Finding the Odd Number Pair

The question asks us to identify the number pair that does not follow the same pattern as the other pairs provided in the options. We need to examine each pair and find the relationship between the first and second number in the pair.

Analyzing Each Number Pair Option

Analysis of Option 1: 10 – 99

Let's look at the relationship between 10 and 99. If we square the first number, 10, we get:

\(10^2 = 100\)

The second number is 99. We can see that 99 is one less than 100.

\(100 - 1 = 99\)

So, the pattern observed here is: the second number is the square of the first number minus one. This can be written as \(n \rightarrow n^2 - 1\).

Analysis of Option 2: 12 – 143

Now let's examine the second pair, 12 and 143. Let's square the first number, 12:

\(12^2 = 144\)

The second number is 143. Again, we see that 143 is one less than 144.

\(144 - 1 = 143\)

This pair also follows the pattern: the second number is the square of the first number minus one, or \(n \rightarrow n^2 - 1\).

Analysis of Option 3: 14 – 195

Let's look at the third pair, 14 and 195. Squaring the first number, 14, gives us:

\(14^2 = 196\)

The second number is 195. We observe that 195 is one less than 196.

\(196 - 1 = 195\)

This pair also follows the same pattern: the second number is the square of the first number minus one, or \(n \rightarrow n^2 - 1\).

Analysis of Option 4: 8 – 65

Finally, let's analyze the fourth pair, 8 and 65. Squaring the first number, 8, we get:

\(8^2 = 64\)

The second number is 65. In this case, 65 is one more than 64.

\(64 + 1 = 65\)

This pair follows a different pattern: the second number is the square of the first number plus one, or \(n \rightarrow n^2 + 1\).

Identifying the Pattern Difference

From our analysis, we can see that the first three pairs (10-99, 12-143, and 14-195) all follow the pattern where the second number is obtained by squaring the first number and subtracting 1 (\(n^2 - 1\)).

However, the fourth pair (8-65) follows a different pattern, where the second number is obtained by squaring the first number and adding 1 (\(n^2 + 1\)).

Conclusion: The Odd Number Pair

Since the pair 8 – 65 follows a different rule compared to the other three pairs, it is the odd one out.

Revision Table: Number Pair Analysis

Additional Information: Number Patterns and Squares

Finding patterns in number pairs is a common type of question in reasoning tests. These patterns can involve various mathematical operations, including squaring, cubing, addition, subtraction, multiplication, division, or combinations of these.

Squaring a number (\(n^2\)) means multiplying the number by itself. For example, \(5^2 = 5 \times 5 = 25\). Recognizing the squares of common numbers is very helpful for solving these types of pattern questions quickly.

Other common patterns you might encounter include:

• \(n \rightarrow n^2 + n\)
• \(n \rightarrow n^2 - n\)
• \(n \rightarrow n^3\)
• \(n \rightarrow n^3 + 1\)
• \(n \rightarrow 2n + c\) (where c is a constant)
• \(n \rightarrow n \times (n-1)\)

Always test a potential pattern against all given options to confirm it holds true for most of them before identifying the odd one out.