GRAB Code Pattern Explained

The question asks us to figure out the coding rule used to transform the word GRAB into IKTVCEDF and then apply this rule to encode the word LIST.

First, let's analyze the given encoding: GRAB becomes IKTVCEDF. We notice that the original word has 4 letters, while the encoded word has 8 letters. This strongly suggests that each letter in the original word is represented by a pair of letters in the encoded word.

Let's map the letters:

• G $\rightarrow$ IK
• R $\rightarrow$ TV
• A $\rightarrow$ CE
• B $\rightarrow$ DF

To understand the logic, let's look at the positions of these letters in the alphabet (A=1, B=2, ... Z=26):

• G is the 7th letter.
• R is the 18th letter.
• A is the 1st letter.
• B is the 2nd letter.

And the positions of the corresponding encoded letters:

• I is the 9th, K is the 11th.
• T is the 20th, V is the 22nd.
• C is the 3rd, E is the 5th.
• D is the 4th, F is the 6th.

Now, let's compare the positions to find the pattern:

• For G (position 7): The encoded letters I (9) and K (11) are derived from $7+2=9$ and $7+4=11$.
• For R (position 18): The encoded letters T (20) and V (22) are derived from $18+2=20$ and $18+4=22$.
• For A (position 1): The encoded letters C (3) and E (5) are derived from $1+2=3$ and $1+4=5$.
• For B (position 2): The encoded letters D (4) and F (6) are derived from $2+2=4$ and $2+4=6$.

The consistent rule is: Each letter is replaced by two letters. The first is 2 positions after the original letter in the alphabet, and the second is 4 positions after the original letter. If the original letter's position is $P$, the encoded letters are at positions $(P+2)$ and $(P+4)$.

LIST Encoding Using GRAB Pattern

Now, we apply the same established pattern (Letter $\rightarrow$ Letter at P+2, Letter at P+4) to encode the word LIST.

1. L: The position of L is 12.
   • The first encoded letter is at position $12+2=14$, which is N.
   • The second encoded letter is at position $12+4=16$, which is P.
   Therefore, L is encoded as NP.
2. I: The position of I is 9.
   • The first encoded letter is at position $9+2=11$, which is K.
   • The second encoded letter is at position $9+4=13$, which is M.
   Therefore, I is encoded as KM.
3. S: The position of S is 19.
   • The first encoded letter is at position $19+2=21$, which is U.
   • The second encoded letter is at position $19+4=23$, which is W.
   Therefore, S is encoded as UW.
4. T: The position of T is 20.
   • The first encoded letter is at position $20+2=22$, which is V.
   • The second encoded letter is at position $20+4=24$, which is X.
   Therefore, T is encoded as VX.

To get the final encoded word for LIST, we concatenate the encoded pairs for each letter:

NP + KM + UW + VX = NPKMWVX

Final Encoded Word for LIST

The encoded word we derived is NPKMWVX. Now, let's compare this with the given options:

1. NPKMUWXV
2. NPKMUVWX
3. NPKMUW VX
4. NPKMUVXW

Our derived sequence NPKMWVX contains the exact same letters in the same order as Option 3, NPKMUW VX. The only difference is the space inserted between 'UW' and 'VX'. Assuming this space is part of the required format, Option 3 is the correct representation.

Thus, in this code language, LIST is written as NPKMUW VX.