Understanding Number Relations in Sets

The question asks us to identify a set of numbers from the given options that shares the same relationship between its elements as found in the two provided sets: (15, 20, 4) and (30, 30, 3). We are instructed to perform operations only on the whole numbers themselves, without breaking them down into individual digits.

Analyzing the Given Number Sets

Let's examine the relationship between the three numbers in each set. Let the numbers in a set be represented as A, B, and C. The given sets are:

• Set 1: (A, B, C) = (15, 20, 4)
• Set 2: (A, B, C) = (30, 30, 3)

We need to find a pattern or a mathematical relationship that connects A, B, and C which is consistent across both sets.

Let's try different common operations relating A, B, and C:

• Could B be related to A and C using simple arithmetic?
• Maybe B is a result of an operation involving A and C.

Consider Set 1 (15, 20, 4):

• Sum: $15 + 4 = 19$ (not 20)
• Difference: $15 - 4 = 11$ (not 20) or $4 - 15 = -11$ (not 20)
• Product: $15 \times 4 = 60$ (not 20)
• Division: $15 \div 4 = 3.75$ (not 20) or $4 \div 15$ (not 20)

Let's try combining operations or involving a constant factor. What if B is derived from the product of A and C?

In Set 1: $A \times C = 15 \times 4 = 60$. B is 20. We can see that $60 \div 3 = 20$. So, it looks like $B = (A \times C) \div 3$.

Verifying the Pattern on the Second Set

Let's test the proposed relationship $B = (A \times C) \div 3$ on Set 2 (30, 30, 3).

• A = 30, B = 30, C = 3
• According to the pattern: $(A \times C) \div 3 = (30 \times 3) \div 3 = 90 \div 3 = 30$.
• This result (30) matches the value of B in Set 2 (30).

The relationship $B = (A \times C) \div 3$ holds true for both given sets. This is the pattern we need to look for in the options.

Applying the Pattern to the Options

We will now check each option to see which set follows the relation $B = (A \times C) \div 3$.

Option 1: (44, 187, 44)

• A = 44, B = 187, C = 44
• Calculate $(A \times C) \div 3$: $(44 \times 44) \div 3 = 1936 \div 3$.
• 1936 is not perfectly divisible by 3. $1936 \div 3 \approx 645.33$. This is not equal to 187.
• Option 1 does not follow the pattern.

Option 2: (30, 190, 15)

• A = 30, B = 190, C = 15
• Calculate $(A \times C) \div 3$: $(30 \times 15) \div 3 = 450 \div 3$.
• $450 \div 3 = 150$. This is not equal to 190.
• Option 2 does not follow the pattern.

Option 3: (35, 120, 19)

• A = 35, B = 120, C = 19
• Calculate $(A \times C) \div 3$: $(35 \times 19) \div 3 = 665 \div 3$.
• 665 is not perfectly divisible by 3. $665 \div 3 \approx 221.67$. This is not equal to 120.
• Option 3 does not follow the pattern.

Option 4: (60, 400, 20)

• A = 60, B = 400, C = 20
• Calculate $(A \times C) \div 3$: $(60 \times 20) \div 3 = 1200 \div 3$.
• $1200 \div 3 = 400$. This is equal to 400, which is the value of B in this set.
• Option 4 follows the pattern.

Based on the analysis, the set (60, 400, 20) exhibits the same relationship between its numbers as the given sets (15, 20, 4) and (30, 30, 3), which is $B = (A \times C) \div 3$.

Summary of Option Verification

The table clearly shows that only Option 4 matches the established number relation pattern.

Revision Table: Key Concepts

Additional Information: Logical Reasoning and Number Analogy

This type of question falls under logical reasoning, specifically number analogy or number puzzles. The goal is to decipher the underlying logical or mathematical rule that connects the numbers in a given set or pair of sets and apply that rule to find a matching option.

Strategies for solving number relation problems often involve:

• Analyzing position: Look at the first, second, and third numbers (A, B, C). How might C relate to A? How might B be derived from A and C?
• Considering basic operations: Test addition, subtraction, multiplication, division, squares, cubes, square roots, etc., between the numbers.
• Looking for ratios or proportions: Sometimes numbers are related by a constant multiplier or divisor.
• Combining operations: The relation might involve multiple steps, like in this case (multiplication followed by division).
• Testing consistency: Ensure the identified pattern works for all provided examples (in this case, both sets).

Practice with various types of number relation and analogy problems helps improve pattern recognition skills, which are vital for quantitative aptitude and logical reasoning sections in competitive exams.