Find the odd number pair from the following alternatives: 4-16, 8-24, 14-26, 16-36.

Introduction / Context:
This odd man out question involves comparing structural properties of number pairs. Here the main idea is to notice that in three pairs the first number is a power of 2, while in one pair it is not, making that pair different from the others.

Given Data / Assumptions:

• Pairs: 4 - 16, 8 - 24, 14 - 26, 16 - 36.
• We examine the nature of the first numbers and also the general structure of the pairs.
• Powers of 2 such as 2^2, 2^3, and 2^4 are important in this pattern.

Concept / Approach:
Look at the first number in each pair and ask whether it is a pure power of 2. Powers of 2 are numbers like 4, 8, 16, 32, and so on, obtained by repeated doubling. If three first terms are powers of 2 and one is not, the pair with the non power first term is the odd one out. This simple property is usually enough to solve the question.

Step-by-Step Solution:
In 4 - 16, the first number 4 is 2^2, a power of 2. In 8 - 24, the first number 8 is 2^3, again a power of 2. In 16 - 36, the first number 16 is 2^4, which is also a power of 2. In 14 - 26, the first number 14 cannot be written as 2^n for any integer n; it is not a pure power of 2. Therefore the pair 14 - 26 has a first term that is structurally different from the first terms in the other three pairs.

Verification / Alternative check:
You can verify by factorization. Powers of 2 have prime factorization containing only the prime 2. For 4, 8, and 16, factorizations are 2^2, 2^3, and 2^4. For 14, the factorization is 2 * 7, which includes another prime besides 2. This clearly shows that 14 does not belong to the same special set as 4, 8, and 16, confirming that 14 - 26 is the odd pair.

Why Other Options Are Wrong:

• 4 - 16: Starts with 4, a power of 2, and structurally matches the patterns in 8 - 24 and 16 - 36.
• 8 - 24: Begins with 8, another power of 2, so it is not the odd pair.
• 16 - 36: Also begins with a pure power of 2 and shares the same special property.

Common Pitfalls:
Candidates sometimes try to force a direct arithmetic relation between each first and second number and may get confused by the different multipliers. While such relations exist, they are not uniform across all pairs. The intended pattern is simpler: look only at the nature of the first numbers as powers of 2. Ignoring this structural property can make the question seem harder than it really is.

Final Answer:
14 - 26