Understanding Number Relations in Sets

The question asks us to find an option where the numbers share the same relationship as the numbers in the set (12, 60, 84). To solve this, we first need to analyze the relationship between the numbers in the given set.

Analyzing the Given Set (12, 60, 84)

Let's look at the numbers in the set (12, 60, 84). We can try to find a pattern based on multiplication, division, addition, or subtraction, often relating the first number to the subsequent numbers.

• Relating the second number (60) to the first number (12):
• We can see that 60 is a multiple of 12.
• Let's find the factor: \( \frac{60}{12} = 5 \)
• So, the second number is the first number multiplied by 5. \( 60 = 12 \times 5 \)
• Relating the third number (84) to the first number (12):
• We can see that 84 is also a multiple of 12.
• Let's find the factor: \( \frac{84}{12} = 7 \)
• So, the third number is the first number multiplied by 7. \( 84 = 12 \times 7 \)

The relationship in the given set (12, 60, 84) appears to be: (first number, first number \(\times\) 5, first number \(\times\) 7).

Checking the Options for the Same Number Relation

Now, let's apply this discovered relationship to each of the given options to find the set that follows the same pattern.

Option 1: (16, 80, 112)

• First number = 16
• Check the second number: Is \( 80 = 16 \times 5 \)?
• Calculation: \( 16 \times 5 = 80 \). Yes, it matches.
• Check the third number: Is \( 112 = 16 \times 7 \)?
• Calculation: \( 16 \times 7 = 112 \). Yes, it matches.

Option 1 follows the relationship (x, \(x \times 5\), \(x \times 7\)) where \(x = 16\).

Option 2: (14, 75, 98)

• First number = 14
• Check the second number: Is \( 75 = 14 \times 5 \)?
• Calculation: \( 14 \times 5 = 70 \). No, \( 75 \neq 70 \).

Option 2 does not follow the relationship.

Option 3: (15, 85, 105)

• First number = 15
• Check the second number: Is \( 85 = 15 \times 5 \)?
• Calculation: \( 15 \times 5 = 75 \). No, \( 85 \neq 75 \).

Option 3 does not follow the relationship.

Option 4: (13, 65, 81)

• First number = 13
• Check the second number: Is \( 65 = 13 \times 5 \)?
• Calculation: \( 13 \times 5 = 65 \). Yes, it matches.
• Check the third number: Is \( 81 = 13 \times 7 \)?
• Calculation: \( 13 \times 7 = 91 \). No, \( 81 \neq 91 \).

Option 4 does not follow the relationship.

Conclusion

Based on the analysis, only Option 1 (16, 80, 112) shares the same number relation as the given set (12, 60, 84).

Revision Table: Number Relation Analysis

Additional Information on Number Relation Questions

Number relation questions, often found in logical reasoning or quantitative aptitude sections, require identifying the underlying pattern or rule that connects the numbers in a given set or series. These patterns can involve basic arithmetic operations (addition, subtraction, multiplication, division), powers, roots, prime numbers, or a combination of these.

• Tips for Solving:
• Look for differences or ratios between consecutive numbers.
• Check if numbers are multiples or factors of each other.
• Consider if numbers are related to common series like primes, squares, or cubes.
• Test different simple arithmetic operations first.
• Apply the identified pattern rigorously to the options.

Practicing various types of number relation and number pattern questions helps improve the ability to quickly spot the underlying rule.