Understanding the Number Relationship

The question asks us to identify the relationship between the numbers in the set (11, 13, 17) and find another set from the options that shares the same relationship.

Let's carefully examine the numbers in the given set: 11, 13, and 17.

• 11 is a prime number (divisible only by 1 and itself).
• 13 is a prime number (divisible only by 1 and itself).
• 17 is a prime number (divisible only by 1 and itself).

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

The primary characteristic of the set (11, 13, 17) appears to be that all three numbers are prime numbers.

Analyzing the Options

Now, let's check each option to see which one contains a set of numbers where all elements are prime numbers.

Option 1: (61, 63, 65)

• 61 is a prime number.
• 63 is not a prime number because it is divisible by numbers other than 1 and 63 (e.g., 3, 7, 9, 21). For example, 63 = 9 × 7.
• 65 is not a prime number because it is divisible by numbers other than 1 and 65 (e.g., 5, 13). For example, 65 = 5 × 13.

Since 63 and 65 are not prime numbers, this set does not match the relationship in the given set.

Option 2: (29, 31, 33)

• 29 is a prime number.
• 31 is a prime number.
• 33 is not a prime number because it is divisible by numbers other than 1 and 33 (e.g., 3, 11). For example, 33 = 3 × 11.

Since 33 is not a prime number, this set does not match the relationship in the given set.

Option 3: (41, 43, 53)

• 41 is a prime number.
• 43 is a prime number.
• 53 is a prime number.

All three numbers in this set (41, 43, 53) are prime numbers. This matches the relationship observed in the given set (11, 13, 17).

Option 4: (9, 25, 17)

• 9 is not a prime number because it is divisible by 3 (9 = 3 × 3).
• 25 is not a prime number because it is divisible by 5 (25 = 5 × 5).
• 17 is a prime number.

Since 9 and 25 are not prime numbers, this set does not match the relationship in the given set.

Conclusion

Based on the analysis, the relationship in the given set (11, 13, 17) is that all three numbers are prime numbers. Option 3, the set (41, 43, 53), is the only option where all three numbers are also prime numbers.

Revision Table: Number Properties

Additional Information: Prime Numbers and Number Analogy

Number analogy questions often test your ability to find patterns or relationships between numbers in a given set and apply that same logic to find a matching set. Common relationships include arithmetic progression (constant difference), geometric progression (constant ratio), squares, cubes, prime numbers, odd/even numbers, sums, differences, products, or combinations of these.

Identifying prime numbers is a fundamental skill in number theory and is frequently used in logical reasoning and quantitative aptitude questions. Remember that 1 is not considered a prime number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, and so on.

In this specific problem, recognizing the prime nature of all numbers in the initial set was the key to solving the analogy.