In the pairs 43-6, 28-4, 50-7 and 36-5, identify the odd pair based on whether the second number is a factor of the first.

Introduction / Context:
This odd one out question uses pairs of numbers where the hidden pattern is based on divisibility. In particular, we check whether the second number divides the first number exactly. Divisibility and factors are core concepts in number theory and are frequently used to build quick reasoning questions in competitive exams.

Given Data / Assumptions:
The number pairs given are 43-6, 28-4, 50-7 and 36-5. Each pair is written as first number dash second number. We assume the dash is just a separator and does not indicate subtraction. We check whether the second number is a factor of the first number in each pair.

Concept / Approach:
A factor of a number is an integer that divides that number exactly without leaving any remainder. To identify the odd pair, we can test each pair to see whether the first number is divisible by the second number. If exactly one pair has the property first number divisible by second number, while the others do not, that pair becomes the odd one out. This method is quick, systematic and well suited to this type of puzzle.

Step-by-Step Solution:
Step 1: For the pair 43-6, check 43 ÷ 6. The result is not an integer and leaves a remainder, so 6 is not a factor of 43. Step 2: For the pair 28-4, check 28 ÷ 4. The result is exactly 7 with no remainder, so 4 is a factor of 28. Step 3: For the pair 50-7, check 50 ÷ 7. The result is not an integer and has a remainder, so 7 is not a factor of 50. Step 4: For the pair 36-5, check 36 ÷ 5. The result is again not an integer and leaves a remainder, so 5 is not a factor of 36. Step 5: Summarize the findings: only in the pair 28-4 does the second number divide the first number exactly. Step 6: Therefore, 28-4 is the unique pair with a factor relationship and hence is the odd one out.

Verification / Alternative check:
As a quick verification, list the pairs and mark which second numbers are factors of their first numbers. Only 4 divides 28 exactly, while 6 does not divide 43, 7 does not divide 50 and 5 does not divide 36 without remainders. No other simple property, such as parity of the numbers or sum of digits, produces such a clean separation of one pair from the rest.

Why Other Options Are Wrong:
43-6 is not the odd pair because the second number 6 is not a factor of 43, which is similar to most other pairs. 50-7 is not the odd pair because 7 is not a factor of 50. 36-5 is not the odd pair because 5 is not a factor of 36. 28-4 is the odd pair because 4 divides 28 exactly, making this pair different in factor relationship.

Common Pitfalls:
One common mistake is to interpret the dash as subtraction and look at differences instead of divisibility, which can lead to confusion. Another pitfall is to attempt complicated operations such as ratios or averages instead of checking simple divisibility first. To handle such questions efficiently, always test for basic factor and multiple relationships between numbers in a pair.

Final Answer:
The pair in which the second number is a factor of the first, and which is therefore the odd one out, is 28-4.