Finding the Odd Number Pair

The question asks us to identify the number pair that does not follow the same pattern as the others among the given options. We need to examine each pair to find a common relationship between the first number and the second number.

Analyzing the Number Pairs

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

• Option 1: 7 - 81

If we take the first number, 7, add 2 to it, we get \(7 + 2 = 9\). Squaring this result gives \(9^2 = 81\). So, the pattern seems to be \((n+2)^2\), where \(n\) is the first number.

• Option 2: 8 - 100

Following the same potential pattern, take the first number, 8, add 2: \(8 + 2 = 10\). Squaring this gives \(10^2 = 100\). This pair fits the \((n+2)^2\) pattern.

• Option 3: 11 - 169

Let's test the pattern again. Take the first number, 11, add 2: \(11 + 2 = 13\). Squaring this gives \(13^2 = 169\). This pair also fits the \((n+2)^2\) pattern.

• Option 4: 5 - 47

Now, apply the pattern to the first number, 5. Add 2: \(5 + 2 = 7\). Squaring this gives \(7^2 = 49\). The second number in this pair is 47, not 49. This pair does not fit the \((n+2)^2\) pattern.

Based on the analysis, the pattern followed by options 1, 2, and 3 is that the second number is the square of the first number plus two \((n+2)^2\). Option 4, 5 - 47, does not follow this pattern.

Summary of Analysis

Conclusion: Identifying the Odd Pair

Since options 1, 2, and 3 all follow the pattern where the second number is the square of the first number plus two, option 4, which is 5 - 47, is the pair that is different from the others. It is the odd number pair.

Revision Table: Number Patterns and Squares

Understanding number patterns and square numbers is key to solving such problems. Here is a quick review:

• Number Pattern: A sequence or set of numbers that follows a specific rule or set of rules. Identifying the rule is crucial.
• Square Number: A number obtained by multiplying an integer by itself. For example, 9 is a square number because \(3 \times 3 = 9\), or \(3^2\).
• Common Patterns: Look for addition, subtraction, multiplication, division, powers (squares, cubes), sequences (arithmetic, geometric), or combinations of these operations.

Additional Information: Solving Odd Pair Questions

When tackling questions asking for the 'odd one out' or 'odd pair', consider these strategies:

• Examine the relationship within each pair (e.g., sum, difference, product, ratio, power, digit properties).
• Look for a common rule or pattern that applies to most items.
• The item that does not follow this common rule is usually the odd one out.
• Sometimes, the pattern might involve the position of the numbers or properties of the numbers themselves (e.g., prime vs. composite, even vs. odd).
• Test your hypothesized pattern against all options to confirm its validity.