Which of the following letter-number clusters will replace the question mark…

Concept

In a letter-number series, examine each letter position and the number as separate columns. Convert letters to their alphabet positions (A = 1, ..., Z = 26), apply the same change down each column, and wrap around after A or Z when necessary.

Application

1. Write the three letters of every cluster in separate columns and keep the number as a fourth column.

2. First-letter positions are 6, 2, 24, 20. Each step subtracts 4 with wraparound, so the next position is 16, which is P.

3. Second-letter positions are 15, 11, 7, 3. Subtracting 4 again gives 25 after wraparound, which is Y.

4. Third-letter positions are 19, 15, 11, 7. Subtracting 4 gives 3, which is C.

5. The numbers are 143, 120, 97, 74. Each step subtracts 23, so the next number is 51.

Cross-check and contrast

Applying the same changes to TCG74 gives T to P, C to Y, G to C, and 74 to 51.

• PUC51 has middle-letter position 21 (U), while the continued second-letter column gives position 25.

• LYC51 has first-letter position 12 (L), while the continued first-letter column gives position 16.

• PYS51 has third-letter position 19 (S), while the continued third-letter column gives position 3.

Therefore, the next cluster is PYC51.