Odd-man-out in a near-square-difference series: Identify the term that does not fit: 16, 19, 21, 30, 46, 71, 107

Introduction / Context:The target series appears to add consecutive square numbers starting from 3^2 onward after an initial irregularity. Spotting the consistent square increments reveals which entry breaks the rule.

Given Data / Assumptions:

• Series: 16, 19, 21, 30, 46, 71, 107
• Observed differences: +3, +2, +9, +16, +25, +36

Concept / Approach:From 21 onward the differences are perfect squares in order: 9(=3^2), 16(=4^2), 25(=5^2), 36(=6^2). To be consistent, the increments before 21 should have been 1, 4 rather than 3, 2.

Step-by-Step Solution:If the pattern is +1, +4, +9, +16, +25, +36, then:16 + 1 = 17 (should replace 19)17 + 4 = 2121 + 9 = 30, then +16, +25, +36 yield 46, 71, 107

Verification / Alternative check:Replacing 19 with 17 fixes the entire sequence into consecutive square jumps.

Why Other Options Are Wrong:30 and 46 comply with +9 and +16; 20 is not even in the list.

Common Pitfalls:Forgetting that odd-man-out questions ask for the inconsistent existing term, not the corrected term.

Final Answer:19