Finding the Relationship in Number Sets

The question asks us to identify the relationship between the numbers in the given sets and find an option set that follows the same relationship. We are given two example sets: (11, 13, 143) and (17, 11, 187).

Let's analyze the first set (11, 13, 143). We need to find a mathematical operation involving the first two numbers (11 and 13) that results in the third number (143). Common operations include addition, subtraction, multiplication, division, squaring, etc.

• Addition: \(11 + 13 = 24\), which is not 143.
• Subtraction: \(13 - 11 = 2\), which is not 143.
• Multiplication: \(11 \times 13 = 143\). This matches the third number in the set.

Now let's check if this relationship holds true for the second given set (17, 11, 187). The first two numbers are 17 and 11, and the third is 187.

• Multiplication: \(17 \times 11 = 187\). This also matches the third number in this set.

The relationship observed in both given sets is that the third number is the product of the first two numbers. Let's represent a set as \((A, B, C)\). The relationship is \(A \times B = C\).

Applying the Relationship to Options

We will now test each option to see which one follows the established relationship \(A \times B = C\), where A is the first number, B is the second, and C is the third.

Option 1: (3, 4, 7)

Here, \(A = 3\), \(B = 4\), \(C = 7\).

Let's check the relationship: \(A \times B = 3 \times 4 = 12\).

Since \(12 \neq 7\), this option does not follow the relationship.

Option 2: (3, 4, 13)

Here, \(A = 3\), \(B = 4\), \(C = 13\).

Let's check the relationship: \(A \times B = 3 \times 4 = 12\).

Since \(12 \neq 13\), this option does not follow the relationship.

Option 3: (3, 4, 12)

Here, \(A = 3\), \(B = 4\), \(C = 12\).

Let's check the relationship: \(A \times B = 3 \times 4 = 12\).

Since \(12 = 12\), this option follows the relationship.

Option 4: (3, 4, 1)

Here, \(A = 3\), \(B = 4\), \(C = 1\).

Let's check the relationship: \(A \times B = 3 \times 4 = 12\).

Since \(12 \neq 1\), this option does not follow the relationship.

Conclusion

Based on our analysis, only Option 3 (3, 4, 12) follows the same number relationship as the given sets (11, 13, 143) and (17, 11, 187), where the third number is the product of the first two.

Revision Table: Number Set Reasoning

Additional Information: Solving Number Analogy Questions

Number analogy questions are a common type in reasoning and quantitative aptitude tests. The key to solving them is systematically checking for common mathematical relationships between the numbers provided in the example set(s). Here are some strategies:

• Look for arithmetic operations: Check if the third number is the sum, difference, product, or quotient of the first two, or a combination of these.
• Consider powers and roots: The numbers might be related by squares, cubes, square roots, or cube roots.
• Check for patterns involving digits: Although this question specifically disallowed breaking down digits, many analogy questions might involve operations on individual digits.
• Look for sequential patterns: In some cases, the numbers might follow a sequence like arithmetic progression (AP) or geometric progression (GP), or have differences/ratios with a specific pattern.
• Try combinations: Sometimes the relationship might be a bit more complex, like \((A+B)^2 = C\) or \((A \times 2) + B = C\).
• Be systematic: Test common relationships in a structured way before looking for more complex ones.
• Use the given examples: Ensure that the relationship you identify holds true for *all* the example sets provided in the question.

By practicing and becoming familiar with common types of number relationships, you can solve these problems more efficiently.