Question

In a coding system, each letter in a word is replaced by the letter that is two positions ahead in the alphabet (e.g., A becomes C, B becomes D, ..., Z becomes B). If the word "CAT" is coded using this system, what will be the code for the word "DOG"?

Hint:

Remember: In coding-decoding, identify the pattern (e.g., shifting letters by a fixed number) and apply it consistently to each letter. Use alphabet positions (A=1, Z=26) for clarity.

Answer 1

Given: \[ \text{Word} = \text{DOG}, \quad \text{Rule: Each letter is replaced by the letter two positions ahead in the alphabet} \] Step 1: Understand the Coding Rule
The alphabet is ordered from A (position 1) to Z (position 26). The coding process involves shifting each letter forward by two positions. For example, A (1) becomes C (3), B (2) becomes D (4). This shift wraps around the alphabet, so Y (25) becomes A (25 + 2 = 27; 27 - 26 = 1), and Z (26) becomes B (26 + 2 = 28; 28 - 26 = 2). The formula for the coded letter's position is \( \text{Original position} + 2 \), with a modulo 26 operation to handle alphabet wrapping.
Step 2: Code the Word "DOG"
Apply the rule to each letter in "DOG":
- D: Original position is 4. New position: \( 4 + 2 = 6 \). The 6th letter is F.
- O: Original position is 15. New position: \( 15 + 2 = 17 \). The 17th letter is Q.
- G: Original position is 7. New position: \( 7 + 2 = 9 \). The 9th letter is I.
Therefore, the coded form of "DOG" is FQI.
Step 3: Verify with Example "CAT"
To confirm the rule, code the word "CAT":
- C: Original position is 3. New position: \( 3 + 2 = 5 \). The 5th letter is E.
- A: Original position is 1. New position: \( 1 + 2 = 3 \). The 3rd letter is C.
- T: Original position is 20. New position: \( 20 + 2 = 22 \). The 22nd letter is V.
"CAT" is coded as ECV. This confirms the rule's consistency. Recalculating "DOG" yields FQI, matching the prior result.
Answer: The correct answer is option (1): FQI.