Analyzing the Letter-Cluster Analogy

This question is based on a letter-cluster analogy. We need to identify the relationship between the first pair of letter clusters (NEAREST : PICVGWV) and the second pair (OFFICER : QJHMEIT) and then apply the same relationship to find the missing cluster for SERVICE.

Deciphering the Pattern: NEAREST to PICVGWV

Let's examine the relationship between the letters in NEAREST and PICVGWV. We can look at the shift in position for each corresponding letter in the alphabet:

• N (14th letter) $\rightarrow$ P (16th letter) = +2 positions
• E (5th letter) $\rightarrow$ I (9th letter) = +4 positions
• A (1st letter) $\rightarrow$ C (3rd letter) = +2 positions
• R (18th letter) $\rightarrow$ V (22nd letter) = +4 positions
• E (5th letter) $\rightarrow$ G (7th letter) = +2 positions
• S (19th letter) $\rightarrow$ W (23rd letter) = +4 positions
• T (20th letter) $\rightarrow$ V (22nd letter) = +2 positions

The pattern observed is a sequence of shifts: +2, +4, +2, +4, +2, +4, +2.

Validating the Pattern: OFFICER to QJHMEIT

Let's verify if this pattern holds true for the second pair, OFFICER to QJHMEIT:

• O (15th letter) $\rightarrow$ Q (17th letter) = +2 positions
• F (6th letter) $\rightarrow$ J (10th letter) = +4 positions
• F (6th letter) $\rightarrow$ H (8th letter) = +2 positions
• I (9th letter) $\rightarrow$ M (13th letter) = +4 positions
• C (3rd letter) $\rightarrow$ E (5th letter) = +2 positions
• E (5th letter) $\rightarrow$ I (9th letter) = +4 positions
• R (18th letter) $\rightarrow$ T (20th letter) = +2 positions

The pattern (+2, +4, +2, +4, +2, +4, +2) is consistent across both examples.

Applying the Pattern to SERVICE

Now, we apply the established pattern (+2, +4, +2, +4, +2, +4, +2) to the letter cluster SERVICE:

• S (19th letter) + 2 = U (21st letter)
• E (5th letter) + 4 = I (9th letter)
• R (18th letter) + 2 = T (20th letter)
• V (22nd letter) + 4 = Z (26th letter)
• I (9th letter) + 2 = K (11th letter)
• C (3rd letter) + 4 = G (7th letter)
• E (5th letter) + 2 = G (7th letter)

Following this pattern, the letter cluster for SERVICE is UITZKGG.

Conclusion

Comparing our result with the given options, the cluster UITZKGG matches option 1.