Three of the following four numbers share a similar property and form a group. Which number does not belong to this group?

Introduction / Context:
This is a numerical classification question. You are given several numbers and must select the one that does not share a common property possessed by the others. Such questions check your ability to recognise patterns in divisibility and factorisation.

Given Data / Assumptions:

• The numbers given are 20, 35, 45, 80 and 50.
• All of them are positive integers.
• Each number is a multiple of 5.
• We are looking for a more specific property that separates one number from the other three among the original options.

Concept / Approach:
Because all the numbers are divisible by 5, that alone cannot be the basis for classification. A deeper look at the prime factorisation is helpful. We can check whether the numbers are also divisible by 2 or 3, because those are small primes that often appear in reasoning patterns. If most of the numbers share an additional factor (like 2 or 3) along with 5, and one number does not, that number will be the odd one out.

Step-by-Step Solution:
Step 1: Factorise 20. We have 20 = 2 * 2 * 5 = 4 * 5. So 20 is a multiple of 5 and also a multiple of 2.Step 2: Factorise 45. We have 45 = 3 * 3 * 5 = 9 * 5. So 45 is a multiple of 5 and also a multiple of 3.Step 3: Factorise 80. We have 80 = 2 * 2 * 2 * 2 * 5 = 16 * 5. So 80 is a multiple of 5 and also a multiple of 2.Step 4: Factorise 35. We have 35 = 5 * 7. So 35 is a multiple of 5 and 7, but it is not divisible by 2 or 3.Step 5: Observe that in the original set 20, 35, 45 and 80, three numbers (20, 45, 80) are multiples of 5 and at least one of the small primes 2 or 3.Step 6: Specifically, 20 and 80 are multiples of 2, and 45 is a multiple of 3. All three therefore share the structure \"5 times 2 or 3\".Step 7: The number 35 is the only one that is a product of 5 and 7 and does not involve 2 or 3 in its prime factorisation.Step 8: Therefore, 35 is arithmetically different from the others and is the odd one out.

Verification / Alternative check:
A quick alternative check is to test divisibility. Check each number for divisibility by 2 or 3. 20 is even, so it is divisible by 2. 45 is divisible by 3 because 4 + 5 = 9, which is divisible by 3. 80 is even and therefore divisible by 2. 35 is neither even nor divisible by 3 because 3 + 5 = 8, which is not divisible by 3. Thus, three of the numbers (20, 45, 80) share the property \"divisible by 5 and also by 2 or 3\", while 35 does not.

Why Other Options Are Wrong:
20 is not the odd one out because it fits the pattern of being a multiple of 5 and a multiple of 2. 45 fits as a multiple of 5 and 3. 80 fits as a multiple of 5 and 2. Any added practice number like 50 also remains a multiple of 5 and 2, so it is not special. Only 35, with its prime factorisation 5 * 7, fails to have 2 or 3 as an additional factor and therefore breaks the dominant pattern.

Common Pitfalls:
Some learners initially focus on superficial details such as whether the number is two digit or not, or whether it ends in 0 or 5. However, all are multiples of 5, so the real pattern is a bit subtler. Another error is to pick the largest or smallest number without doing any factor analysis. In any classification question, always check divisibility by small prime numbers to see hidden similarities and differences.

Final Answer:
The number which does not belong to the group is 35.