Solving Numerical Analogy: 132 to 501, 2364 to ?

This question asks us to find the relationship between the first two numbers in a pair and apply that same relationship to the third number to find the fourth missing number. The given analogy is 132 : 501 :: 2364 : ?

We need to identify the pattern or rule that connects 132 and 501. Let's explore different possibilities:

Analyzing the Relationship between 132 and 501

Let's look at the digits of the numbers and potential mathematical operations or properties.

• Addition/Subtraction: $501 - 132 = 369$. Adding 369 to 2364 gives $2364 + 369 = 2733$, which is not among the options.
• Multiplication/Division: $501 \div 132 \approx 3.79$. Multiplying 2364 by approximately 3.79 would yield a number around 8960, not in the options.
• Digit-based relationships: Let's examine the digits:
  • Sum of Digits:
    • Sum of digits for 132: $1 + 3 + 2 = 6$.
    • Sum of digits for 501: $5 + 0 + 1 = 6$.

    The sum of the digits is the same for both numbers in the first pair.

  • Other digit operations (like product of digits, squaring digits, reversing digits) do not seem to yield a simple relationship that connects 132 and 501 directly to 6. The sum of digits appears to be the most likely pattern.

Applying the Sum of Digits Rule to 2364

Assuming the relationship is that the sum of digits is constant between the two numbers in each pair, let's apply this rule to the second pair (2364 : ?).

First, calculate the sum of digits for the number 2364:

Sum of digits for 2364 = $2 + 3 + 6 + 4 = 15$.

Now, we need to find the option among the given choices whose digits sum up to 15.

Evaluating the Options

Let's calculate the sum of digits for each provided option:

Based on the sum of digits calculation, only option 1 (5073) has a sum of digits equal to 15, which is the same as the sum of digits for 2364.

Conclusion for Numerical Analogy

The relationship between the first pair (132 and 501) is that they have the same sum of digits (6). Applying this rule to the third number (2364), we find its sum of digits is 15. The fourth number must also have a sum of digits equal to 15. Among the given options, only 5073 satisfies this condition.

Revision Table: Key Concepts

Additional Information: Types of Numerical Analogies

Numerical analogy questions can involve various types of relationships between numbers. Some common types include:

• Basic arithmetic operations (addition, subtraction, multiplication, division).
• Squaring or cubing numbers or their digits.
• Operations on individual digits (sum of digits, product of digits, reversing digits).
• Prime numbers, composite numbers, or other number properties.
• Sequential patterns or series logic.

Solving these problems requires careful observation and systematic testing of possible relationships.