The question asks us to find the "index sum" for the word "CAT". We are given a specific system where letters are assigned numerical values based on their position in the alphabet: A=1, B=2, C=3, and so on, up to Z=26.
To solve this, we first need to determine the numerical index for each letter in the word "CAT":
We can represent this mapping:
| Letter | Alphabetical Position (Index) |
|---|---|
| C | 3 |
| A | 1 |
| T | 20 |
The "index sum" is simply the total obtained by adding the indices of all the letters in the word.
For the word "CAT", the calculation is as follows:
Index Sum = Index(C) + Index(A) + Index(T)
Using the values we found:
\(\text{Index Sum} = 3 + 1 + 20\)
\(\text{Index Sum} = 24\)
Therefore, the index sum of the word "CAT", using the A=1, B=2, ..., Z=26 system, is 24.
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