The problem requires finding the numerical code for the letter 'A' based on the given coded words.

Coding Logic Identification

We are given two words and their corresponding codes:

• 'PART' is coded as '2467'
• 'AIDS' is coded as '1573'

The task is to find the code for the letter 'A'. We need to identify the relationship between the letters of the words and the digits in their codes. This type of problem usually involves a consistent substitution cipher where each letter maps to a specific digit.

Letter-to-Digit Mapping

Let's list the letters and digits for each word:

• PART: Letters {P, A, R, T} correspond to digits {2, 4, 6, 7}.
• AIDS: Letters {A, I, D, S} correspond to digits {1, 5, 7, 3}.

To find the code for 'A', we look for common elements between the two sets:

• Common Letter: The only letter present in both 'PART' and 'AIDS' is 'A'.
• Common Digit: The only digit present in both codes '2467' and '1573' is '7'.

Since 'A' is the only common letter and '7' is the only common digit, we can conclude that the code for the letter 'A' is '7'.

Determining Code for 'A'

Based on the common element analysis:

• The letter 'A' appears in both words.
• The digit '7' appears in both codes.
• Therefore, 'A' corresponds to '7'.

This matches Option A.