Decoding the Code: PARK, RACE, and CARE Puzzle Logic

This question involves a type of coding-decoding reasoning problem. We need to figure out the numerical code for the word 'CARE' based on the codes provided for 'PARK' and 'RACE'. The key is to find a consistent pattern or mapping between the letters and the numbers.

Analyzing Given Codes

The problem provides the following information:

• 'PARK' is coded as '3749'
• 'RACE' is coded as '4762'

Deriving the Letter-to-Number Mapping

Let's break down the codes word by word to identify the code for each letter:

From 'PARK' = '3749', we can infer potential mappings:

• P corresponds to 3
• A corresponds to 7
• R corresponds to 4
• K corresponds to 9

From 'RACE' = '4762', we get more mappings:

• R corresponds to 4
• A corresponds to 7
• C corresponds to 6
• E corresponds to 2

By comparing the mappings from both words, we can see consistency:

• The letter 'A' maps to '7' in both 'PARK' and 'RACE'.
• The letter 'R' maps to '4' in both 'PARK' and 'RACE'.

This consistency suggests that each letter consistently represents a specific number. We can summarize the established code mappings in the following table:

Applying the Mapping to Code CARE

Now, we use the derived letter-to-number mappings to find the code for the word 'CARE':

• The letter 'C' maps to 6.
• The letter 'A' maps to 7.
• The letter 'R' maps to 4.
• The letter 'E' maps to 2.

Combining these numerical codes in the order of the letters in 'CARE', we get the final code.

Therefore, the code for 'CARE' is 6742.