Series Pattern Analysis

The given series consists of letter-number clusters. We need to find the pattern governing the changes in letters and numbers to determine the missing cluster.

Letter Patterns

Let's analyze the patterns for each letter position separately. We'll use the alphabetical positions (A=1, B=2, ... Z=26).

• First Letter Pattern: D (4), V (22), N (14), F (6)
  • D (4) to V (22): Difference = 22 - 4 = 18.
  • V (22) to N (14): Difference = 14 - 22 = -8.
  • N (14) to F (6): Difference = 6 - 14 = -8.
  • The observed pattern is +18, -8, -8. The next step should be +18.
  • F (6) + 18 = 24. The 24th letter is X.
• Second Letter Pattern: E (5), W (23), O (15), G (7)
  • E (5) to W (23): Difference = 23 - 5 = 18.
  • W (23) to O (15): Difference = 15 - 23 = -8.
  • O (15) to G (7): Difference = 7 - 15 = -8.
  • The pattern is +18, -8, -8. The next step should be +18.
  • G (7) + 18 = 25. The 25th letter is Y.
• Third Letter Pattern: U (21), M (13), E (5), W (23)
  • U (21) to M (13): Difference = 13 - 21 = -8.
  • M (13) to E (5): Difference = 5 - 13 = -8.
  • E (5) to W (23): Difference = 23 - 5 = 18.
  • The pattern is -8, -8, +18. The next step should be -8.
  • W (23) - 8 = 15. The 15th letter is O.

Combining the results for the letters, the next sequence is XYO.

Number Pattern

Let's analyze the number sequence: 7, 24, 41, 58.

• 7 to 24: Difference = 24 - 7 = 17.
• 24 to 41: Difference = 41 - 24 = 17.
• 41 to 58: Difference = 58 - 41 = 17.
• The pattern is a constant addition of 17.
• The next number is 58 + 17 = 75.

Completing the Series

Combining the letter pattern (XYO) and the number pattern (75), the missing cluster is XYO75.

This matches Option C.