Understanding Number Set Relations

This question asks us to identify a numerical relationship or pattern that connects the numbers within a given set. We are provided with two sets that share the same hidden rule. Our task is to discover this rule and then find which of the given options follows the identical pattern.

Analyzing the Given Number Sets

Let's look at the two sets provided:

• Set 1: (30, 14, 8)
• Set 2: (84, 12, 36)

Let's denote the numbers in a set as (A, B, C). So, for Set 1, A=30, B=14, C=8. For Set 2, A=84, B=12, C=36. We need to find a mathematical operation or combination of operations relating A, B, and C that holds true for both sets.

Discovering the Pattern or Rule

We can try different combinations of operations on B and C to see if they relate to A. Let's consider simple arithmetic operations like addition, subtraction, multiplication, and division, or combinations of these.

Testing Potential Relationships on Set 1 (30, 14, 8):

• B + C = 14 + 8 = 22 (Not A)
• B * C = 14 * 8 = 112 (Not A)
• Let's try combinations: Maybe A is related to a sum or difference involving multiples of B and C.
• Consider 2C: \(2 \times 8 = 16\). B + 2C = \(14 + 16 = 30\). This matches A in Set 1!

So, a possible pattern is \(A = B + 2C\).

Verifying the Pattern on Set 2 (84, 12, 36):

Let's test the proposed pattern \(A = B + 2C\) on Set 2 (84, 12, 36), where A=84, B=12, C=36.

• Calculate B + 2C: \(12 + 2 \times 36\)
• \(12 + 72 = 84\). This matches A in Set 2!

The pattern \(A = B + 2C\) successfully describes the relationship between the numbers in both given sets.

Checking the Options for the Same Pattern

Now we will apply the pattern \(A = B + 2C\) to each of the given options to see which one follows the rule.

As shown in the table, only the set (108, 18, 45) satisfies the pattern \(A = B + 2C\).

Conclusion

The relationship between the numbers in the given sets (30, 14, 8) and (84, 12, 36) is described by the formula \(A = B + 2C\). By applying this rule to the options, we find that the set (108, 18, 45) follows the same pattern.

Revision Table: Number Set Relationships

Understanding patterns in number sets is a common type of logical reasoning question. Key strategies include:

• Identify the positions of the numbers (First, Second, Third).
• Explore relationships between pairs of numbers (e.g., Second and Third).
• Explore relationships between the first number and a combination of the other two.
• Test simple arithmetic operations (addition, subtraction, multiplication, division).
• Test combinations of operations (e.g., multiplying one number and adding another).
• Look for patterns involving squares, cubes, or other mathematical properties.
• Verify the found pattern on all given example sets.
• Apply the verified pattern to each option systematically.

Additional Information: Number Analogies

Questions involving number sets with similar relations are often called Number Analogies. They test your ability to identify logical rules governing numerical relationships. These rules can be simple arithmetic, more complex formulas, or even based on properties of numbers (like prime numbers, squares, etc.). Practicing different types of number analogy problems helps improve pattern recognition skills crucial for various aptitude tests.

In this specific case, the pattern was a linear combination of the second and third numbers to obtain the first number: \(First = Second + 2 \times Third\).