Understanding the Coding Pattern for TREAT to WOHXW

The problem asks us to find the coding pattern used to transform the word 'TREAT' into 'WOHXW' and then apply this pattern to the word 'PARTY'. Let's analyze the relationship between the letters of 'TREAT' and 'WOHXW'. We can do this by looking at their positions in the English alphabet.

• T is the 20th letter.
• R is the 18th letter.
• E is the 5th letter.
• A is the 1st letter.
• T is the 20th letter.

Similarly for 'WOHXW':

• W is the 23rd letter.
• O is the 15th letter.
• H is the 8th letter.
• X is the 24th letter.
• W is the 23rd letter.

Now, let's find the difference in positions between the corresponding letters:

• T (20) to W (23): The shift is $23 - 20 = +3$.
• R (18) to O (15): The shift is $15 - 18 = -3$.
• E (5) to H (8): The shift is $8 - 5 = +3$.
• A (1) to X (24): The shift is $24 - 1 = +23$. However, if we consider wrapping around the alphabet (A is 1, going back 3 steps: Z is 26, Y is 25, X is 24), the shift is $-3$.
• T (20) to W (23): The shift is $23 - 20 = +3$.

The pattern observed is a sequential addition and subtraction of 3: +3, -3, +3, -3, +3.

Applying the Pattern to PARTY

Now, we apply the same pattern (+3, -3, +3, -3, +3) to the letters of the word 'PARTY':

• P: P is the 16th letter. Applying the first step (+3): $16 + 3 = 19$. The 19th letter is S.
• A: A is the 1st letter. Applying the second step (-3): $1 - 3 = -2$. Wrapping around the alphabet (from A, count back 3: Z, Y, X), the 24th letter is X. Mathematically, this is $(1 + 26) - 3 = 24$.
• R: R is the 18th letter. Applying the third step (+3): $18 + 3 = 21$. The 21st letter is U.
• T: T is the 20th letter. Applying the fourth step (-3): $20 - 3 = 17$. The 17th letter is Q.
• Y: Y is the 25th letter. Applying the fifth step (+3): $25 + 3 = 28$. Wrapping around the alphabet (from Y, count forward 3: Z, A, B), the 2nd letter is B. Mathematically, this is $(25 + 3) \pmod{26} = 28 \pmod{26} = 2$.

Combining these resulting letters, we get the coded word: SXUQB.

Final Coded Word Check

The coded word for 'PARTY' using the identified pattern is 'SXUQB'. Let's compare this with the given options:

• Option 1: RCTVA
• Option 2: YTRAP
• Option 3: SXTQB
• Option 4: OZQSX
• Option 5: SXUQB

Our calculated code 'SXUQB' matches Option 5.