In a certain letter code, OFFICIAL is written as QHHKEKCN by shifting each letter forward in the alphabet. Using the same code, how is LANGUAGE written?

Introduction / Context:
This problem is a classic example of a letter coding question using a Caesar cipher type shift. The word OFFICIAL is encoded as QHHKEKCN, and we must identify the pattern of shifting applied to each letter. Then we use that same pattern to encode the word LANGUAGE. Such questions test precision in counting letter positions and applying a constant shift through the alphabet.

Given Data / Assumptions:
Original word: OFFICIAL. Coded word: QHHKEKCN. We must encode LANGUAGE using the same rule. All letters are capital English letters A to Z.

Concept / Approach:
We convert each letter of OFFICIAL into its alphabet position and compare it with the corresponding letter in QHHKEKCN. If we see a constant increment for every letter, we can conclude that the coding uses a fixed forward shift. Once the size of this shift is confirmed, we apply it consistently to each letter of LANGUAGE to derive its coded form.

Step-by-Step Solution:
Step 1: Find positions for the letters in OFFICIAL and QHHKEKCN. O is 15, Q is 17. F is 6, H is 8. F is 6, H is 8 again. I is 9, K is 11. C is 3, E is 5. I is 9, K is 11. A is 1, C is 3. L is 12, N is 14. Step 2: Observe the shifts. In each case, the coded letter is 2 positions ahead of the original: 15 to 17, 6 to 8, 9 to 11, 3 to 5, 1 to 3, and 12 to 14. Thus the rule is: add 2 to the letter's alphabet position. Step 3: Apply the +2 shift to LANGUAGE. L is 12, plus 2 gives 14 which is N. A is 1, plus 2 gives 3 which is C. N is 14, plus 2 gives 16 which is P. G is 7, plus 2 gives 9 which is I. U is 21, plus 2 gives 23 which is W. A is 1, plus 2 gives 3 which is C. G is 7, plus 2 gives 9 which is I. E is 5, plus 2 gives 7 which is G. So LANGUAGE becomes NCPIWCIG.

Verification / Alternative check:
We can verify by reversing the rule for the coded word NCPIWCIG. Subtracting 2 from each coded letter should bring us back to LANGUAGE. For example, N (14) minus 2 is L (12), C (3) minus 2 is A (1), P (16) minus 2 is N (14), and so on. Performing this for all letters reconstructs LANGUAGE exactly, proving that the shift of +2 is correct and consistently applied.

Why Other Options Are Wrong:
NCPWICIG and the other variants alter the order of letters or place the W in a different position, which does not match the exact +2 shift applied letter by letter. Any option that changes the relative positions of letters or uses a different final letter cannot come from a uniform +2 Caesar type shift.

Common Pitfalls:
A common mistake is to test only the first few letters and then guess at the rest, which can be dangerous when options are very similar. Another pitfall is to forget that the same shift must work for every letter, not just some of them. Always compute the alphabet positions carefully and verify the rule for all letters in the sample word before applying it to the target word. This careful approach prevents confusion among nearly identical coded options.

Final Answer:
Using the same +2 letter shift, LANGUAGE is written as NCPIWCIG in the code language.