Understanding the Alphabetical Pattern Logic

The question asks us to identify a pattern in letter sequences based on the English alphabet and apply it. We are given two examples: XTXY relates to CYCD, and GCGH relates to LHLM. We need to find what LHLM relates to using the same logic.

Analyzing the First Pair: XTXY to CYCD

Let's examine the relationship between the letters in XTXY and CYCD. We look at the positions of these letters in the English alphabet (A=1, B=2, ..., Z=26).

• X (24th letter) relates to C (3rd letter).
• T (20th letter) relates to Y (25th letter).
• X (24th letter) relates to C (3rd letter).
• Y (25th letter) relates to D (4th letter).

Let's check if adding a fixed number to the position works. If we add 5 to the position of each letter:

• X (24) + 5 = 29. Since there are only 26 letters, we find the position by taking the remainder after dividing by 26, or by wrapping around. 29 corresponds to the 3rd letter (29 - 26 = 3), which is C. So, X + 5 = C.
• T (20) + 5 = 25, which is Y.
• X (24) + 5 = 29. 29 - 26 = 3, which is C.
• Y (25) + 5 = 30. 30 - 26 = 4, which is D.

The pattern is confirmed: each letter is shifted forward by 5 positions in the alphabet.

Verifying the Second Pair: GCGH to LHLM

Now, let's apply the same +5 logic to the second pair to ensure consistency.

• G (7th letter) relates to L (12th letter).
• C (3rd letter) relates to H (8th letter).
• G (7th letter) relates to L (12th letter).
• H (8th letter) relates to M (13th letter).

Let's check the addition:

• G (7) + 5 = 12, which is L.
• C (3) + 5 = 8, which is H.
• G (7) + 5 = 12, which is L.
• H (8) + 5 = 13, which is M.

The +5 pattern holds true for the second pair as well.

Applying the Logic to Find the Related Word for LHLM

The question asks: "To which of the given options is LHLM related, following the same logic?". This means we should treat LHLM as the input word and apply the +5 shift to find the related output word.

Let's find the related word for LHLM:

• L (12th letter) + 5 = 17th letter, which is Q.
• H (8th letter) + 5 = 13th letter, which is M.
• L (12th letter) + 5 = 17th letter, which is Q.
• M (13th letter) + 5 = 18th letter, which is R.

Combining these letters, we get the word QMQR.

Conclusion

By applying the established pattern of adding 5 to the alphabetical position of each letter, we find that LHLM relates to QMQR.

Comparing this result with the given options:

• 1. QNPX
• 2. QMQR
• 3. QMPR
• 4. QLPR

The calculated word QMQR matches option 2.