Understanding Letter Series Completion

This question asks us to find the letter cluster that completes a given series: RJXU, ZANB, ?, PITP, XZJW. To solve this, we need to identify the pattern or rule that transforms one letter cluster into the next.

Analyzing the Pattern in the Letter Series

Let's look at the position of each letter in the alphabet (A=1, B=2, ..., Z=26) and see how the letters change from one cluster to the next.

Step-by-Step Pattern Identification

Let's analyze the shift for each position from RJXU to ZANB:

• 1st letter: R (18) to Z (26). The shift is \(26 - 18 = +8\).
• 2nd letter: J (10) to A (1 or 27). The shift is \(27 - 10 = +17\) or \(10 - 9 = 1\). If we consider A as 1 after wrapping around from Z, the shift is \(10 \rightarrow 26 \rightarrow 1\), which is \(+17\) or \(-9\). Let's assume a consistent magnitude change. A shift of \(-9\) seems more likely given other patterns.
• 3rd letter: X (24) to N (14). The shift is \(14 - 24 = -10\).
• 4th letter: U (21) to B (2 or 28). The shift is \(28 - 21 = +7\).

So, the likely shifts are +8, -9, -10, +7 for the four letter positions respectively.

Applying the Pattern to Find the Missing Cluster

Now, let's apply these shifts to the second cluster, ZANB, to find the third cluster:

• 1st letter: Z (26). Apply +8 shift. \(26 + 8 = 34\). \(34 - 26 = 8\). The 8th letter is H.
• 2nd letter: A (1 or 27). Apply -9 shift. \(27 - 9 = 18\). The 18th letter is R.
• 3rd letter: N (14). Apply -10 shift. \(14 - 10 = 4\). The 4th letter is D.
• 4th letter: B (2 or 28). Apply +7 shift. \(2 + 7 = 9\). The 9th letter is I.

The missing cluster is HRDI.

Verifying the Pattern with Subsequent Clusters

Let's check if applying the same shifts (+8, -9, -10, +7) to HRDI gives PITP, and then from PITP to XZJW.

From HRDI to PITP:

• 1st letter: H (8) + 8 = 16 (P). Correct.
• 2nd letter: R (18) - 9 = 9 (I). Correct.
• 3rd letter: D (4) - 10 = -6. \(-6 + 26 = 20\) (T). Correct (wrapping around).
• 4th letter: I (9) + 7 = 16 (P). Correct.

From PITP to XZJW:

• 1st letter: P (16) + 8 = 24 (X). Correct.
• 2nd letter: I (9) - 9 = 0. \(0 + 26 = 26\) (Z). Correct (wrapping around).
• 3rd letter: T (20) - 10 = 10 (J). Correct.
• 4th letter: P (16) + 7 = 23 (W). Correct.

The pattern of shifts (+8, -9, -10, +7) is consistent throughout the series.

Conclusion

Based on the analysis, the letter cluster that replaces the question mark is HRDI.

Revision Table: Letter Series Pattern

Additional Information on Letter Series Reasoning

Letter series questions are common in logical reasoning tests. They require you to identify the sequence or pattern based on the alphabetical position of letters. Patterns can involve:

• Adding or subtracting a constant number to the position value.
• Adding or subtracting a changing number (e.g., +1, +2, +3...).
• Alternating patterns.
• Skipping a fixed number of letters.
• Vowel/consonant patterns.
• Reverse alphabetical order.

For questions involving clusters of letters, the pattern might apply independently to each position within the cluster, as seen in this problem, or there might be a pattern between corresponding letters across clusters.