This question involves decoding a word based on a specific pattern applied to another word. We are given that 'INSPIRE' is coded as 'JPTTJZF'. We need to figure out the rule used for this transformation and then apply it to the word 'FORGIVE'.

Analysing the Code Pattern: INSPIRE to JPTTJZF

Let's look at the letters of the original word 'INSPIRE' and their corresponding letters in the coded word 'JPTTJZF'. We can also consider their positions in the alphabet (A=1, B=2, ... Z=26).

• I (9) at position 1 → J (10)
• N (14) at position 2 → P (16)
• S (19) at position 3 → T (20)
• P (16) at position 4 → T (20)
• I (9) at position 5 → J (10)
• R (18) at position 6 → Z (26)
• E (5) at position 7 → F (6)

Now, let's examine the shift in the alphabetical position for each letter:

• Position 1 (I → J): \(10 - 9 = +1\)
• Position 2 (N → P): \(16 - 14 = +2\)
• Position 3 (S → T): \(20 - 19 = +1\)
• Position 4 (P → T): \(20 - 16 = +4\)
• Position 5 (I → J): \(10 - 9 = +1\)
• Position 6 (R → Z): \(26 - 18 = +8\)
• Position 7 (E → F): \(6 - 5 = +1\)

The sequence of shifts is: +1, +2, +1, +4, +1, +8, +1.

We can observe a pattern here based on the position of the letter in the word:

• Letters at odd positions (1st, 3rd, 5th, 7th) have a shift of +1.
• Letters at even positions (2nd, 4th, 6th) have shifts of +2, +4, +8 respectively. The shifts for even positions follow a sequence where the shift is doubled for each subsequent even position (\(2^1, 2^2, 2^3, ...\) or simply 2, 4, 8, ...).

So, the coding rule is: Add 1 to the alphabetical position for letters at odd positions. Add \(2^n\) to the alphabetical position for letters at even positions, where n is the index of the even position (1st even is \(n=1\), 2nd even is \(n=2\), 3rd even is \(n=3\), etc., corresponding to word positions 2, 4, 6, etc.).

Applying the Coding Rule to FORGIVE

Now let's apply this rule to the word 'FORGIVE'. 'FORGIVE' has 7 letters, just like 'INSPIRE'.

Combining the coded letters in order, we get GQSKJDF.

Coding-Decoding Revision Table

Additional Information on Coding-Decoding

Coding-decoding questions test your ability to identify patterns in how words, letters, or numbers are transformed. Common patterns include:

• Letter Shifting: Each letter is shifted by a fixed number of positions (e.g., +1, -2) or a varying number.
• Position Change: Letters within the word might be rearranged (e.g., reversed, swapped in pairs).
• Opposite Letters: Each letter is replaced by its opposite letter in the alphabet (e.g., A <> Z, B <> Y).
• Vowel/Consonant Rules: Different rules apply to vowels and consonants.
• Mixed Patterns: A combination of the above rules, often based on the position of the letter in the word (like in this question) or whether it's a vowel or consonant.
• Number/Symbol Coding: Letters are replaced by numbers or symbols based on a rule.

Solving these questions requires careful observation, breaking down the transformation, and testing different potential patterns.