Choose the odd number out: 10, 25, 45, 54, 60, 75, 80.

Introduction / Context:
In many odd-one-out sets, divisibility by a common factor distinguishes most elements from a single exception. Here, observe multiples of 5 versus a number that is not a multiple of 5.

Given Data / Assumptions:

• Multiples of 5 among the terms: 10, 25, 45, 60, 75, 80
• 54 is not a multiple of 5

Concept / Approach:
Apply the divisibility rule for 5: numbers ending with 0 or 5 are multiples of 5. Scan each term’s last digit to classify quickly.

Step-by-Step Solution:
10 → ends with 0 ⇒ multiple of 525/45/60/75/80 → end with 5 or 0 ⇒ multiples of 554 → ends with 4 ⇒ not a multiple of 5 ⇒ odd element

Verification / Alternative check:
Compute remainders modulo 5: 54 mod 5 = 4, while the others give remainder 0.

Why Other Options Are Wrong:
10/45/75 are clear multiples of 5, hence part of the majority set.

Common Pitfalls:
Overthinking with primes or digit sums; the simplest divisibility cue (last digit) is sufficient here.

Final Answer:
54