Four number pairs are given: 3 – 6, 5 – 10, 7 – 12 and 9 – 18. In each pair, the number on the left is related to the number on the right according to a specific rule. Three of the pairs follow the same rule, while one pair breaks the pattern. Based on this relationship, which number pair is the odd one out among the given alternatives?

Introduction / Context:
This question belongs to the aptitude topic of odd one out and number relationships. You are given four number pairs and asked to identify which pair does not follow the same rule as the others. Such questions test your ability to detect numerical patterns, especially multiplication or proportional relationships between two numbers in each pair.

Given Data / Assumptions:

• Given pairs: 3 – 6, 5 – 10, 7 – 12, 9 – 18.
• Each pair has a left number and a right number.
• Three pairs share a common rule; one pair violates that rule.
• We assume basic arithmetic rules like multiplication and division are to be checked first.

Concept / Approach:
In odd one out questions with number pairs, a very common pattern is that the second number is a multiple of the first. The simplest check is to see whether the right side is exactly double, triple, or follows some other easy multiplier of the left side. If three pairs share the same multiplier and one does not, that nonconforming pair is the odd one out.

Step-by-Step Solution:
Step 1: Check the pair 3 – 6. Here, 6 = 3 * 2. So the rule could be "right number is double the left number". Step 2: Check the pair 5 – 10. Here, 10 = 5 * 2, which matches the same doubling rule. Step 3: Check the pair 9 – 18. Here, 18 = 9 * 2, again following the same pattern. Step 4: Check the pair 7 – 12. If the same rule applied, we would expect 7 * 2 = 14. However, the given right number is 12, not 14, so this pair does not follow the doubling rule. Step 5: Since three pairs follow the exact relationship "right number = 2 * left number" and one does not, the nonmatching pair is the odd one out.

Verification / Alternative check:
Another way to verify is to compute right / left for each pair: 6 / 3 = 2, 10 / 5 = 2, 18 / 9 = 2, but 12 / 7 is not an integer and is approximately 1.71. Only three ratios are exactly 2, confirming that those three pairs share the same rule, and the remaining pair is different. This validates that our identified odd pair is correct.

Why Other Options Are Wrong:
3 – 6 is correct according to the rule because 6 is exactly double 3. 5 – 10 is correct because 10 is exactly double 5. 9 – 18 is correct because 18 is exactly double 9. Only 7 – 12 fails the doubling condition, because 12 is not equal to 7 * 2.

Common Pitfalls:
Students sometimes look for complicated patterns, such as adding different constants or mixing multiplication and addition, when a simple and consistent rule like doubling is sufficient. Another mistake is to perform approximate mental calculations and assume that 12 is "close enough" to 14, which is not acceptable in precise aptitude reasoning. Always check exact operations and maintain consistency across all pairs.

Final Answer:
The number pair that does not follow the same rule and is therefore the odd one out is 7 – 12.