Finding the Odd Number Pair in Number Series

In this question, we are asked to identify the odd number pair from the given alternatives. To do this, we need to look for a pattern or relationship that exists between the two numbers in each pair. Once we find a common pattern for most pairs, the pair that does not follow this pattern will be the odd one out.

Analyzing the Given Number Pairs

Let's examine each pair to see if we can find a relationship between the first number and the second number:

• Pair 1: 12 - 156
• Pair 2: 6 - 42
• Pair 3: 8 - 72
• Pair 4: 10 - 90

Identifying the Pattern

Let the first number in the pair be \(n\) and the second number be \(m\). We look for a formula relating \(m\) to \(n\).

• For Pair 2 (6 - 42): If we multiply the first number (6) by one more than itself (\(6+1 = 7\)), we get \(6 \times 7 = 42\). So, \(m = n \times (n+1)\).
• For Pair 3 (8 - 72): If we apply the same pattern, multiply the first number (8) by one more than itself (\(8+1 = 9\)), we get \(8 \times 9 = 72\). So, \(m = n \times (n+1)\).
• For Pair 1 (12 - 156): Applying the pattern, multiply the first number (12) by one more than itself (\(12+1 = 13\)), we get \(12 \times 13 = 156\). So, \(m = n \times (n+1)\).
• For Pair 4 (10 - 90): Applying the pattern, multiply the first number (10) by one more than itself (\(10+1 = 11\)), we get \(10 \times 11 = 110\). This is not 90. Let's try multiplying by one less than itself (\(10-1 = 9\)). We get \(10 \times 9 = 90\). This follows the pattern \(m = n \times (n-1)\).

From this analysis, we can see that three of the pairs (12-156, 6-42, and 8-72) follow the pattern where the second number is the first number multiplied by (first number + 1). The pair 10-90 follows a different pattern where the second number is the first number multiplied by (first number - 1).

Conclusion

Since the pair 10 - 90 does not follow the same pattern as the other three pairs, it is the odd number pair among the given alternatives.

Revision Table: Understanding Number Patterns

Additional Information: Solving Odd Pair Questions

To solve odd pair or odd one out questions based on numbers, consider the following common patterns:

• Arithmetic Progression: Numbers increasing or decreasing by a constant difference.
• Geometric Progression: Numbers related by a constant multiplier or divisor.
• Squares and Cubes: Numbers that are perfect squares or cubes, or related to them (\(n^2\), \(n^3\), \(n^2+1\), \(n^3-1\), etc.).
• Prime Numbers: Checking if numbers are prime or composite.
• Digit Operations: Sum of digits, product of digits, etc.
• Relationships between elements in a pair: Such as addition, subtraction, multiplication, division, or combination of these, often related to the first number itself (like \(n+c\), \(n-c\), \(n \times c\), \(n/c\), \(n^2\), \(n^2+c\), \(n \times (n+1)\), \(n \times (n-1)\), etc., where \(c\) is a constant or related to \(n\)).

Systematic checking of common patterns is key to solving such problems.