In a certain code language, the digits of numbers stand for letters. If 3456 is coded as ROPE and 15526 is coded as APPLE, then what word is represented by the code 54613?

Introduction / Context:
This coding decoding question presents a digit to letter substitution. Each distinct digit corresponds to exactly one letter, and the same mapping is used across several codes. You are given two known number word pairs and asked to decode a third numeric string into a meaningful arrangement of letters. This type of question tests your ability to notice consistent symbol to letter mappings.

Given Data / Assumptions:
- 3456 is coded as ROPE.
- 15526 is coded as APPLE.
- We need to decode 54613 using the same digit to letter mapping.
- Each digit always represents the same letter whenever it appears.

Concept / Approach:
The strategy is to align the positions of digits with the positions of letters in the known codes. This allows us to deduce which digit corresponds to which letter. Once we know the mapping for all digits that appear in the unknown code 54613, we simply substitute the corresponding letters in the same order to obtain the required word. No arithmetic operations are involved, only symbolic substitution.

Step-by-Step Solution:
Step 1: From 3456 = ROPE, match each position: 3 → R, 4 → O, 5 → P, 6 → E. Step 2: From 15526 = APPLE, match each position: 1 → A, 5 → P, 5 → P, 2 → L, 6 → E. Step 3: Combine information from both words to get the full mapping: 1 → A, 2 → L, 3 → R, 4 → O, 5 → P, 6 → E. Step 4: Now decode 54613 digit by digit using this mapping. Step 5: 5 → P, 4 → O, 6 → E, 1 → A, 3 → R. Thus 54613 corresponds to POEAR.

Verification / Alternative check:
We can verify the mapping by reconfirming the original codes. Using our mapping, 3456 becomes R (3), O (4), P (5), E (6), which is ROPE. Similarly, 15526 becomes A (1), P (5), P (5), L (2), E (6), which reconstructs APPLE perfectly. Because it is consistent, the same mapping must apply to 54613 as well.

Why Other Options Are Wrong:
- Option RPPEO misplaces several letters and does not follow the precise digit to letter order we deduced.
- Option ROPEA incorrectly attaches A to the end, which does not match the sequence 54613.
- Option PAREO corresponds to a completely different digit sequence; it is not the correct translation of 54613 under the established mapping.

Common Pitfalls:
A common mistake is to focus only on part of the code or to assume that the letters must form an existing English word. In many coding decoding questions, the resulting string may not be a meaningful word, but the mapping must still be strictly followed. Always base your answer on consistent positional mapping rather than guesswork about English vocabulary.

Final Answer:
Using the digit to letter mapping derived from the given information, 54613 decodes to POEAR.