In this aptitude reasoning question on numerical pairs, find the odd number pair in which the relationship between the two numbers does not follow the same pattern as in the other options.

Introduction / Context:
This aptitude question tests the ability to identify the odd number pair based on a hidden numerical pattern. Such odd one out questions are common in competitive exams because they quickly check whether a student can compare several pairs and discover a consistent rule. Here, four pairs of numbers are given, and you must decide which pair does not follow the same relationship between the first and second number.

Given Data / Assumptions:
- Four number pairs are given as options.- The correct answer is the pair that does not fit the common rule followed by the other three pairs.- All calculations are done using simple operations like addition and subtraction.

Concept / Approach:
The standard approach in such questions is to look for a numerical pattern that works for most of the pairs. A very common pattern is to check the difference between the two numbers in each pair. If three pairs show a similar type of difference and one pair does not, that different pair is the odd one out. We will therefore compare the differences between the numbers in each pair.

Step-by-Step Solution:
Step 1: For 41 - 72, the difference is 72 - 41 = 31.Step 2: For 12 - 30, the difference is 30 - 12 = 18.Step 3: For 51 - 42, the difference is 51 - 42 = 9.Step 4: For 11 - 20, the difference is 20 - 11 = 9.Step 5: Observe that in three pairs (12 - 30, 51 - 42, 11 - 20) the absolute differences are multiples of 9 (18, 9, 9), whereas in 41 - 72 the difference is 31, which is not a multiple of 9.

Verification / Alternative check:
You can quickly recheck the pattern by focusing only on the size of the difference. If you divide 18, 9, and 9 by 9, you get whole numbers. When you divide 31 by 9, you do not get a whole number. This confirms that exactly three pairs share the same rule and one pair does not.

Why Other Options Are Wrong:
12 - 30: Difference is 18, which is a multiple of 9, so it fits the pattern.51 - 42: Difference is 9, also a multiple of 9, so it follows the same rule.11 - 20: Difference is 9, again a multiple of 9, so it fits the pattern.

Common Pitfalls:
Many students try unnecessary operations like squares or products and overlook the simple difference pattern. Some also make calculation mistakes while subtracting, which may lead them to mark the wrong pair as the odd one out. Always check subtraction carefully.

Final Answer:
The only pair whose difference is not a multiple of 9 is 41 - 72, so it is the odd number pair.