Number Series — Find the Wrong Term (Descending Differences as Multiples of 11) Identify the incorrect number: 325, 259, 202, 160, 127, 105, 94.
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A94
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B127
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C202
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D259
Answer
Correct Answer: 202
Explanation
Introduction / Context:Many wrong-number questions rely on successive differences forming a clean pattern. Here, the cleanest structure is differences descending by 11 each step, a hallmark of exam puzzle design.
Given Data / Assumptions:
- Sequence: 325, 259, 202, 160, 127, 105, 94
- Exactly one number is wrong.
- Test first differences for a tidy progression (e.g., equal steps or steps reducing by a fixed amount).
Concept / Approach:Compute consecutive differences and look for a simple descending pattern, especially multiples of a constant such as 11.
Step-by-Step Solution:325 → 259 = −66259 → 202 = −57 (suspect)202 → 160 = −42160 → 127 = −33127 → 105 = −22105 → 94 = −11All differences except −57 are multiples of 11: −66, −42, −33, −22, −11.If we replace 202 with 204, the differences become −66, −55, −44, −33, −22, −11, which is a perfect arithmetic ladder descending by 11 each time.
Verification / Alternative check:Only the transition 259 → 202 breaks the “descending multiples of 11” rule. Adjusting that term to 204 aligns the entire sequence; therefore, 202 is the wrong entry.
Why Other Options Are Wrong:
- 259, 127, 94: These participate correctly in the neat −66, −44, −22, −11 cadence (once the erroneous 202 is fixed) and are not incorrect.
Common Pitfalls:Stopping after one irregular step without testing whether a single correction yields a perfectly consistent pattern across all differences.
Final Answer:202