Analyzing Number Relationships in Sets

The question asks us to identify a set of numbers that shares the same relationship between its elements as the two provided sets. We are given two example sets: (85, 24, 133) and (97, 36, 145). We need to find a consistent rule or pattern that connects the three numbers within each set.

Let's denote the numbers in a set as \(a\), \(b\), and \(c\), where \(a\) is the first number, \(b\) is the second, and \(c\) is the third. We must perform operations on the whole numbers themselves, not their individual digits.

Discovering the Pattern

Let's examine the relationship between the numbers in the given sets:

Set 1: (85, 24, 133)

• Relationship between the first and second number (\(a\) and \(b\)): \(85 - 24 = 61\)
• Relationship between the third and first number (\(c\) and \(a\)): \(133 - 85 = 48\)

Set 2: (97, 36, 145)

• Relationship between the first and second number (\(a\) and \(b\)): \(97 - 36 = 61\)
• Relationship between the third and first number (\(c\) and \(a\)): \(145 - 97 = 48\)

We observe that in both given sets, two consistent relationships hold true:

1. The difference between the first number and the second number is always 61 (\(a - b = 61\)).
2. The difference between the third number and the first number is always 48 (\(c - a = 48\)).

These two rules define the relationship between the numbers in the given sets.

Checking the Options

Now, we will check each option to see which set follows these same two rules:

Option 1: (79, 18, 127)

• Check Rule 1 (\(a - b = 61\)): \(79 - 18 = 61\). This matches the rule.
• Check Rule 2 (\(c - a = 48\)): \(127 - 79 = 48\). This also matches the rule.

This set satisfies both identified relationships.

Option 2: (71, 15, 124)

• Check Rule 1 (\(a - b = 61\)): \(71 - 15 = 56\). This does not match \(61\).
• Check Rule 2 (\(c - a = 48\)): \(124 - 71 = 53\). This does not match \(48\).

This set does not satisfy the relationships.

Option 3: (86, 23, 135)

• Check Rule 1 (\(a - b = 61\)): \(86 - 23 = 63\). This does not match \(61\).
• Check Rule 2 (\(c - a = 48\)): \(135 - 86 = 49\). This does not match \(48\).

This set does not satisfy the relationships.

Option 4: (67, 12, 111)

• Check Rule 1 (\(a - b = 61\)): \(67 - 12 = 55\). This does not match \(61\).
• Check Rule 2 (\(c - a = 48\)): \(111 - 67 = 44\). This does not match \(48\).

This set does not satisfy the relationships.

Conclusion

Only the set (79, 18, 127) from the options follows the same numerical relationships (\(a - b = 61\) and \(c - a = 48\)) observed in the given sets (85, 24, 133) and (97, 36, 145).

Revision Table - Number Relationship Patterns

Additional Information - Solving Number Analogy Questions

Number analogy and set relationship questions test your ability to identify mathematical patterns and logical rules connecting numbers. Here are some common approaches to solve such problems:

• Analyze the Given Examples: Spend time finding relationships within the provided sets. Look for differences, sums, products, quotients, squares, cubes, or combinations thereof between the numbers.
• Look for Consistent Rules: The rule must apply to ALL given examples. If you find a rule that works for one set but not the other, it's not the correct pattern.
• Test Simple Operations First: Start with basic arithmetic operations (addition, subtraction, multiplication, division) before moving to more complex ones (squares, cubes, roots, digit-based operations - though digit-based were restricted in this specific question).
• Consider Relationships Between Pairs: The relationship might be between the first and second number, first and third, or second and third. Or it could involve all three numbers together.
• Check All Options: Once you think you've found the rule, apply it to each of the options provided. Only one option will follow the exact same rule(s) as the given examples.
• Be Mindful of Constraints: Pay attention to any specific instructions, such as the constraint in this question about not breaking down numbers into constituent digits.

Practicing with different types of number relationship problems will help you quickly recognize common patterns.