In the number pairs 36 - 48, 56 - 44, 78 - 66 and 33 - 64, find the odd pair based on the difference between the two numbers.

Introduction / Context:
This is a classic odd one out question from quantitative aptitude where you are given several number pairs and asked to identify which pair does not follow the same numerical rule. These questions test your ability to compare numbers, spot hidden relationships, and recognize simple arithmetic patterns quickly, such as constant differences between paired values.

Given Data / Assumptions:
We are given the four pairs: 36 - 48, 56 - 44, 78 - 66 and 33 - 64. Each option consists of two integers connected by a dash. We interpret the dash simply as a separator between the first and second number in each pair. We look for a common arithmetic relationship, most naturally the difference between the two numbers.

Concept / Approach:
Odd one out problems with number pairs frequently rely on a constant difference, a constant ratio, or some property such as both numbers being multiples of a fixed value. Here, the simplest and most revealing approach is to compute the absolute difference between the two numbers in each pair. If three pairs share the same difference and one pair has a different difference, then the one that breaks the pattern is the required odd pair.

Step-by-Step Solution:
Step 1: For 36 - 48, the absolute difference is |36 - 48| = 12. Step 2: For 56 - 44, the absolute difference is |56 - 44| = 12. Step 3: For 78 - 66, the absolute difference is |78 - 66| = 12. Step 4: For 33 - 64, the absolute difference is |33 - 64| = 31. Step 5: We observe that the first three pairs all have a constant difference of 12, whereas the last pair has a much larger difference of 31. Step 6: Therefore, the pair 33 - 64 does not follow the same constant difference rule and is the odd one out.

Verification / Alternative check:
To verify, recompute the differences quickly: 36 to 48 is a jump of 12, 56 to 44 is again 12 in the opposite direction, and 78 to 66 is also 12 in the opposite direction. The final pair 33 to 64 clearly involves a change of 31, which is not close to 12 and cannot be explained by the same rule. No other simple pattern, such as constant ratio or common factors, produces such a neat grouping of three similar pairs versus one different pair.

Why Other Options Are Wrong:
36 - 48 is not the odd pair because its difference of 12 matches the pattern seen in 56 - 44 and 78 - 66. 56 - 44 is not the odd pair since its difference is also 12, consistent with the same rule. 78 - 66 is not the odd pair for the same reason, as it again gives a difference of 12. 33 - 64 is the only pair whose numbers differ by 31 instead of 12, so it breaks the pattern.

Common Pitfalls:
A common error is to focus only on the larger numbers or to compare the sums of the numbers in each pair rather than their differences. Some learners may also try unnecessarily complex operations, such as multiplying or dividing the numbers, which is not needed here. When you see similar looking pairs, it is usually best to check simple differences first, as this often reveals the intended pattern very quickly.

Final Answer:
The pair whose numbers do not differ by 12 and is therefore the odd one out is 33 - 64.