In this number classification question, the pairs 7 : 22, 12 : 37, 8 : 33 and 15 : 46 are given. Three of these pairs follow a similar numerical pattern. Which number pair is different from the others?

Introduction / Context:
This is a number pair classification problem, where each option consists of two numbers related by a certain arithmetic rule. You are given the pairs 7 : 22, 12 : 37, 8 : 33 and 15 : 46. Three of these follow an identical arithmetic pattern, while one does not. The goal is to find the odd pair by identifying the underlying rule that connects the numbers in the majority of the pairs.

Given Data / Assumptions:
• The number pairs are: (7, 22), (12, 37), (8, 33) and (15, 46).• We suspect a linear relation of the form second = 3 * first + constant.• The correct pattern should apply to three pairs and fail for exactly one pair.

Concept / Approach:
Check whether multiplying the first number by 3 and then adding a constant yields the second number. For 7 : 22, 3 * 7 + 1 = 21 + 1 = 22. For 12 : 37, 3 * 12 + 1 = 36 + 1 = 37. For 15 : 46, 3 * 15 + 1 = 45 + 1 = 46. So in three pairs the second number equals 3 times the first number plus 1. Now test this rule on 8 : 33. We get 3 * 8 + 1 = 25, which is not 33. Hence 8 : 33 does not conform to the same pattern and is the odd one out.

Step-by-Step Solution:
Step 1: For the pair 7 : 22, compute 3 * 7 + 1 = 21 + 1 = 22. The rule second = 3 * first + 1 works here.Step 2: For 12 : 37, compute 3 * 12 + 1 = 36 + 1 = 37. Again, the rule holds.Step 3: For 15 : 46, compute 3 * 15 + 1 = 45 + 1 = 46. The rule still holds.Step 4: For 8 : 33, compute 3 * 8 + 1 = 24 + 1 = 25, which does not equal 33.Step 5: Therefore, 8 : 33 fails to follow the pattern that works for the other three pairs.Step 6: Hence 8 : 33 is the different, or odd, number pair.

Verification / Alternative check:
If we look for other patterns, such as adding a fixed number or squaring, we do not find a simple rule that fits as neatly as second = 3 * first + 1 for three of the pairs. Only 7 : 22, 12 : 37 and 15 : 46 can be described with the same linear formula. The pair 8 : 33 fits neither this rule nor any obvious variant that only excludes one pair. Thus selecting 8 : 33 as the odd one is the most consistent choice.

Why Other Options Are Wrong:
7 : 22: Follows the second = 3 * first + 1 rule.12 : 37: Also fits the same pattern.15 : 46: Again matches the rule exactly.None of these: Incorrect because we clearly have three pairs that follow a pattern and one that does not.

Common Pitfalls:
Without testing each pair, some students guess randomly, or they try a more complicated formula and get lost. The key strategy is to look for a simple arithmetic relation like multiplication plus a constant and then verify it systematically across all options. Doing so reveals that 8 : 33 is the only pair that does not satisfy the simple linear rule satisfied by the others.

Final Answer:
The number pair that is different from the others is 8 : 33.