The numbers 75, 85, 95 and 115 follow a particular numeric pattern. Three of these numbers are alike in a specific way and form a group. Which one of the four numbers does not belong to that group?

Introduction / Context:
This logical reasoning question involves classification of numbers based on a hidden pattern. Such questions often appear in aptitude tests to check your comfort with number sequences and your ability to spot relationships among numbers quickly. Your task is to find which number among 75, 85, 95 and 115 does not fit a simple, consistent rule that connects the other three numbers.

Given Data / Assumptions:
The numbers provided are 75, 85, 95 and 115.
All four numbers are positive, two-digit or three-digit integers and multiples of 5.
Exactly three of these numbers should form a group based on a single clear numeric relation, and one number must be the odd one out.
We assume that the intended pattern is simple and exam friendly, such as an arithmetic progression or another basic relationship.

Concept / Approach:
When dealing with number-classification questions, you should first check for basic patterns such as divisibility, arithmetic progression, geometric progression, or special properties like perfect squares or cubes. Since all four numbers are multiples of 5, divisibility alone will not separate them. A quick and powerful check is to see whether three of the four numbers lie in a regular sequence, leaving one that breaks the pattern.

Step-by-Step Solution:
Step 1: Arrange the numbers in ascending order: 75, 85, 95, 115. Step 2: Check the differences between consecutive numbers: 85 - 75 = 10, 95 - 85 = 10, 115 - 95 = 20. Step 3: Try forming an arithmetic progression from three numbers. Consider 75, 95 and 115. Step 4: Compute the differences in this subset: 95 - 75 = 20 and 115 - 95 = 20, so 75, 95 and 115 form an arithmetic progression with common difference 20. Step 5: Check whether 85 fits into this arithmetic progression. If we extend the sequence backwards or forwards using the same difference 20, we get 55, 75, 95, 115, 135 and so on. There is no place where 85 appears in this sequence. Step 6: Therefore, 75, 95 and 115 follow one simple rule – they are equally spaced by 20 – while 85 breaks this pattern.

Verification / Alternative check:
Another way to verify is to examine positions in the sequence starting at 75 with step 20. We can write the sequence as 75, 95, 115, 135 and so on. Each term is 75 plus a multiple of 20. Substituting 85 into the expression 75 + 20k, we would get 85 minus 75 equal to 10, which is not a multiple of 20. Hence 85 cannot be part of this particular arithmetic progression, confirming that it is the odd number out.

Why Other Options Are Wrong:
75: It is the first term of the arithmetic progression 75, 95, 115, so it is part of the main group.
95: This is the second term in the same progression and fits the pattern perfectly.
115: This is the third term of the progression with common difference 20, so it clearly belongs to the group.

Common Pitfalls:
Many candidates get distracted by the fact that all numbers are multiples of 5 or look at divisibility by 3, 4 or 9. While these checks are sometimes useful, here they do not give a clean split where exactly three numbers share the property. Always check for simple sequences like equal differences or equal ratios, because exam setters frequently use arithmetic progressions in such questions.

Final Answer:
The only number that does not lie on the arithmetic progression with common difference 20 is 85.