Difficulty: Easy
Correct Answer: EQV
Explanation:
Introduction / Context:
This question is based on an alphabetical series where each term is a group of three letters. You must observe how each letter in a particular position moves from one term to the next. The correct answer is the group that continues the established pattern after CMP in the sequence WAX, YED, AIJ, CMP, ?.
Given Data / Assumptions:
Concept / Approach:
We examine each position (first, second and third letters) independently across the terms. For each position, we convert letters to their numerical positions and look for consistent arithmetic changes. If each position follows its own clear rule, we can apply those rules to generate the next term and compare with the options.
Step-by-Step Solution:
Step 1: First letters of the terms: W, Y, A, C.
Convert to numbers: W = 23, Y = 25, A = 1, C = 3.
From 23 to 25 is +2, from 25 to 1 (via wrap-around) is +2 (since 25 + 2 = 27, 27 - 26 = 1), and from 1 to 3 is +2. So the first letters are increasing by +2 each time in a circular alphabet.
Step 2: The next first letter after C (3) is 3 + 2 = 5, which is E.
Step 3: Second letters: A, E, I, M.
Convert to numbers: A = 1, E = 5, I = 9, M = 13.
Differences are +4, +4 and +4. So the second letters increase by +4.
Step 4: The next second letter after M (13) is 13 + 4 = 17, which is Q.
Step 5: Third letters: X, D, J, P.
Convert to numbers: X = 24, D = 4, J = 10, P = 16.
To move from 24 to 4, we add 6 with wrap-around: 24 + 6 = 30, 30 - 26 = 4. From 4 to 10 is +6, and from 10 to 16 is also +6. So the rule here is +6.
Step 6: The next third letter after P (16) is 16 + 6 = 22, which is V.
Step 7: Combine the next first, second and third letters: E (first), Q (second), V (third). The missing term is EQV.
Verification / Alternative check:
Write all five terms with numeric positions:
WAX (23, 1, 24), YED (25, 5, 4), AIJ (1, 9, 10), CMP (3, 13, 16), EQV (5, 17, 22). In each column, the numbers follow +2, +2, +2 for the first position, +4, +4, +4 for the second position and +6, +6, +6 for the third position. Thus EQV clearly maintains the pattern.
Why Other Options Are Wrong:
Option A (ERU): The second letter R (18) does not match the required +4 step from M (13), which should be Q (17).
Option C (DQV): The first letter D (4) breaks the +2 sequence from C (3) which should move to E (5).
Option D (DRU): Both the first and second letters ignore the established +2 and +4 rules respectively, so this group does not fit the pattern.
Common Pitfalls:
Many test-takers look only at one or two letters and guess without confirming the full pattern. Others forget to handle wrap-around from Z back to A correctly. To avoid mistakes, always convert letters to numbers, apply the arithmetic changes systematically to each position and then convert back to letters only after you are sure of the pattern.
Final Answer:
The group of letters that correctly completes the series is EQV, which corresponds to option B.
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