Odd One Out — Among 29, 53, 85, and 125, choose the number that does not share the common number-theory property with the others (consider prime vs composite vs perfect power).

Introduction / Context:This odd-one-out item checks your ability to compare number-theory properties such as primality, compositeness, and whether a value is a perfect power (like a square or a cube). The goal is to identify the single number that belongs to a distinctly different class from the rest.

Given Data / Assumptions:

• Numbers given: 29, 53, 85, 125.
• Standard definitions: prime numbers have exactly two positive divisors; composites have more than two; a perfect power such as a perfect cube has the form n^3.

Concept / Approach:The most discriminative checks here are: (1) prime vs composite, and (2) perfect power status.

Step-by-Step Solution:Check 29: 29 is prime.Check 53: 53 is prime.Check 85: 85 = 5 * 17, so composite but not a perfect square or cube.Check 125: 125 = 5^3, a perfect cube and therefore a special perfect power.Observation: Only one number is a perfect cube (125). The others are not perfect powers.

Verification / Alternative check:Even if you group by prime vs composite, you get two primes (29, 53) and two composites (85, 125). The cube test uniquely isolates 125.

Why Other Options Are Wrong:

• 29: Prime, not a perfect cube.
• 53: Prime, not a perfect cube.
• 85: Composite, but not a perfect power.

Common Pitfalls:Learners often stop at prime vs composite and miss the stronger discriminator: perfect power.

Final Answer:125