Difficulty: Medium
Correct Answer: EFH
Explanation:
Introduction / Context:
This problem deals with a three letter alphabet series: MNP, STV, YZB, and a missing term. We must find the group of letters that continues the sequence logically. The puzzle tests understanding of fixed step increments and wrap around behaviour in the alphabet, concepts that are frequently examined in aptitude and reasoning sections of competitive exams.
Given Data / Assumptions:
Concept / Approach:
The main idea is to map each letter to its numeric position and then examine how these numbers change from term to term for each of the three positions. By identifying a fixed step size that repeats, we can extend the pattern to find the next term. Since the sequence includes letters close to the end of the alphabet, we must also carefully handle wrap around when positions exceed 26.
Step-by-Step Solution:
Step 1: Convert MNP to numbers: M(13), N(14), P(16).Step 2: Convert STV: S(19), T(20), V(22).Step 3: Convert YZB: Y(25), Z(26), B(2).Step 4: Observe the first letters: 13 (M), 19 (S), 25 (Y). Each transition adds 6: 13 + 6 = 19 and 19 + 6 = 25.Step 5: To find the next first letter, add 6 to 25: 25 + 6 = 31. Since the alphabet has 26 letters, subtract 26 to wrap around, giving 31 - 26 = 5, which corresponds to E.Step 6: Observe the second letters: 14 (N), 20 (T), 26 (Z). Here also the step is +6 each time.Step 7: Add 6 to 26: 26 + 6 = 32, and after wrap around 32 - 26 = 6, corresponding to F.Step 8: Observe the third letters: 16 (P), 22 (V), 2 (B). The step is again +6 modulo 26.Step 9: Add 6 to 2 to get 8, which is the letter H.Step 10: Combining these results, the next term is EFH.
Verification / Alternative check:
Checking the full pattern, we have first letters M(13), S(19), Y(25), E(5); second letters N(14), T(20), Z(26), F(6); and third letters P(16), V(22), B(2), H(8). In each case the step from one term to the next is +6 modulo 26. Among the options, only EFH fits this pattern exactly, confirming it as the right answer.
Why Other Options Are Wrong:
GHJ, JKM, and CDB do not follow the +6 step for all three positions when placed after YZB. They would require inconsistent or incorrect increments in at least one position and therefore break the pattern. Hence they must be rejected in favour of EFH.
Common Pitfalls:
Candidates sometimes ignore wrap around and treat Y to E as a random change, or they focus only on one of the three letters. Others may miscalculate numeric values near the end of the alphabet. Using modular arithmetic logic, where positions greater than 26 wrap back to the beginning, avoids these mistakes.
Final Answer:
The missing group that correctly completes the series is EFH.
Discussion & Comments