Difficulty: Medium
Correct Answer: N,C
Explanation:
Introduction / Context:
The given problem presents an alphabet series with two missing terms: Z, S, W, O, T, K, Q, G, ?, ?. Many such series are actually combinations of two simpler subsequences interleaved together. Our goal is to separate the sequence into sub series, detect their individual patterns, and then combine the results to find the missing letters.
Given Data / Assumptions:
Concept / Approach:
We separate the series into letters at odd positions and letters at even positions. Many reasoning questions use this approach, where each subsequence follows an independent pattern of fixed backward or forward jumps in the alphabet. Once each subsequence is recognised, the missing letters can be filled in easily.
Step-by-Step Solution:
1. Label the positions:
1: Z, 2: S, 3: W, 4: O, 5: T, 6: K, 7: Q, 8: G, 9: ?, 10: ?
2. Take letters at odd positions: 1, 3, 5, 7, 9.
Odd position subsequence: Z, W, T, Q, ?
3. Convert to positions: Z(26), W(23), T(20), Q(17).
4. Differences: 26 to 23 is -3, 23 to 20 is -3, 20 to 17 is -3.
5. The pattern is clear: each step moves 3 letters backward.
6. So the next odd term is 17 - 3 = 14 which is N. Hence the 9th term must be N.
7. Now take letters at even positions: 2, 4, 6, 8, 10.
Even position subsequence: S, O, K, G, ?
8. Convert these to positions: S(19), O(15), K(11), G(7).
9. Differences: 19 to 15 is -4, 15 to 11 is -4, 11 to 7 is -4.
10. So this subsequence moves 4 letters backward at each step.
11. The next even term is 7 - 4 = 3 which is C. Thus the 10th term must be C.
12. Combining both results, the missing letters are N and C, in that order.
Verification / Alternative check:
Write out the full completed series:
Z, S, W, O, T, K, Q, G, N, C.
Odd positions: Z, W, T, Q, N are 26, 23, 20, 17, 14 (each step minus 3).
Even positions: S, O, K, G, C are 19, 15, 11, 7, 3 (each step minus 4).
Both subsequences are perfectly consistent, confirming that N, C is correct.
Why Other Options Are Wrong:
Common Pitfalls:
Many students look at all terms together and try to find a linear pattern, which is very difficult here. The key is to notice that the sequence alternates between two independent patterns. Forgetting to separate odd and even positions often leads to confusion and random guessing. Always try to split letter series into subsequences when obvious single track rules do not appear.
Final Answer:
The pair of letters that correctly completes the series is N, C.
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