In the alphabet series CMW, HRB, ?, RBL, WGQ, BLV, choose the missing three letter group that continues the pattern.

Difficulty: Medium

Correct Answer: MWG

Explanation:


Introduction / Context:
This is an alphabetic series involving three letter groups. Each letter position appears to follow its own pattern. The key idea is to observe how each group changes from one step to the next and to deduce the transformation rule that applies to all three letters simultaneously.


Given Data / Assumptions:

  • Series: CMW, HRB, ?, RBL, WGQ, BLV.
  • Each group consists of three letters.
  • The missing group must fit a consistent transformation observed between neighbouring groups.


Concept / Approach:
An efficient approach is to treat each three letter group as a vector of letter positions. We then compare consecutive groups to see how each letter is shifted inside the alphabet. If the same positional shift is applied to all three letters, we can extend that rule to find the unknown group.


Step-by-Step Solution:
Step 1: Convert CMW and HRB into positions: C=3, M=13, W=23 and H=8, R=18, B=2.Step 2: Compute shifts from the first to the second group: 3 to 8 is +5, 13 to 18 is +5, 23 to 2 is +5 modulo 26.Step 3: Therefore, the transformation rule from one group to the next is adding 5 positions to each letter in the alphabet, wrapping around after Z.Step 4: Apply this rule to HRB to get the missing third group: H(8)+5=13 (M), R(18)+5=23 (W), B(2)+5=7 (G). So the missing group is MWG.Step 5: Verify the rule forward: MWG plus 5 gives RBL, and RBL plus 5 gives WGQ, and WGQ plus 5 gives BLV, all matching the given series.


Verification / Alternative check:
Writing out the full chain with the +5 rule shows no contradictions: CMW → HRB → MWG → RBL → WGQ → BLV. Every step obeys the same shift, so the pattern is highly consistent. Any group that does not arise from repeated +5 shifts is incompatible with the series.


Why Other Options Are Wrong:
Groups such as WMX, LVF, LWG or NVH do not produce a constant +5 progression between all neighbouring terms. When we attempt to apply a single uniform shift to or from these options, we quickly find that at least one letter breaks the pattern, so they cannot represent the missing group.


Common Pitfalls:
Some learners try to assign different rules to each letter position, which complicates the series unnecessarily. In many exam questions, a single constant shift is applied to all letters. Recognising modular arithmetic on letters is an important skill for these series.


Final Answer:
The three letter group that correctly completes the sequence is MWG.

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