In the number '45787259’, if the digits before 8 are added by 2 and the digits after 8 are subtracted by 1, then how many digits appear after the prime digit, in the new number formed?

The correct answer is Six.

Let us break down the logical steps to find the solution:

Step 1: Analyze the original number
The original number given in the question is 45787259. We need to perform different operations on the digits depending on their position relative to the digit 8.

Step 2: Apply the operations
Let us separate the digits of the number 45787259:

• Digits before 8: 4, 5, 7
• The middle digit: 8
• Digits after 8: 7, 2, 5, 9

Now, perform the operations as instructed:

For the digits before 8, add 2 to each digit:

$=\; 6$

$5\; +\; 2\; =\; 7$$7\; +\; 2\; =\; 9$

The digit 8 remains unchanged: 8

For the digits after 8, subtract 1 from each digit:$-\; 1\; =\; 6$$1\; =\; 1$

$5\; -\; 1\; =\; 4$$9\; -\; 1\; =\; 8$Step 3: Form the new number
Combining the modified digits in order, we get the new number:
67986148

Step 4: Identify the prime digit in the new number
Let us look at the digits of the new number: 6, 7, 9, 8, 6, 1, 4, 8.
Recall that a prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

• 6, 9, 8, and 4 are composite numbers.
• 1 is neither prime nor composite.
• 7 is a prime number.

Thus, the only prime digit in the new number is 7.

Step 5: Count the digits after the prime digit
In the new number 67986148, the prime digit 7 is at the second position. The digits appearing after 7 are:
9, 8, 6, 1, 4, 8

Counting these digits, we get a total of 6 digits.