Directions: Identify the number that completes the analogy. Apply each operation to the complete number, not to its individual digits.

? : 8421 :: 4813 : 4833 :: 7625 : 7645

The correct option is 8401.

Step-by-Step Explanation:

To identify the number that completes the analogy, we need to analyze the mathematical pattern connecting the numbers in each given pair.

Let's examine the second given pair:

$4813:4833$

Subtracting the first number from the second number:

$4833-4813=20$

This shows that the second number is obtained by adding 20 to the first number.

Now, let's check the third pair to confirm the rule:

$7625:7645$

Subtracting the first number from the second number:

$7645-7625=20$

The pattern holds true across both given pairs: adding 20 to the first term yields the second term.

Now, apply this exact operation to the first pair:

$?:8421$

Let $x$ represent the missing number $?$. According to the rule:

$x+20=8421$

Solving for $x$:

$x=8421-20=8401$

Therefore, the number that completes the analogy is 8401.