Finding the Odd Number Pair

In this question, we need to identify the number pair that does not follow the same pattern as the others. Let's examine each pair to find the relationship between the first and second numbers.

Analyzing the Number Pairs

We will look for a common rule or pattern that connects the two numbers in each pair. A common pattern in such questions involves multiplication, squaring, cubing, or operations based on the numbers themselves.

• Pair 1: 7 - 56

  Let the first number be \(n\). Here, \(n = 7\). The second number is 56.

  Let's see if there's a relationship based on \(n\).

  Is it \(n \times (n+1)\)?

  \(7 \times (7+1) = 7 \times 8 = 56\).

  This pair follows the pattern \(n \times (n+1)\).

• Pair 2: 10 - 110

  Let the first number be \(n\). Here, \(n = 10\). The second number is 110.

  Using the potential pattern \(n \times (n+1)\):

  \(10 \times (10+1) = 10 \times 11 = 110\).

  This pair also follows the pattern \(n \times (n+1)\).

• Pair 3: 9 - 90

  Let the first number be \(n\). Here, \(n = 9\). The second number is 90.

  Using the potential pattern \(n \times (n+1)\):

  \(9 \times (9+1) = 9 \times 10 = 90\).

  This pair also follows the pattern \(n \times (n+1)\).

• Pair 4: 8 - 96

  Let the first number be \(n\). Here, \(n = 8\). The second number is 96.

  Using the potential pattern \(n \times (n+1)\):

  \(8 \times (8+1) = 8 \times 9 = 72\).

  The second number in this pair is 96, not 72. So, this pair does not follow the pattern \(n \times (n+1)\).

Identifying the Odd Pair

Based on the analysis, pairs 1, 2, and 3 all follow the pattern where the second number is obtained by multiplying the first number by one more than the first number (\(n \times (n+1)\)). Pair 4, however, does not follow this rule, as \(8 \times (8+1) = 72\), not 96.

Therefore, the pair 8 - 96 is the odd one out among the given alternatives.

Summary of Patterns

The pair 8 - 96 is the only one that does not fit the established pattern.

Revision Table: Odd Number Pair Questions

Additional Information: Solving Number Series and Analogy Problems

Number series and analogy problems are common in reasoning tests. They require logical thinking and the ability to spot patterns. Here are some tips:

• Always examine all the given options or numbers before concluding a pattern.
• Test simple arithmetic operations first: addition, subtraction, multiplication, division.
• Consider operations involving the number itself, like \(n^2\), \(n^2 \pm 1\), \(n \times (n+1)\), \(n^3\), etc.
• Look for patterns involving prime numbers, composite numbers, odd/even numbers.
• Sometimes the pattern might involve the sum or difference of digits.
• Practice with different types of questions to get familiar with common patterns.

In this specific odd number pair question, the pattern \(n \times (n+1)\) is a frequent one to look for.