This question asks us to identify the letter-cluster pair that does not follow the same pattern as the others. To do this, we need to carefully analyze the transformation rule applied to the first word to get the second word in each pair.

Pattern Analysis

Let's examine the common pattern found in the first three given letter-cluster pairs. We will represent a six-letter word as a sequence of letters, for example, ABCDEF, where A, B, C are the first three letters and D, E, F are the last three letters.

• The observed pattern for transforming the word ABCDEF is to take the last three letters (DEF) and place them at the beginning of the new word.
• Following this, the first three letters (ABC) are reversed (becoming CBA) and then placed at the end of the new word.
• Therefore, the transformation rule is: ABCDEF becomes DEFCBA.

Applying the Pattern to Each Letter-Cluster Option

1. BORDER : DERROB

• Original word: BORDER
• First three letters: BOR
• Last three letters: DER
• Reverse of the first three letters: ROB
• Applying the pattern (DEFCBA): DER + ROB = DERROB
• This transformation perfectly matches the given pair BORDER : DERROB.

2. SUMMER : MERMUS

• Original word: SUMMER
• First three letters: SUM
• Last three letters: MER
• Reverse of the first three letters: MUS
• Applying the pattern (DEFCBA): MER + MUS = MERMUS
• This transformation also perfectly matches the given pair SUMMER : MERMUS.

3. MUTUAL : UALTUM

• Original word: MUTUAL
• First three letters: MUT
• Last three letters: UAL
• Reverse of the first three letters: TUM
• Applying the pattern (DEFCBA): UAL + TUM = UALTUM
• This transformation too perfectly matches the given pair MUTUAL : UALTUM.

4. UNIQUE : QEUNIU

• Original word: UNIQUE
• First three letters: UNI
• Last three letters: QUE
• Reverse of the first three letters: INU
• Applying the pattern (DEFCBA): QUE + INU = QUEINU
• The given pair, however, is UNIQUE : QEUNIU.
• Since QEUNIU is not the same as the expected QUEINU, this pair does not follow the established letter-cluster pattern.

Conclusion

Based on the detailed pattern analysis, the letter-cluster pairs BORDER : DERROB, SUMMER : MERMUS, and MUTUAL : UALTUM all consistently follow the rule of taking the last three letters and appending the reversed first three letters. However, the pair UNIQUE : QEUNIU deviates from this consistent pattern. Therefore, it is the one that does NOT belong to the group.