In a code language, each letter of a word is replaced by a number to form a single continuous code. The word FATE is written as 61205 using this rule. Using the same coding pattern, what is the code for the word LEAN?

Introduction / Context:
This question is about converting letters to numbers using a positional code. The word FATE is written as 61205 in the code language. The challenge is to figure out how each letter's position in the alphabet is reflected in the code, and then to use the same system to encode the word LEAN. This tests familiarity with alphabetical positions and careful grouping of digits.

Given Data / Assumptions:

• FATE is written as 61205.
• Target word: LEAN.
• Letters are encoded based on their positions in the English alphabet.
• The final code is a single string formed by concatenating the numeric codes of each letter without spaces.

Concept / Approach:
To decode the pattern, compare FATE with 61205. The letters F, A, T and E are the 6th, 1st, 20th and 5th letters of the alphabet respectively. If we take these positions and write them in sequence as 6, 1, 20, 5 we get the string 61205, which matches the given code exactly. Therefore, the rule is simply to replace each letter by its alphabetical position and then write the numbers consecutively. We can apply this straightforward rule to LEAN.

Step-by-Step Solution:
Step 1: Confirm the pattern for FATE. Positions are F = 6, A = 1, T = 20, E = 5. Step 2: Concatenate these values: 6, 1, 20, 5 → 61205, matching the given code. Step 3: Now take the word LEAN. Identify each letter's position in the alphabet: L is the 12th letter → 12. E is the 5th letter → 5. A is the 1st letter → 1. N is the 14th letter → 14. Step 4: Write these numeric codes in order: 12, 5, 1, 14. Step 5: Concatenate them to form a single code string: 125114.

Verification / Alternative check:
To verify, we can reverse the process for FATE: splitting 61205 as 6, 1, 20, 5 leads back to F, A, T and E based on positions, confirming that the encoding rule is correct. For LEAN, splitting 125114 as 12, 5, 1, 14 gives back L, E, A and N. Checking the answer options shows that 125114 is present as option A and agrees perfectly with this reasoning.

Why Other Options Are Wrong:
Options B, C, D and E change one or more digits in the sequence, which would correspond to different alphabet positions and therefore different letters. For example, 125115 would map to L, E, A, O, not LEAN. Since the code must strictly follow the alphabetical positions of L, E, A and N, any deviation from 12, 5, 1 and 14 is incorrect. Only 125114 reproduces the intended word.

Common Pitfalls:
A typical mistake is to miscount the position of a letter, particularly for letters in the second half of the alphabet. Another common error is misgrouping the digits when reading or writing codes, especially for letters with two digit positions like 12 or 14. To avoid this, it helps to memorise or quickly reconstruct the alphabet with position numbers and to carefully check each letter's index before writing the final code string.

Final Answer:
Using alphabetical positions as the code, the word LEAN is written as 125114.