Finding the Odd Number Pair in a Series

The question asks us to identify the number pair that does not follow the same mathematical operation relating the first number to the second number, unlike the other pairs provided. We need to examine each number pair and determine the rule.

Analyzing the Number Pairs

Let's look closely at the relationship between the first and second number in each pair:

• Pair 1: 20 ∶ 11
• Pair 2: 6 ∶ 4
• Pair 3: 15 ∶ 9
• Pair 4: 12 ∶ 7

We need to find a consistent mathematical operation or set of operations that links the first number to the second number in most of these pairs. Let's try some common operations:

• Subtraction: 20 - 11 = 9, 6 - 4 = 2, 15 - 9 = 6, 12 - 7 = 5. No clear pattern here.
• Division: 20 / 11 ≈ 1.82, 6 / 4 = 1.5, 15 / 9 ≈ 1.67, 12 / 7 ≈ 1.71. No clear pattern here either.
• Let's consider operations involving division and addition/subtraction.

Discovering the Pattern

Let's test a possible pattern: dividing the first number by 2 and then adding a constant value.

• For 20 ∶ 11: $20 \div 2 = 10$. To get 11, we add 1. So, the pattern could be $\frac{\text{First Number}}{2} + 1$. Let's check this with other pairs.
• For 6 ∶ 4: $\frac{6}{2} + 1 = 3 + 1 = 4$. This matches the second number.
• For 12 ∶ 7: $\frac{12}{2} + 1 = 6 + 1 = 7$. This matches the second number.

It appears the common pattern is indeed $\frac{\text{First Number}}{2} + 1 = \text{Second Number}$.

Applying the Pattern to Find the Odd Pair

Now, let's apply this pattern to the remaining pair, 15 ∶ 9, to see if it follows the rule.

• For 15 ∶ 9: According to the pattern, the second number should be $\frac{15}{2} + 1$.
• Calculation: $\frac{15}{2} + 1 = 7.5 + 1 = 8.5$.

The expected second number based on the pattern is 8.5, but the given second number is 9. Therefore, the pair 15 ∶ 9 does not follow the established pattern.

Summary of Findings

As shown in the table, the pair 15 ∶ 9 is the only one that does not fit the pattern where the second number is obtained by dividing the first number by two and adding one.

Conclusion: Identifying the Odd Pair

Based on our analysis, the odd number pair is 15 ∶ 9 because it is the only pair that does not follow the mathematical operation $\frac{\text{First Number}}{2} + 1$ to get the second number. The other pairs (20 ∶ 11, 6 ∶ 4, and 12 ∶ 7) all adhere to this rule.

Revision Table: Odd Number Pair Analysis

Reviewing the method used to find the odd number pair in a series:

• Examine the relationship between numbers in each pair.
• Test different mathematical operations (addition, subtraction, multiplication, division, combined operations).
• Identify a consistent pattern applicable to most pairs.
• Verify if the remaining pair follows the same pattern.
• The pair that does not follow the pattern is the odd one out.

Additional Information: Number Series and Patterns

Finding patterns in number series or pairs is a common type of logical reasoning question. These patterns can involve various mathematical concepts:

• Arithmetic Progression: Adding or subtracting a constant value.
• Geometric Progression: Multiplying or dividing by a constant value.
• Combined Operations: Using multiple operations, like in this problem (division and addition).
• Square/Cube Numbers: Relating numbers to squares or cubes or their roots.
• Digit Operations: Sum of digits, product of digits, etc.
• Prime Numbers: The sequence involves prime numbers.
• Fibonacci Sequence: The next number is the sum of the previous two.

Practice with different types of number patterns helps in quickly identifying the rule and the odd one out in such questions.