Choose the missing term from the given alternatives that will correctly complete the letter series ejo, tyd, ins, xch, ?

Introduction / Context:

This is a non standard letter series where each term is a three letter group. The relationship from one group to the next is not immediately obvious, so the problem tests deeper pattern recognition in the positions of letters. Instead of a simple forward or backward shift, each position within the group follows its own rule. Such questions are useful for checking how well a candidate can track multiple patterns simultaneously across different positions in a letter block.

Given Data / Assumptions:

• The given series of three letter groups is ejo, tyd, ins, xch, ?.
• We must determine the next three letter group that continues all observed patterns.
• All letters are from the English alphabet and follow the usual A to Z order.
• Each of the three positions within the group may have its own independent sequence.

Concept / Approach:

The best approach is to treat each position first letter, second letter, and third letter as separate series. For each position, we convert letters to their numerical positions (A as 1, B as 2, and so on) and then inspect the pattern. Often such series feature alternating additions and subtractions by fixed numbers. Once we find a consistent rule for each of the three independent sequences, we can compute the next letter for every position and combine them to form the missing term.

Step-by-Step Solution:

Step 1: First letters: e, t, i, x correspond to 5, 20, 9, 24. Step 2: Observe differences: 5 to 20 is plus 15, 20 to 9 is minus 11, 9 to 24 is plus 15. So the pattern alternates between plus 15 and minus 11, so the next step should be 24 minus 11 = 13, which is m. Step 3: Second letters: j, y, n, c correspond to 10, 25, 14, 3. Here too the pattern alternates: plus 15, minus 11, plus 15, so the next should be 3 minus 11. Using the 26 letter cycle, 3 minus 11 gives 18 which is r. Step 4: Third letters: o, d, s, h correspond to 15, 4, 19, 8. Now the pattern is minus 11, plus 15, minus 11, so the next step is plus 15 from 8, yielding 23 which is w. Step 5: Combine the results from each position: first letter m, second letter r, third letter w, giving the group mrw.

Verification / Alternative check:

Write out the numerical positions clearly to verify. First position: 5, 20, 9, 24, 13 with pattern plus 15, minus 11, plus 15, minus 11. Second position: 10, 25, 14, 3, 18 with the same alternation. Third position: 15, 4, 19, 8, 23 also follows minus 11, plus 15, minus 11, plus 15. In each case, the rule is a consistent alternation of adding 15 and subtracting 11 in the 1 to 26 modular alphabet. The resulting group mrw therefore fits all three position wise rules perfectly.

Why Other Options Are Wrong:

Option nrw changes the first letter from m to n, breaking the strict plus 15, minus 11 cycle for the first position. Option nsx alters both the second and third letters, making the internal differences inconsistent with the earlier transitions. Option nsw again fails to match the exact required numerical shifts. Option mqw changes the second and third letters to q and w, which no longer respect the alternating plus 15 and minus 11 pattern. Only mrw preserves the required arithmetic behavior at every position.

Common Pitfalls:

Candidates often look for one single rule across whole groups, such as rotation or reversal, without decomposing the pattern by position. Another common mistake is to work only with letters, not converting them to numbers, which makes it harder to track consistent differences like plus 15 or minus 11. Some learners also apply the wrong modulo logic when subtracting, forgetting that after going below A you should wrap around to the end of the alphabet. Careful numerical treatment of each position avoids these errors.

Final Answer:

The three letter group that correctly continues the alternating positional pattern is mrw.