In this numerical odd-man-out question on number pairs, four pairs are given: 16–28, 20–30, 30–40 and 40–50. In three of these pairs, the difference between the second and first number is 10, whereas in one pair the difference is 12. Which option represents the odd pair based on this constant-difference rule?

Introduction / Context:
This question is an odd-man-out problem involving simple number pairs. The pairs mentioned in the stem are 16–28, 20–30, 30–40 and 40–50, mapped to options A, B, C and D. In many basic aptitude questions, relationships between two numbers in a pair are often based on a constant difference, such as adding a fixed number. Here, three of the pairs have a difference of 10 between the second and first number, while one pair has a different difference. The task is to find which pair breaks the constant-difference pattern.

Given Data / Assumptions:
Option A represents the pair 16–28.
Option B represents the pair 20–30.
Option C represents the pair 30–40.
Option D represents the pair 40–50.
In three pairs, second number − first number = 10.
One pair has a difference not equal to 10 and is the odd one out.

Concept / Approach:
The core concept is checking the difference between numbers in each pair. If the difference is constant in three cases and different in one case, the inconsistent pair is the odd one. The pattern in this question is simple addition, so no advanced calculations are required. This type of question tests attention to detail and basic arithmetic accuracy rather than complex reasoning.

Step-by-Step Solution:
Step 1: For 16–28, compute 28 − 16 = 12. Step 2: For 20–30, compute 30 − 20 = 10. Step 3: For 30–40, compute 40 − 30 = 10. Step 4: For 40–50, compute 50 − 40 = 10. Step 5: Observe that three pairs have a difference of 10, while the pair 16–28 has a difference of 12. Step 6: Conclude that the pair in option A is the odd one out.
Verification / Alternative check:
An alternative view is to consider how you would generate the second number from the first. For options B, C and D, you can obtain the second number by adding 10 to the first (20 + 10 = 30, 30 + 10 = 40 and 40 + 10 = 50). However, for option A, adding 10 to 16 gives 26, not 28. To get 28 from 16, you must add 12 instead. This confirms that the first pair does not follow the same rule as the others.

Why Other Options Are Wrong:
Option B (20–30) follows the rule second = first + 10 and therefore fits into the main group of consistent pairs.
Option C (30–40) also follows the same rule, with a difference of 10 between the two numbers.
Option D (40–50) again maintains the constant difference of 10 and is not the odd one out.
Option A (16–28) uses a difference of 12 instead of 10 and therefore breaks the pattern.

Common Pitfalls:
A common mistake is to overthink the pattern and attempt more complicated operations such as multiplication or ratios, when a simple difference check is sufficient. Another pitfall is arithmetic error, such as miscalculating 28 − 16 or 30 − 20 under time pressure. In odd-man-out questions, always test the simplest numeric relationships first, such as addition or subtraction, and carefully verify the calculations.

Final Answer:
The pair that does not follow the constant difference of 10 and is therefore the odd one out is 16–28, represented by option A.