In the alphabet series XPK, VNJ, TLH, RJE, which of the following three letter groups should appear next to continue the pattern?

Introduction / Context:
This question features a three letter alphabet series: XPK, VNJ, TLH, RJE, ?. We are asked to identify the next group of three letters that continues the pattern. In such problems, each position (first, second and third letter) often follows its own arithmetic rule. Simultaneously handling three separate sub series and ensuring that one option satisfies all of them tests a candidate's ability to manage multiple constraints in alphabet based reasoning.

Given Data / Assumptions:

• Terms in the series: XPK, VNJ, TLH, RJE, ?.• First letters: X, V, T, R, ?.• Second letters: P, N, L, J, ?.• Third letters: K, J, H, E, ?.• Alphabet positions: A=1, B=2, ..., Z=26, with cyclic movement if needed.

Concept / Approach:
We treat the first, second and third letters as three independent number series and look for patterns in their differences. In many three letter series, the first and second letters may decrease steadily, while the third letter may follow a separate sequence of increasing or decreasing steps. When the differences between successive letters form recognizable sequences, such as constant steps or step sizes that increase by one each time, we can extrapolate those sequences to find the next term.

Step-by-Step Solution:
Step 1: First letters: X, V, T, R.Positions: X=24, V=22, T=20, R=18.Step 2: Differences: 24 → 22: −2, 22 → 20: −2, 20 → 18: −2.Step 3: The first letters decrease by 2 each time, so the next first letter is 18 − 2 = 16, which is P.Step 4: Second letters: P, N, L, J.Positions: P=16, N=14, L=12, J=10.Step 5: Differences: 16 → 14: −2, 14 → 12: −2, 12 → 10: −2.Step 6: Thus the second letters also decrease by 2 each time, so the next second letter is 10 − 2 = 8, which is H.Step 7: Third letters: K, J, H, E.Positions: K=11, J=10, H=8, E=5.Step 8: Differences: 11 → 10: −1, 10 → 8: −2, 8 → 5: −3.Step 9: Here the negative step sizes increase in magnitude by 1 each time: −1, −2, −3. The next step should be −4.Step 10: Apply −4 to 5 (E): 5 − 4 = 1, which is A.Step 11: Therefore, the next term must be PHA.

Verification / Alternative check:
We can summarise the complete numeric pattern as follows: first letters 24, 22, 20, 18, 16 (all −2), second letters 16, 14, 12, 10, 8 (all −2), and third letters 11, 10, 8, 5, 1 (−1, −2, −3, −4). Substituting PHA into the series gives XPK, VNJ, TLH, RJE, PHA, which satisfies the decreasing by 2 pattern in the first two positions and the steadily increasing negative difference in the third position. No other option matches all three sub series at once.

Why Other Options Are Wrong:
PHB differs from PHA only in the last letter, but B corresponds to position 2, which would require a −3 step from 5, repeating the previous difference instead of moving to −4. OIA and OIB have different first and second letters and do not maintain the −2 decrement pattern across the first two columns. As a result, these options disrupt at least one of the three numeric sequences and cannot be accepted as the correct continuation of the series.

Common Pitfalls:
A typical mistake is to recognise the constant −2 pattern in the first two letters and then guess an option whose first two letters fit, without fully checking the third letter sequence. Another pitfall is to overlook that the third letter differences themselves are forming a separate series of −1, −2, −3, −4. The safest way to avoid such errors is always to convert all letters to numeric positions, compute differences carefully for each column and ensure that the chosen option satisfies every identified pattern without exception.

Final Answer:
PHA