Four number pairs are given. In each pair, the number on the right is related to the number on the left. Three pairs show the same square rule. Select the odd number pair.

Introduction / Context:
This is a typical number pair odd man out question where each pair shows a mathematical relationship between the left and right numbers. Your task is to detect the common rule, usually a square or multiple, and then find the pair that does not satisfy it.

Given Data / Assumptions:

• Pairs: 14 - 196, 16 - 256, 12 - 144, 18 - 344.
• Most pairs follow the same rule; one pair does not.
• We expect a simple operation like squaring or multiplication.

Concept / Approach:
When you see pairs like 14 and 196 or 16 and 256, it is natural to check squares because 14^2 and 16^2 are common perfect squares. If three pairs show a right number equal to the left number squared, then any pair breaking this pattern will be the odd one.

Step-by-Step Solution:
Check 14 - 196: 14^2 = 196, so the right number is the square of the left. Check 16 - 256: 16^2 = 256, again right is left squared. Check 12 - 144: 12^2 = 144, so the same square rule holds. Check 18 - 344: 18^2 = 324, not 344, so this pair does not follow the square rule. Therefore 18 - 344 is the only pair where the right value is not the square of the left value.

Verification / Alternative check:
You can also confirm by simple subtraction. If the relation is a square, then right minus left squared should be zero. For the first three pairs, 196 - 14^2, 256 - 16^2, and 144 - 12^2 are all zero. For 18 - 344, 344 - 18^2 equals 344 - 324, which is 20, not zero. This confirms that the fourth pair does not satisfy the same rule.

Why Other Options Are Wrong:

• 14 - 196: Obeys the rule right = left^2, so it belongs with the main set.
• 16 - 256: Also satisfies the same square relationship.
• 12 - 144: Matches the square rule, so it is not odd.

Common Pitfalls:
Sometimes candidates may try to force more complex patterns when a simple square rule is enough. Overcomplicating the relation by adding or subtracting constants can create confusion. In exam conditions, always check basic operations such as squares, cubes, and simple multiples before considering more advanced rules.

Final Answer:
18 - 344