Odd One Out — In 1:4, 10:24, 8:18, 22:46, three follow the rule “second = 2*first + 2”. Find the exception.

Introduction / Context:Linear mappings of the form y = m*x + c are common in pair-classification problems. We identify the lone pair that fails the dominant mapping.

Given Data / Assumptions:

• Pairs: 1:4, 10:24, 8:18, 22:46 (interpreted as (x, y)).
• Candidate rule observed from three items: y = 2*x + 2.

Concept / Approach:Test each pair against y = 2*x + 2 and isolate the pair that violates it.

Step-by-Step Solution:For 1:4 — 2*1 + 2 = 4 ✓For 8:18 — 2*8 + 2 = 18 ✓For 22:46 — 2*22 + 2 = 46 ✓For 10:24 — 2*10 + 2 = 22 ≠ 24 ✗Hence, 10:24 is the exception.

Verification / Alternative check:Attempting y = 2*x + c with a single c for all pairs yields c = 2 for three items; no single c satisfies 10:24 simultaneously.

Why Other Options Are Wrong:

• 1:4 — satisfies y = 2*x + 2.
• 8:18 — satisfies y = 2*x + 2.
• 22:46 — satisfies y = 2*x + 2.

Common Pitfalls:Assuming proportion (y = k*x) and missing the additive constant; always test both multiplicative and affine forms.

Final Answer:10 : 24