In this number-pair odd-man-out question, select the pair that does not follow the same constant-difference rule.

Introduction / Context:
This odd-man-out question involves simple number pairs. In three of the pairs, the second number is obtained by adding the same constant to the first number. In one pair, the difference is smaller, which makes that pair the odd one out. The problem is designed to check your ability to detect constant differences quickly.

Given Data / Assumptions:

• Number pairs: 101 – 105, 103 – 107, 102 – 106 and 104 – 106.
• We look at the increase from the first number to the second number in each pair.
• We assume no hidden operations beyond simple addition.

Concept / Approach:
An efficient way to approach such problems is to compute the difference second - first for each pair. If three of these differences are equal and one is not, the pair with the different difference is the odd-man-out. Here, we will see that three pairs have a difference of +4 and one pair has a difference of only +2.

Step-by-Step Solution:
Step 1: For 101 – 105, compute the difference: 105 - 101 = 4. So this pair follows second = first + 4. Step 2: For 103 – 107, compute the difference: 107 - 103 = 4. This pair also follows second = first + 4. Step 3: For 102 – 106, compute the difference: 106 - 102 = 4. This again matches the same rule. Step 4: For 104 – 106, compute the difference: 106 - 104 = 2. This pair follows second = first + 2, not +4. Step 5: Summarise. Three pairs show an increment of 4, while one pair shows an increment of only 2. Step 6: Conclude that 104 – 106 is the odd pair because its difference is different from the others.

Verification / Alternative check:
We can also observe that in the first three pairs both numbers are odd or both are even, and the gap of 4 preserves that parity. For example, 101 and 105 are odd, 103 and 107 are odd and 102 and 106 are even. In the last pair, 104 and 106 are both even, but that alone does not isolate this pair. The key distinguishing factor remains the smaller difference of 2 compared to 4 for the others. Thus, our conclusion is fully supported by the difference pattern.

Why Other Options Are Wrong:
101 – 105 is not odd because it follows the rule second = first + 4. 103 – 107 also follows the same rule. 102 – 106 continues this pattern with an increment of 4. These three pairs are therefore similar in structure and cannot be labelled as odd-men-out. Only 104 – 106 violates the constant-difference rule, so the other three are not the answer.

Common Pitfalls:
A common mistake is to look at the parity of the numbers and become confused because all pairs involve numbers with the same parity. Another error is to just glance at the numbers without actually calculating the differences. In questions of this type, taking a few seconds to compute and compare differences is essential. This simple step quickly reveals the intended pattern and prevents guessing.

Final Answer:
The odd number pair is 104 – 106, because the difference between the two numbers is 2, whereas in all other pairs the difference is 4.