Solving Number Analogy Questions

In this question, we are given two sets of numbers: (52, 34, 43) and (61, 33, 47). Our task is to find the relationship between the numbers in these sets and then identify the option set that follows the same relationship. The rule is to treat the numbers as whole entities and not break them down into individual digits.

Analyzing the Given Sets to Find the Pattern

Let's examine the first set: (52, 34, 43). Let's call the numbers A, B, and C respectively. So, A = 52, B = 34, C = 43.

We need to find a relationship between 52, 34, and 43. Let's try some basic operations:

• A + B = 52 + 34 = 86
• A - B = 52 - 34 = 18
• B + C = 34 + 43 = 77
• B - C = 34 - 43 = -9
• A + C = 52 + 43 = 95
• A - C = 52 - 43 = 9

Let's consider if one number is related to the sum or difference of the other two. We saw that A + B = 86. Notice that 43 is exactly half of 86.

So, a possible relationship is that the third number (C) is half the sum of the first two numbers (A and B).

Mathematically, this can be written as: \( C = \frac{A + B}{2} \) or \( A + B = 2C \).

Verifying the Pattern with the Second Set

Now, let's check if this relationship holds for the second set: (61, 33, 47). Here, A = 61, B = 33, and C = 47.

Let's apply the potential relationship \( C = \frac{A + B}{2} \):

\( \frac{61 + 33}{2} = \frac{94}{2} = 47 \)

This matches the third number C, which is 47. So, the relationship \( A + B = 2C \) or \( C = \frac{A + B}{2} \) is consistent across both given sets.

Applying the Pattern to the Options

We will now test each option set (A, B, C) to see if it satisfies the relationship \( A + B = 2C \).

Option 1: (58, 26, 42)

• A = 58, B = 26, C = 42
• Calculate A + B: \( 58 + 26 = 84 \)
• Calculate 2C: \( 2 \times 42 = 84 \)
• Since \( 84 = 84 \), the relationship \( A + B = 2C \) holds for this set.

Option 2: (57, 35, 42)

• A = 57, B = 35, C = 42
• Calculate A + B: \( 57 + 35 = 92 \)
• Calculate 2C: \( 2 \times 42 = 84 \)
• Since \( 92 \neq 84 \), the relationship does not hold for this set.

Option 3: (63, 41, 58)

• A = 63, B = 41, C = 58
• Calculate A + B: \( 63 + 41 = 104 \)
• Calculate 2C: \( 2 \times 58 = 116 \)
• Since \( 104 \neq 116 \), the relationship does not hold for this set.

Option 4: (69, 30, 45)

• A = 69, B = 30, C = 45
• Calculate A + B: \( 69 + 30 = 99 \)
• Calculate 2C: \( 2 \times 45 = 90 \)
• Since \( 99 \neq 90 \), the relationship does not hold for this set.

Conclusion

Only Option 1, the set (58, 26, 42), satisfies the relationship \( A + B = 2C \) that was identified in the given sets (52, 34, 43) and (61, 33, 47). Therefore, Option 1 is the correct answer.

Revision Table: Key Concepts for Number Analogy

Solving number analogy problems relies on identifying the mathematical or logical relationship between the numbers in the given sets. Here are common types of relationships:

• Arithmetic operations (addition, subtraction, multiplication, division)
• Combinations of operations (e.g., sum of first two equals twice the third)
• Squares, cubes, or roots
• Prime numbers, composite numbers
• Consecutive numbers or numbers with a fixed difference
• Relationships based on digits (though explicitly disallowed in this specific question)

Always test the potential relationship on all provided examples before applying it to the options.

Additional Information: Quantitative Reasoning Practice

Number analogy is a common type of question in quantitative reasoning and logical reasoning sections of competitive exams. Practicing these types of problems helps improve number sense, pattern recognition skills, and logical thinking. Pay close attention to any specific rules or constraints mentioned in the question, such as the rule about not breaking down numbers into digits in this problem.