If the word "ENCRYPT" is coded as "VMXIBKG" using a reverse alphabet substitution, then how will the word "ARC" be coded in the same code language?

Introduction / Context:
This coding question uses a reverse alphabet substitution, often called an Atbash cipher. In such a code, letters at opposite ends of the alphabet are paired together: A with Z, B with Y, C with X and so on. The example "ENCRYPT" coded as "VMXIBKG" indicates that this reverse substitution is being used. We must apply the same mapping to the word ARC.

Given Data / Assumptions:

• "ENCRYPT" is written as "VMXIBKG".
• We must encode "ARC" in the same code language.
• The mapping pairs letters symmetrically: A with Z, B with Y, C with X, D with W, E with V, F with U, G with T, H with S, I with R, J with Q, K with P, L with O and M with N, and vice versa.
• The order of letters in the word is preserved; only each letter is replaced by its mirror partner.

Concept / Approach:
The approach is to verify that ENCRYPT is indeed mapped using the reverse alphabet rule. We then use the same mapping table to convert each letter of ARC. Because this mapping is symmetric, encoding and decoding use the same table. Once we know the partners of A, R and C, we simply write them in order to form the coded word.

Step-by-Step Solution:
Step 1: Check a few letter pairs from ENCRYPT and VMXIBKG. E becomes V, and E and V are opposite letters because their positions add to 27 (5 plus 22). Similarly, N becomes M (14 plus 13), C becomes X (3 plus 24) and R becomes I (18 plus 9). Step 2: These examples confirm that each letter is replaced by its reverse alphabet partner. Step 3: Use the reverse mapping for the letters of ARC. A is the first letter; its mirror partner is Z, the twenty sixth letter. Step 4: The letter R is the eighteenth letter, so its partner is I, the ninth letter. Step 5: The letter C is the third letter, so its partner is X, the twenty fourth letter. Step 6: Putting these together, A, R and C map to Z, I and X, giving the coded word ZIX.

Verification / Alternative check:
To verify, we can check that if we apply the same mapping to ZIX we get back ARC. Z maps back to A, I maps back to R and X maps back to C under the same reverse alphabet rule. This confirms that the substitution is symmetric and that ZIX is the correct encoding of ARC.

Why Other Options Are Wrong:
The options PQE, ZSX and QTB would correspond to different substitutions that do not follow the reverse alphabet rule. In particular, C must map to X in an Atbash cipher, so any answer without X as the last letter cannot be correct. Likewise, A must map to Z, so any answer that does not begin with Z breaks the mapping. Only ZIX respects all these constraints.

Common Pitfalls:
A common error is to think that the code uses a fixed shift instead of the symmetric Atbash mapping. Another mistake is misremembering which letters are paired together, especially near the middle of the alphabet. Writing out the alphabet in forward and reverse order on scrap paper is an effective way to avoid confusion and apply the mapping consistently.

Final Answer:
Using the reverse alphabet substitution, the word "ARC" is coded as ZIX.