Understanding How to Find the Odd Number Pair

In this question, we are given four pairs of numbers. Our goal is to find the pair that does not follow the same rule or pattern as the other three pairs. This is a common type of logical reasoning question where you need to identify the underlying relationship between the numbers in each pair.

Analyzing Each Number Pair

Let's examine each given number pair and try to find a consistent relationship between the first number and the second number in the pair. We can look for patterns like arithmetic operations, relationships between digits, or other mathematical rules.

• Pair 1: 223 – 12

  Let's check the relationship based on the digits of the first number (223).

  Sum of digits = \(2 + 2 + 3 = 7\) (Not 12)

  Product of digits = \(2 \times 2 \times 3 = 12\) (Matches the second number)

  This pair seems to follow the rule: the second number is the product of the digits of the first number.

• Pair 2: 342 – 24

  Let's check the relationship based on the digits of the first number (342).

  Sum of digits = \(3 + 4 + 2 = 9\) (Not 24)

  Product of digits = \(3 \times 4 \times 2 = 24\) (Matches the second number)

  This pair also seems to follow the rule: the second number is the product of the digits of the first number.

• Pair 3: 643 – 72

  Let's check the relationship based on the digits of the first number (643).

  Sum of digits = \(6 + 4 + 3 = 13\) (Not 72)

  Product of digits = \(6 \times 4 \times 3 = 72\) (Matches the second number)

  This pair also seems to follow the rule: the second number is the product of the digits of the first number.

• Pair 4: 864 – 96

  Let's check the relationship based on the digits of the first number (864).

  Sum of digits = \(8 + 6 + 4 = 18\) (Not 96)

  Product of digits = \(8 \times 6 \times 4 = 192\) (Does not match the second number, which is 96)

  This pair does NOT follow the rule where the second number is the product of the digits of the first number.

Identifying the Number Pattern

Based on the analysis of the first three pairs (223-12, 342-24, and 643-72), we can observe a consistent pattern:

The second number in the pair is obtained by multiplying the individual digits of the first number.

Finding the Odd Number Pair Out

We tested this pattern on all four pairs:

• 223 – 12: Product of digits of 223 is \(2 \times 2 \times 3 = 12\). Matches 12.
• 342 – 24: Product of digits of 342 is \(3 \times 4 \times 2 = 24\). Matches 24.
• 643 – 72: Product of digits of 643 is \(6 \times 4 \times 3 = 72\). Matches 72.
• 864 – 96: Product of digits of 864 is \(8 \times 6 \times 4 = 192\). Does NOT match 96.

Therefore, the number pair 864 – 96 is the one that does not follow the identified pattern, making it the odd number pair among the given alternatives.

Revision Table: Number Pair Patterns

Additional Information: Types of Number Series Patterns

Finding patterns in number series or pairs is a key skill in logical reasoning. Besides the product of digits pattern seen here, other common types of patterns include:

• Arithmetic sequences (adding or subtracting a constant)
• Geometric sequences (multiplying or dividing by a constant)
• Patterns based on squares, cubes, or other powers
• Patterns based on differences or sums of consecutive terms
• Alternating patterns (two different patterns applied alternately)
• Patterns involving the sum or manipulation of digits (like this question)

Practicing different types of number patterns helps in quickly identifying the rule in such reasoning questions.