In this number pair reasoning question, four pairs are given where the second number is related to the first number. Select the odd pair that does not follow the same square pattern as the others.

Introduction / Context:
This question tests recognition of patterns in number pairs. Each option shows a pair where the first number is linked to the second number by some rule. Your task is to identify which pair does not follow the same rule. Such pair based patterns often involve squares, cubes, or small arithmetic operations and are standard in quantitative aptitude and reasoning sections.

Given Data / Assumptions:
- The pairs given are 12 – 121, 14 – 169, 16 – 215, and 18 – 289.- The second number in each pair is close to the square of a number near the first value.- We assume a relationship involving perfect squares.

Concept / Approach:
One natural observation is that 121 is 11^2, 169 is 13^2, and 289 is 17^2. These are squares of odd numbers that are 1 less than the first number in each pair. To confirm, we test whether each second number is equal to the square of (first number minus 1). If three pairs follow this pattern and one does not, the non matching pair is the odd one out.

Step-by-Step Solution:
Step 1: For 12 – 121, compute (12 − 1)^2. This gives 11^2 = 121, which matches the second number.Step 2: For 14 – 169, compute (14 − 1)^2. This gives 13^2 = 169, again matching the second number.Step 3: For 18 – 289, compute (18 − 1)^2. This gives 17^2 = 289, which again matches the second number.Step 4: For 16 – 215, compute (16 − 1)^2. This gives 15^2 = 225, while the second number is 215, which does not match.Step 5: Thus, three pairs follow the rule second number = (first number − 1)^2, but one pair does not.

Verification / Alternative check:
Another quick check is to compare how far each second number is from the nearest perfect square. 121, 169, and 289 are themselves perfect squares. However, 215 lies between 14^2 = 196 and 15^2 = 225 and is not a perfect square, confirming that the relation breaks for this pair.

Why Other Options Are Wrong:
12 – 121: Correctly follows second = (12 − 1)^2.14 – 169: Correctly follows second = (14 − 1)^2.18 – 289: Correctly follows second = (18 − 1)^2.

Common Pitfalls:
Some candidates try to relate the second number directly to the first by simple multiplication or addition and miss the square pattern. When numbers such as 121, 169, and 289 appear, it is a strong hint to think in terms of perfect squares.

Final Answer:
The odd pair is 16 – 215 because its second number is not equal to the square of one less than the first number, unlike the other three pairs.