Understanding the Number Analogy Pattern

This question involves finding a logical or arithmetic relationship between two pairs of numbers. We need to identify the pattern in the first pair ($21463 : 43685$) and apply it to the second pair ($38521 : ?$) to find the missing number.

Analyzing the First Pair Relationship

Let's examine the transformation from the first number, $21463$, to the second number, $43685$. We compare each digit at the corresponding position:

• The first digit: $2$ becomes $4$.
• The second digit: $1$ becomes $3$.
• The third digit: $4$ becomes $6$.
• The fourth digit: $6$ becomes $8$.
• The fifth digit: $3$ becomes $5$.

It is clear that each digit in $21463$ has been increased by $2$ to produce the digits in $43685$.

Establishing the Core Pattern

This digit-by-digit increase by 2 can be consistently represented as adding the number $22222$ to the original number.

Let's verify this using mathematical notation:

$21463 + 22222 = 43685$

The calculation confirms that adding $22222$ is the correct pattern applied to the first pair.

Applying the Pattern to Find the Missing Number

Now, we apply the identified pattern, adding $22222$, to the second number, $38521$, to find the missing number:

$38521 + 22222 = ?$

Let's perform the addition step-by-step:

The result of the addition is $60743$.

Selecting the Correct Option

We compare the obtained result with the provided options:

• Option 1: $50643$
• Option 2: $67890$
• Option 3: $60753$
• Option 4: $60743$

The calculated missing number, $60743$, matches Option 4.