Number series (cyclic adjustments: +10, then +a, then −a+10 with a reducing by 8) Sequence: 16 26 56 36 46 68 56 … Choose the next two numbers that fit the evolving increment cycle.
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A80 66
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B64 82
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C66 80
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D78 68
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E66 82
Answer
Correct Answer: 66 80
Explanation
Introduction / Context:Not all series are simple arithmetic or geometric progressions. Some use a repeating three-step cycle with changing magnitudes. Recognizing the higher-level cycle and how its parameters evolve is essential.
Given Data / Assumptions:
- Sequence: 16, 26, 56, 36, 46, 68, 56, …
- Observed increments: +10, +30, −20, +10, +22, −12, …
Concept / Approach:Group the changes into triplets. The pattern is: add 10, then add a, then subtract (a − 10). The parameter a decreases by 8 each cycle: first a = 30, next a = 22, next a = 14, and so on.
Step-by-Step Solution:
Start 16 → +10 = 26.26 → +30 = 56.56 → −20 (which is 30 − 10) = 36.36 → +10 = 46.46 → +22 (a decreased by 8) = 68.68 → −12 (22 − 10) = 56.Next cycle: +10 → 56 + 10 = 66; then +a with a reduced by another 8 → a = 14, so 66 + 14 = 80.Verification / Alternative check:Continuing would give the third step of this cycle as −4 (14 − 10), validating the evolving pattern.
Why Other Options Are Wrong:
- 80 66 / 64 82 / 78 68 / 66 82: They break the established three-step cycle or use incorrect values for the evolving parameter a.
Common Pitfalls:Assuming a single fixed difference or ratio without examining the sequence of increments themselves.
Final Answer:66 80