Finding the Different Number Pair

The question asks us to identify the number-pair that is different from the rest among the given four options. We need to look for a pattern or relationship between the two numbers in each pair.

Let's examine each pair and try to find a rule connecting the first number (let's call it \(n\)) to the second number.

Analyzing Each Number Pair

We will test a common pattern often found in such problems: relating the second number to the square of the first number.

• Pair 1: 7 : 51

  The first number is 7. Let's square it: \(7^2 = 49\). The second number is 51. We can see that \(49 + 2 = 51\). So, the pattern seems to be \(n : n^2 + 2\).

• Pair 2: 10 : 98

  The first number is 10. Let's square it: \(10^2 = 100\). The second number is 98. We can see that \(100 - 2 = 98\). So, the pattern here seems to be \(n : n^2 - 2\).

• Pair 3: 8 : 66

  The first number is 8. Let's square it: \(8^2 = 64\). The second number is 66. We can see that \(64 + 2 = 66\). This pair follows the pattern \(n : n^2 + 2\).

• Pair 4: 13 : 171

  The first number is 13. Let's square it: \(13^2 = 169\). The second number is 171. We can see that \(169 + 2 = 171\). This pair also follows the pattern \(n : n^2 + 2\).

Identifying the Different Pair

Let's summarize the patterns observed for each number-pair:

From the analysis, we can see that three number-pairs (7 : 51, 8 : 66, and 13 : 171) follow the pattern \(n : n^2 + 2\), where \(n\) is the first number and the second number is \(n^2 + 2\). The number-pair 10 : 98 follows a different pattern, which is \(n : n^2 - 2\).

Therefore, the number-pair that is different from the rest is 10 : 98.

Revision Table: Number Pair Patterns

The pair 10 : 98 is the odd one out because it follows a different rule compared to the other three pairs.

Additional Information: Number Series and Analogy Questions

Number series and number analogy questions, like this one involving number-pairs, are common in logical reasoning tests. They assess your ability to identify patterns and relationships between numbers.

Common patterns include:

• Arithmetic progression (adding/subtracting a constant)
• Geometric progression (multiplying/dividing by a constant)
• Squares or cubes of numbers
• Combinations of arithmetic/geometric operations with squares/cubes
• Prime numbers
• Fibonacci sequence
• Operations on digits of the number

To solve these questions, it's helpful to try different types of patterns systemically. Squaring or cubing the numbers is often a good starting point when the numbers grow rapidly, as seen in this number-pair problem.