Understanding the Cipher Language

This question involves decoding a cipher language where words are transformed into coded forms. We are given two examples:

• 'BIKE' is coded as 'YFHB'
• 'CAR' is coded as 'ZXO'

We need to find the code for 'SCOOTER' using the same cipher rule.

Analyzing the Coding Pattern

Let's look at the relationship between the letters in the original words and their coded forms. We can use the position of each letter in the English alphabet (A=1, B=2, ..., Z=26) to find the pattern.

Analyzing BIKE to YFHB:

Let's compare the letter positions:

For the letters I, K, and E, the coded letter's position is 3 less than the original letter's position.

Analyzing CAR to ZXO:

Let's compare the letter positions:

For A and R, the coded letter's position is 3 less than the original letter's position. For C, C(3) becomes Z(26), which is also a shift of -3 when considering wrapping around the alphabet (C → B → A → Z).

Deducing the Cipher Rule

From the analysis of both examples, it appears that each letter in the original word is replaced by the letter that is 3 positions before it in the English alphabet. When shifting backward from letters near the beginning of the alphabet (A, B, C), the counting wraps around from Z.

Let's represent this mathematically using modular arithmetic. The position of a letter \(L\) is \(Pos(L)\). The coded position \(Pos(L')\) is given by:

\(Pos(L') = (Pos(L) - 3 - 1 \pmod{26}) + 1\)

Alternatively, and perhaps simpler for backward shifts with wrap-around:

\(Pos(L') = (Pos(L) - 3)\)

If \(Pos(L') \le 0\), add 26. For example:

• A (1): \(1 - 3 = -2\). Wrap around: \(-2 + 26 = 24\). 24 is X. So A → X.
• B (2): \(2 - 3 = -1\). Wrap around: \(-1 + 26 = 25\). 25 is Y. So B → Y.
• C (3): \(3 - 3 = 0\). Wrap around: \(0 + 26 = 26\). 26 is Z. So C → Z.
• D (4): \(4 - 3 = 1\). 1 is A. So D → A.

This rule consistently explains both 'BIKE' → 'YFHB' and 'CAR' → 'ZXO'.

Applying the Rule to SCOOTER

Now, let's apply this "shift -3" rule to each letter of the word 'SCOOTER'.

Resulting Code for SCOOTER

Combining the coded letters, 'SCOOTER' is coded as 'PZLLQBO'.

Comparing with Options

Let's check the given options:

1. TAPPIYB
2. PYVVAHJ
3. PZLLQBO
4. JZKKMCO

The coded word 'PZLLQBO' matches Option 3.