Find the next two numbers that continue the alternating pattern. Sequence: 8, 12, 9, 13, 10, 14, 11, ____ , ____
Verbal Reasoning
Number Series
Difficulty: Easy
Choose an option
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A14 11
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B15 12
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C8 15
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D15 19
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E8 5
Answer
Correct Answer: 15 12
Explanation
Introduction / Context:Here two simple progressions are interleaved: one affects odd-position terms and the other affects even-position terms. Recognizing the interleave is the key step.
Given Data / Assumptions:
- Series: 8, 12, 9, 13, 10, 14, 11, …
- We must supply the next two terms.
Concept / Approach:Separate the series into odd and even indices; examine each subsequence independently.
Step-by-Step Solution:
Odd positions: 1st=8, 3rd=9, 5th=10, 7th=11 → increases by +1.Even positions: 2nd=12, 4th=13, 6th=14 → increases by +1.After the 7th term (11, odd), the 8th term is the next even subsequence value: 14 + 1 = 15.The 9th term resumes the odd subsequence: 11 + 1 = 12.Verification / Alternative check:Write the two subsequences explicitly: odd = 8, 9, 10, 11, 12, … and even = 12, 13, 14, 15, … Interleaving them gives …, 11, 15, 12 which matches the derived pair.
Why Other Options Are Wrong:
- 14 11: Reverses the order and repeats existing values.
- 8 15 / 8 5: Return to earlier numbers breaks monotonic +1 growth.
- 15 19: Even term 15 is fine, but 19 ignores the +1 odd-step.
Common Pitfalls:Continuing only one subsequence or mixing their orders. Always track position (odd/even) before extending.
Final Answer:15 12