Alphabetical Pattern Analysis

This question requires identifying a pattern in letter sequences based on their alphabetical order. We need to determine the rule connecting the first pair (FAE G to MHLN) and the second pair (IDHJ to PKOQ) to apply it to LGKM.

FAE G to MHLN Relationship

Let's find the position of each letter in the English alphabet (A=1, B=2, ..., Z=26) and examine the relationship:

• F is the 6<0xE1><0xB5><0xAB><0xE1><0xB5><0xA6> letter, and M is the 13<0xE1><0xB5><0xAB><0xE1><0xB5><0xA6> letter.
• A is the 1<0xE1><0xB5><0xAB><0xE1><0xB5><0xA6> letter, and H is the 8<0xE1><0xB5><0xAB><0xE1><0xB5><0xA6> letter.
• E is the 5<0xE1><0xB5><0xAB><0xE1><0xB5><0xA6> letter, and L is the 12<0xE1><0xB5><0xAB><0xE1><0xB5><0xA6> letter.
• G is the 7<0xE1><0xB5><0xAB><0xE1><0xB5><0xA6> letter, and N is the 14<0xE1><0xB5><0xAB><0xE1><0xB5><0xA6> letter.

Now, let's calculate the shift in position for each letter pair:

• M's position (13) minus F's position (6): $13 - 6 = 7$.
• H's position (8) minus A's position (1): $8 - 1 = 7$.
• L's position (12) minus E's position (5): $12 - 5 = 7$.
• N's position (14) minus G's position (7): $14 - 7 = 7$.

This demonstrates a consistent pattern where each letter is replaced by the letter 7 positions after it in the alphabet.

IDHJ to PKOQ Pattern Verification

We verify this "+7 shift" rule with the second example pair:

• I (9) → P (16). The shift is $16 - 9 = 7$.
• D (4) → K (11). The shift is $11 - 4 = 7$.
• H (8) → O (15). The shift is $15 - 8 = 7$.
• J (10) → Q (17). The shift is $17 - 10 = 7$.

The "+7 letter shift" logic is confirmed as the correct pattern.

LGKM Coding Application

Applying the identified "+7 letter shift" rule to the letters in LGKM:

Combining these resulting letters gives us the sequence SNRT.

Result Comparison with Options

Finally, we match our derived sequence SNRT with the given choices:

• 1. NSRT
• 2. NSTR
• 3. SNRT
• 4. SNTR

Our result SNRT corresponds directly to Option 3.