Insert the missing number in 5760, 960, ?, 48, 16, 8 — observe a systematic division pattern from term to term.
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A120
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B160
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C192
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D240
Answer
Correct Answer: 192
Explanation
Introduction / Context:This is a division-based series. Many such puzzles progressively divide by descending integers or a clear sequence of divisors. Identifying the divisor sequence reveals the missing value.
Given Data / Assumptions:
- Known terms: 5760 → 960 → ? → 48 → 16 → 8.
- We assume each step uses a consistent divisor pattern that fits all transitions.
Concept / Approach:Check divisions between adjacent known terms to infer the divisor sequence. Apply the same divisors to fill in the blank term.
Step-by-Step Solution:
5760 ÷ 6 = 960 (fits the first step).If we continue dividing by descending integers: ÷5, ÷4, ÷3, ÷2.Unknown term = 960 ÷ 5 = 192.Check forward: 192 ÷ 4 = 48; 48 ÷ 3 = 16; 16 ÷ 2 = 8. All transitions match perfectly.Verification / Alternative check:Any other divisor sequence would break at least one of the later divisions. The chain ÷6, ÷5, ÷4, ÷3, ÷2 is uniquely consistent.
Why Other Options Are Wrong:
- 120, 160, 240 do not preserve the required later divisions to 48, 16, and 8 when back-checked.
Common Pitfalls:Trying alternating multiplication/division when a simple descending division sequence fits all known links neatly.
Final Answer:192