In this aptitude number classification question, find the odd number out from the series: 120, 36, 6, 2, 1, 1.

Introduction / Context:
This question is a classic example of an odd man out problem in number series. You are given the numbers 120, 36, 6, 2, 1 and 1 and asked to identify which one does not belong to the group. Instead of looking for a stepwise pattern, this problem is best solved by checking which numbers are factors of a particular term in the list.

Given Data / Assumptions:

• Numbers: 120, 36, 6, 2, 1, 1.
• 120 is the largest number in the list.
• We look for a simple factor or divisor relationship among the smaller numbers and 120.
• Exactly one number should fail to match the common property.

Concept / Approach:
When one number in a set is significantly larger than the others, it is often useful to treat it as a base and check whether the remaining numbers are its exact divisors. If all but one are divisors of that large number, then the non-divisor is the odd one out. Divisibility can be checked by straightforward division without leaving any remainder.

Step-by-Step Solution:
Step 1: Test whether 6 is a factor of 120.120 / 6 = 20, so 6 is a divisor of 120.Step 2: Test whether 2 is a factor of 120.120 / 2 = 60, so 2 is a divisor of 120.Step 3: Test whether 1 is a factor of 120.120 / 1 = 120, so 1 is always a divisor of any integer.Step 4: Test whether 36 is a factor of 120.120 / 36 does not give an integer (36 * 3 = 108, 36 * 4 = 144), so 36 is not a divisor of 120.Step 5: Summarize the observation.All numbers in the list except 36 are exact divisors of 120. Therefore 36 is the odd one out.

Verification / Alternative check:
We can also list the common factors of 120 near the given values. 120 has factors 1, 2, 3, 4, 5, 6, 8, 10, 12, 15 and so on. Both 2 and 6 clearly appear in this list, and 1 appears as well. However, 36 does not feature among the factors of 120. This confirms that 36 is structurally different from the other smaller numbers in the series, which are all true factors of 120.

Why Other Options Are Wrong:
120: Although it is the largest number, it serves as the base whose factors appear in the list, so it is consistent with the intended structure of the question.
6: A proper divisor of 120, so it fits the pattern of being exactly divisible into 120.
2: Also a proper divisor of 120, so it belongs to the same group of numbers related to 120 through divisibility.

Common Pitfalls:
Many learners initially look for a stepwise numerical pattern from 120 to 36 to 6 and so on, and get confused by irregular ratios or differences. The key trick here is to notice that several numbers are much smaller and can be natural divisors of 120. Once you shift perspective from progression to factorization, the odd one out becomes easy to identify.

Final Answer:
The odd number out in the series is 36, because it is the only number that is not an exact divisor of 120.