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

Explanation : 

Problem: Find the digit P in 3798125P369 so that the number is divisible by 7

Step 1: Divide into Three-Digit Blocks (from right to left)
– Write as: 037, 981, 25P, 369
– This splits the number into blocks of three: 037|981|25P|369

Step 2: Apply Alternating Addition and Subtraction Rule
– Start from rightmost block: 369
– Then alternate: 369 – 25P + 981 – 037
– Note: This is based on the divisibility rule of 7 where we alternate adding and subtracting blocks of 3 digits

Step 3: Simplify the Expression
369 – (250 + P) + 981 – 37
= 369 – 250 – P + 981 – 37
= 1063 – P

Step 4: Solve for P Using Modulo 7
– For the number to be divisible by 7:
– 1063 – P must be divisible by 7
– 1063 ÷ 7 = 151 remainder 6
– So, 1063 ≡ 6 (mod 7)
– Therefore: 6 – P ≡ 0 (mod 7)
– This means P = 6

Answer: P = 6