Finding the Different Number Pair in Analogy

The question asks us to find the number pair that is different from the other three given pairs. This type of question tests our ability to identify patterns and relationships between numbers.

We are given four number pairs:

• 11 : 143
• 19 : 475
• 23 : 667
• 17 : 323

We need to examine each pair and determine the rule or pattern that connects the first number to the second number.

Analysing the Relationship Between Numbers

Let's consider the possibility that the second number is a multiple of the first number. We can divide the second number by the first number to find the multiplier for each pair.

So, for each pair \( (x, y) \), we found a multiplier \( k \) such that \( y = x \times k \). The multipliers are 13, 25, 29, and 19.

Identifying the Underlying Pattern

Now, let's look closely at these multipliers: 13, 25, 29, and 19. We need to find a property that applies to three of these numbers but not to the fourth.

• The number 13 is a prime number (it is only divisible by 1 and itself).
• The number 25 is a composite number (it is divisible by 1, 5, and 25. Specifically, \(25 = 5 \times 5\)).
• The number 29 is a prime number (it is only divisible by 1 and itself).
• The number 19 is a prime number (it is only divisible by 1 and itself).

Three of the multipliers (13, 29, and 19) are prime numbers, while one multiplier (25) is a composite number.

This reveals the pattern: In three of the number pairs, the second number is the first number multiplied by a prime number. In the remaining pair, the second number is the first number multiplied by a composite number.

Determining the Different Pair

The pair 19 : 475 has a multiplier of 25, which is a composite number. This makes it different from the other three pairs, where the multipliers are prime numbers.

Conclusion

The number pair that is different from the rest is 19 : 475 because the relationship between 19 and 475 is \(475 = 19 \times 25\), where 25 is a composite number, while the other pairs have a prime number as the multiplier.

Revision Table: Number Pair Pattern Analysis

Additional Information: Understanding Prime and Composite Numbers in Patterns

Pattern recognition in number series and analogies often relies on fundamental number properties like being prime or composite. Remembering the definitions helps in identifying the differentiating factor.

• Prime Numbers: These are whole numbers greater than 1 that have only two positive divisors: 1 and themselves. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, etc.
• Composite Numbers: These are whole numbers greater than 1 that have more than two positive divisors. Any whole number greater than 1 that is not prime is composite. The first few composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, etc.

Recognizing whether a number is prime or composite is a useful skill in solving various types of reasoning and quantitative aptitude questions where number properties form the basis of the pattern.