Difficulty: Medium
Correct Answer: 11 5
Explanation:
Introduction / Context:This sequence mixes a small constant decrement with two alternating adjustments whose magnitudes reduce in a steady pattern. We must project the rule two more steps to find the next pair.
Given Data / Assumptions:
Concept / Approach:
Notice a repeating three-step motif: subtract 3, subtract a larger value, then add a value. The larger subtraction and the addition each decrease by 7 on successive cycles.
Step-by-Step Solution:
Cycle 1: 28 → 25 (−3), 25 → 5 (−20), 5 → 21 (+16)Cycle 2: 21 → 18 (−3), 18 → 5 (−13), 5 → 14 (+9)Next cycle decrements: −3, then −6 (since 20 → 13 → 6 decreases by 7), then +2 (since 16 → 9 → 2 also decreases by 7).Apply −3 to 14: 14 − 3 = 11.Apply −6 next: 11 − 6 = 5.Verification / Alternative check:
Projecting further with +2 would give 7, consistent with the established 16 → 9 → 2 trend in the additive leg.
Why Other Options Are Wrong:
10 7, 11 8, 5 10, 10 5 do not align with the strictly “−3, then (−7 less than previous large subtraction), then (+7 less than previous addition)” pattern.
Common Pitfalls:
Assuming a single arithmetic progression or alternating parity sequences fails because the sequence uses a three-step cyclic difference pattern.
Final Answer:
11 5
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