Odd Man Out – Verify the “add perfect squares” motif: 1, 5, 14, 30, 50, 55, 91

Introduction / Context:
Here the natural hypothesis is “add consecutive square numbers.” This is common in reasoning tests. We test each jump to see whether it equals 2^2, 3^2, 4^2, 5^2, 6^2, … The single break identifies the odd term.

Given Data / Assumptions:

• Series: 1, 5, 14, 30, 50, 55, 91
• Target differences: 4, 9, 16, 25, 36, …

Concept / Approach:
Compute differences: 1→5 (+4=2^2); 5→14 (+9=3^2); 14→30 (+16=4^2); next should be +25 to reach 55. Hence 30→55 is correct with +25, but 50 is not on this path, revealing it as the odd term.

Step-by-Step Solution:
1 + 4 = 5 ✔5 + 9 = 14 ✔14 + 16 = 30 ✔Expected next: 30 + 25 = 55 (not 50) ✖Continuing: 55 + 36 = 91 ✔

Verification / Alternative check:
Replacing 50 with 55 preserves the “add squares of 2,3,4,5,6” chain perfectly.

Why Other Options Are Wrong:
5, 55, 91, and 14 all sit exactly where adding perfect squares dictates.

Common Pitfalls:
Missing that 55 appears later, correctly placed, and thinking it duplicates 50’s role; actually 50 is the anomaly.

Final Answer:
50