Numerical Analogy Problem Solving

This question asks us to identify the relationship between pairs of numbers and use that relationship to find a missing number in a similar pair. We are given three pairs, where the second number in each pair is related to the first number in a specific way:

• 3856 : 8563
• 4893 : ?
• 2873 : 8732

Analyzing the Relationship in Numerical Pairs

Let's examine the digits and their positions in the given pairs to understand the pattern. We need to find the rule that transforms the first number into the second number in both the first and third pairs.

Analyzing the First Pair: 3856 to 8563

Let's look at the number 3856. The digits are 3, 8, 5, and 6. The second number is 8563. Let's see how the digits of 3856 are arranged in 8563.

• The digit '3', which is the first digit in 3856, is the last digit in 8563.
• The digit '8', which is the second digit in 3856, is the first digit in 8563.
• The digit '5', which is the third digit in 3856, is the second digit in 8563.
• The digit '6', which is the fourth digit in 3856, is the third digit in 8563.

This pattern suggests that the digits are shifted or rotated. Specifically, it appears that the first digit of the first number is moved to the end to form the second number.

Analyzing the Third Pair: 2873 to 8732

Let's test the hypothesized rule with the third pair: 2873 and 8732. The first number is 2873. Its first digit is '2'.

According to our rule, if we move the first digit ('2') to the end of 2873, we should get the second number. Let's perform this operation:

Starting number: 2873

Digits: 2, 8, 7, 3

Move the first digit (2) to the end:

New sequence: 8, 7, 3, 2

Forming the number: 8732

This matches the second number in the third pair (8732). So, the rule "move the first digit to the end" is consistent for both given pairs.

Applying the Rule to Find the Missing Number

Now we apply the same rule to the second pair: 4893 : ?

The first number is 4893. The first digit is '4'.

According to the rule, we move the first digit ('4') to the end of 4893 to find the missing number.

Starting number: 4893

Digits: 4, 8, 9, 3

Move the first digit (4) to the end:

New sequence: 8, 9, 3, 4

Forming the number: 8934

So, the missing number is 8934.

Checking the Options

Let's compare our result with the given options:

The number 8934 matches Option 1.

Conclusion

Based on the observed pattern in the numerical pairs 3856 : 8563 and 2873 : 8732, where the first digit of the first number is moved to the end to form the second number, applying this rule to 4893 gives us 8934. This matches one of the provided options.

Revision Table: Numerical Analogy

Additional Information: Types of Numerical Analogies

Numerical analogy questions often involve identifying mathematical relationships or patterns based on digit manipulation. Some common types of patterns include:

• Arithmetic Operations: Addition, subtraction, multiplication, division, squares, cubes, etc., applied to the number itself or its digits.
• Digit Manipulation: Rearranging digits (like in this problem), reversing digits, sum/product of digits, difference between digits, etc.
• Number Sequences: Identifying if the numbers follow a specific sequence or series pattern.
• Positional Changes: Rules based on the position of digits within the number.

Solving these types of problems requires careful observation of the given pairs and systematic testing of possible relationships.