 6: Combining these shifted letters gives the code IRJYBO for LUMBER.

Verification / Alternative check:
You can quickly verify by reversing the process. Take the coded word IRJYBO and shift each letter forward by 3 positions: I to L, R to U, J to M, Y to B (with wrap around), B to E and O to R. This reproduces LUMBER and confirms that the rule has been applied correctly, leaving no doubt that IRJYBO is the correct code.

Why Other Options Are Wrong:
The options KTLADQ, ITJABQ, OXPEHU and KRJXBO do not consistently reflect a shift of minus 3 from the letters of LUMBER. Some of these options may have one or two letters that accidentally match a shifted letter, but not all of them follow the same rule for every position. Since the coding rule is uniform across the word, any option that breaks the consistent shift pattern must be rejected.

Common Pitfalls:
Many test takers incorrectly assume a forward shift when the example actually uses a backward shift, or they forget to wrap around correctly when moving from letters near the beginning or end of the alphabet. Others only test the rule on the first one or two letters and rush to a conclusion. Always check the shift across all letters of the example and then apply it systematically to the new word.

Final Answer:
Using the shift of three letters backward in the alphabet, the correct code for LUMBER is IRJYBO.