The second number in the given number pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) are followed in all the number pairs except one. Find that odd number pair.

(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. e.g., 13 – Operations on 13 such as adding /deleting /multiplying etc., to 13 can be performed.

Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

The correct answer is 34 : 44.

To find the odd number pair, let's analyze the mathematical relationship between the first and the second number in each pair, without breaking down the numbers into their constituent digits:

1. For the pair 13 : 16:
The first number is 13. The next consecutive perfect square greater than 13 is:
$4^2=16$
Thus, the second number is the smallest perfect square greater than the first number.

2. For the pair 23 : 25:
The first number is 23. The next consecutive perfect square greater than 23 is:
$5^2=25$
This follows the same logic.

3. For the pair 35 : 36:
The first number is 35. The next consecutive perfect square greater than 35 is:
$6^2=36$
This also follows the same logic.

4. For the pair 34 : 44:
The first number is 34. The next consecutive perfect square greater than 34 should be:
$6^2=36$
However, the second number provided in this pair is 44, which is not a perfect square and does not follow the established pattern.

Therefore, 34 : 44 is the odd pair.