Single perfect square amidst non-squares — pick the odd one out Sequence: 190, 166, 145, 128, 112, 100, 91. Which number is different?

Introduction / Context:
Sometimes the quickest way to isolate an odd term is to check for well-known special classes of numbers (like perfect squares). If only one number belongs to such a class, it is the outlier regardless of the surrounding differences pattern.

Given Data / Assumptions:

• Candidates: 190, 166, 145, 128, 112, 100, 91.
• Check: is any one a perfect square?

Concept / Approach:
Test each term: a perfect square is of the form n^2 for some integer n. Among two-digit or three-digit values, 100 (= 10^2) is an immediate standout. The rest are not perfect squares (no integer √n).

Step-by-Step Solution:
100 = 10^2 ⇒ perfect square.190, 166, 145, 128, 112, 91: none equals m^2 for an integer m. √190 ≈ 13.78, √166 ≈ 12.88, √145 ≈ 12.04, √128 ≈ 11.31, √112 ≈ 10.58, √91 ≈ 9.54, all non-integers.Therefore, 100 uniquely belongs to the “perfect square” category.

Verification / Alternative check:
Even if you attempt to fit a decreasing-difference rule, you will not find a compelling uniform pattern that singles out any term other than 100 by a fundamental property. The square-status criterion is decisive.

Why Other Options Are Wrong:
166, 145, 128, and 112 are not perfect squares and thus share the majority status with 190 and 91; they are not the odd ones out.

Common Pitfalls:
Overcomplicating the pattern hunt and missing simple number classes. Always scan for perfect squares, cubes, or triangular numbers as a first pass.

Final Answer:
100