In the following question, four number pairs are given: 41 – 22, 63 – 93, 82 – 44 and 83 – 64. In three of these pairs, the difference between the two numbers is a multiple of 19, while one pair does not follow this rule. Based on this relationship, which number pair is the odd one out?

Introduction / Context:
This question belongs to the number pair odd one out type in aptitude tests. You are given four pairs of numbers and asked to find which pair does not follow the same numerical rule as the others. Here, the key idea is to look at the difference between the two numbers in each pair and identify a consistent pattern, especially involving a specific factor such as 19.

Given Data / Assumptions:

• Number pairs: 41 – 22, 63 – 93, 82 – 44, 83 – 64.
• We will compute the difference between the two numbers in each pair.
• We are searching for a common factor, particularly 19, in three of the four differences.
• One pair is expected to break this pattern and will be the odd one out.

Concept / Approach:
Odd one out questions on number pairs often use relationships such as sums, products, or differences. A neat and common trick is to check whether the differences between the pair members are multiples of a specific number. If three differences are multiples of a certain integer and one is not, the corresponding pair is the odd one out. We will apply this method using basic subtraction and divisibility checks.

Step-by-Step Solution:
Step 1: For 41 – 22: Difference = 41 - 22 = 19. 19 is clearly a multiple of 19 (19 * 1). Step 2: For 82 – 44: Difference = 82 - 44 = 38. 38 is 19 * 2, so it is also a multiple of 19. Step 3: For 83 – 64: Difference = 83 - 64 = 19. Again, 19 is exactly 19 * 1, a multiple of 19. Step 4: For 63 – 93: Difference = 63 - 93 = -30. For odd one out purposes, we can consider the magnitude, which is 30. Step 5: Check whether 30 is a multiple of 19. Since 19 * 1 = 19 and 19 * 2 = 38, 30 lies between these and is not a multiple of 19. Step 6: We see that three pairs (41 – 22, 82 – 44 and 83 – 64) have differences that are multiples of 19, while the pair 63 – 93 does not.

Verification / Alternative check:
As an alternative, you can simply list the absolute differences: |41 - 22| = 19 |82 - 44| = 38 |83 - 64| = 19 |63 - 93| = 30 Then check divisibility: 19 / 19 = 1 (exact multiple), 38 / 19 = 2 (exact multiple), 19 / 19 = 1 (exact multiple), but 30 / 19 is not an integer. Since only 30 is not a multiple of 19, the pair 63 – 93 clearly breaks the common rule.

Why Other Options Are Wrong:
41 – 22 is not odd because its difference 19 is exactly 19 * 1. 82 – 44 is not odd because its difference 38 is 19 * 2. 83 – 64 is not odd because its difference 19 is again 19 * 1. Only 63 – 93 produces a difference 30 that is not divisible by 19, making it special.

Common Pitfalls:
A common mistake is to focus on the sum of the numbers in each pair or to look for more complex patterns such as squares or cubes, which are not needed here. Another pitfall is to ignore negative signs and get confused. In odd one out problems, it is usually safe to consider the absolute difference between the numbers. Keeping the reasoning simple and checking multiples carefully avoids such errors.

Final Answer:
The pair that does not have a difference which is a multiple of 19 and is therefore the odd one out is 63 – 93.