Difficulty: Medium
Correct Answer: 165
Explanation:
Introduction / Context:Another common construction uses increments equal to consecutive prime numbers. If a final step uses the wrong increment, that last term becomes the odd one out.
Given Data / Assumptions:
Concept / Approach:Compute consecutive differences and map them to the prime list. Any mismatch will surface immediately.
Step-by-Step Solution:
127 − 125 = +2 (prime)130 − 127 = +3 (prime)135 − 130 = +5 (prime)142 − 135 = +7 (prime)153 − 142 = +11 (prime)165 − 153 = +12 (should be +13 next)Therefore, the correct last term should be 153 + 13 = 166. The given 165 is off by −1 and is the outlier.Verification / Alternative check:
Replacing 165 with 166 yields perfect prime increments: +2, +3, +5, +7, +11, +13.Why Other Options Are Wrong:
130, 142, 153 all fit prime-step increments; they are consistent with the intended rule.Common Pitfalls:
Confusing near-prime increments (like +12) with the actual next prime +13.Final Answer:165
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