The number 3798125P369 is divisible by 7. What is the value of the digit P?

(37) (981) (25P) (369)

Then, it calculates the difference between the first two triplets and the last two triplets:
369 – 25P + 981 – 37 = 1350 – 25P – 37 = 1313 – 25P

Dividing 1313 by 7 yields a remainder of 4.

Since 25P must be in the range of 250 to 259 to maintain divisibility by 7, it checks which number in this range, when added to 4, is divisible by 7. The options are 252 and 259.

After calculating, it verifies that the resulting number, 1313 – 256, is divisible by 7.

Thus, the value of P is confirmed to be 6.

Therefore, option (b) is correct.