Difficulty: Medium
Correct Answer: N,C
Explanation:
Introduction / Context:
This question is a typical alphabet series problem where two interleaved sequences run together. You are given the series Z, S, W, O, T, K, Q, G, ?, ? and asked to find the missing pair of letters. Such questions test your ability to separate overlapping patterns, understand alphabetical positions, and work with constant differences inside the English alphabet. Handling interleaved sequences is important for many competitive exams because it checks both observation and systematic reasoning.
Given Data / Assumptions:
Concept / Approach:
The key idea is to split the mixed sequence into two separate sub series: one formed by letters in odd positions and the other by letters in even positions. Many exam questions hide two simple arithmetic progressions inside one combined list. Once we identify the rule for each subsequence using alphabet positions, we can extend each sequence independently to find the ninth and tenth terms. Finally, we join these two results as an ordered pair that replaces the question marks.
Step-by-Step Solution:
Step 1: Write the series with positions: 1 Z, 2 S, 3 W, 4 O, 5 T, 6 K, 7 Q, 8 G, 9 ?, 10 ?.
Step 2: Extract the odd position letters: 1 Z, 3 W, 5 T, 7 Q, 9 ?.
Step 3: Convert these to numbers: Z 26, W 23, T 20, Q 17. The differences are minus 3 each time (26 to 23 to 20 to 17).
Step 4: Continue the pattern one more step: 17 minus 3 equals 14, which corresponds to N. So the 9th term is N.
Step 5: Now extract the even position letters: 2 S, 4 O, 6 K, 8 G, 10 ?.
Step 6: Convert these to numbers: S 19, O 15, K 11, G 7. The difference each time is minus 4 (19 to 15 to 11 to 7).
Step 7: Continue the pattern by subtracting 4 once more: 7 minus 4 equals 3, which is C. So the 10th term is C.
Step 8: Therefore, the pair of missing letters is N at position 9 and C at position 10, written together as N,C.
Verification / Alternative check:
We can quickly re list both subsequences with the newly found terms. Odd positions: Z 26, W 23, T 20, Q 17, N 14 form a clean series decreasing by 3. Even positions: S 19, O 15, K 11, G 7, C 3 form a clean series decreasing by 4. No contradictions appear, and the adjusted full series Z, S, W, O, T, K, Q, G, N, C is now fully determined by simple arithmetic rules on alphabet positions.
Why Other Options Are Wrong:
Pairs like N,D or O,D would break the even position pattern because D has position 4, which does not fit the minus 4 sequence 19, 15, 11, 7, 3. Options that start with O do not respect the minus 3 pattern in the odd positions, because after Q at 17 the next odd position cannot jump back up to O at 15. Only N,C preserves both sequences.
Common Pitfalls:
A common mistake is to search for a single pattern across all ten terms, rather than separating odd and even positions. Another pitfall is working directly with letters without converting them to their numeric positions, which makes the constant differences harder to see. Some candidates also guess based on visual closeness (for example, choosing letters near Q and G) without actually checking the arithmetic differences.
Final Answer:
The missing letters are N,C, so the completed series is Z, S, W, O, T, K, Q, G, N, C.
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