In the sequence 10, 25, 45, 54, 60, 75, 85, which number is the odd one out based on divisibility by 5?

Introduction / Context:
This odd-man-out question uses a very simple divisibility property. You are given a list of numbers and asked to identify which one does not share the same divisibility feature as the others. Such questions help you quickly recall and apply basic divisibility rules, which are extremely useful in mental arithmetic and aptitude tests.

Given Data / Assumptions:
The numbers given are 10, 25, 45, 54, 60 and 85. We assume that the intended property is a standard one taught in school, such as divisibility by 5, 10 or some other small integer. Our task is to find which number fails to meet that common property.

Concept / Approach:
A very common and easy-to-spot rule is divisibility by 5. A number is divisible by 5 if and only if its last digit is 0 or 5. Looking at the list, almost all numbers end with 0 or 5, which strongly suggests that divisibility by 5 is the relevant property here. The number that does not share this property will be the odd one out.

Step-by-Step Solution:
Step 1: Examine the last digit of each number.10 ends with 0 → divisible by 5.25 ends with 5 → divisible by 5.45 ends with 5 → divisible by 5.54 ends with 4 → not divisible by 5.60 ends with 0 → divisible by 5.85 ends with 5 → divisible by 5.Step 2: Observe that every number except 54 ends in 0 or 5 and is divisible by 5.Step 3: 54, ending with 4, does not satisfy the divisibility rule for 5 and so is the odd one out.

Verification / Alternative check:
We can quickly confirm by performing the division 54 / 5, which gives 10.8, not an integer. For all other numbers, division by 5 yields an integer result: 10 / 5 = 2, 25 / 5 = 5, 45 / 5 = 9, 60 / 5 = 12, and 85 / 5 = 17. Therefore, 54 alone is not divisible by 5, which confirms it as the outlier.

Why Other Options Are Wrong:
10, 45 and 85, as well as 25 and 60, clearly share the property of being multiples of 5. Removing any of them as the odd one out would leave a set where the remaining numbers still share the divisibility-by-5 property and 54 still does not, which would be inconsistent. So they cannot be the correct answer.

Common Pitfalls:
Some candidates may overthink the question and look for more complex relationships involving prime factors or sequences, overlooking the very simple and obvious rule. In many exam questions, the simplest shared property is the intended one, especially when last digits are clearly suggestive as in this case.

Final Answer:
The only number that is not divisible by 5 is 54, so it is the odd one out.