In a particular code, the word DOWN is written as "5@9#" and the word NAME is written as "#6%3". Using the same symbol code, how will the word MODE be written?

Introduction / Context:
This is a simple symbol substitution coding question where each letter corresponds to a unique symbol or digit. We are given the codes for DOWN and NAME and asked to find the code for MODE. Since all letters in MODE appear in the given words, we can recover the mapping and directly encode MODE. It is a classic test of careful mapping and substitution without any positional tricks.

Given Data / Assumptions:

• DOWN → 5@9#.
• NAME → #6%3.
• Each letter maps to one symbol consistently across words.
• Target word: MODE.
• No rearrangement occurs; we simply swap letters for symbols.

Concept / Approach:
We first determine the symbol for each letter D, O, W, N from the code of DOWN. Then we extend the mapping using NAME for N, A, M, E. After that, we encode MODE by writing the appropriate symbol for M, O, D, and E in sequence. This is pure substitution with no extra operations.

Step-by-Step Solution:
Step 1: From DOWN → 5@9#, map D → 5, O → @, W → 9, N → #. Step 2: From NAME → #6%3, map N → # (consistent), A → 6, M → %, E → 3. Step 3: The letters in MODE are M, O, D, E. Step 4: Substitute using the mapping: M → % O → @ D → 5 E → 3 Step 5: Combine them in order: % @ 5 3 → %@53.

Verification / Alternative check:
Double-check by reversing the mapping. From %@53, using % → M, @ → O, 5 → D, 3 → E, we get MODE. Also, the words DOWN and NAME decode correctly from their symbol forms. As there is no conflict or ambiguity in the mapping, the code %@53 is uniquely determined for MODE.

Why Other Options Are Wrong:
Option A (6@53) uses 6 as the first symbol, which corresponds to A, not M. Option C (53%#) changes the order and symbols so that it would decode as D E M N. Option D (%#35) also mismatches the letter order and would not read as MODE. Option E (5@%3) begins with 5 which is D, not M, and therefore cannot represent MODE. Only Option B follows the correct letter-to-symbol mapping in the proper sequence.

Common Pitfalls:
One common mistake is failing to cross-check repeated letters like N in both words, which can reveal inconsistencies in a guessed mapping. Another is mixing up the symbol order for the target word. To avoid these, build a neat mapping table and always encode the target word letter by letter, checking each against the table.

Final Answer:
Therefore, in the given symbol code, the word MODE is written as %@53.