If 9A4156B is divisible by 15, then what is the minimum value of A - B?Options :0125

The divisibility rule for 15 is that the number must be divisible by both 3 and 5.

For divisibility by 5, the last digit of the number must be either 0 or 5. Here, the last digit is B. So, B must be 0 or 5.

For divisibility by 3, the sum of all digits in the number must be divisible by 3. Here, if we add up the given digits, we get 9 + 4 + 1 + 5 + 6 = 25. Adding A and B to this sum, we get 25 + A + B. For this to be divisible by 3, (A + B) must be 1 or 4 or 7 or 10, etc.

Now, we need to find the minimum value of (A - B).

If we take B as 0 (the minimum possible value), then A must be 1 (to make A + B = 1, the minimum possible value). So, A - B = 1 - 0 = 1.

If we take B as 5 (the other possible value), then A must be 4 or 7 or 10, etc. (to make A + B divisible by 3). The minimum value here is 4, so A - B = 4 - 5 = -1.

Therefore, the minimum value of A - B is -1. So, the answer is option 2.

The divisibility rule for 15 is that the number must be divisible by both 3 and 5.

For a number to be divisible by 5, its last digit must be either 0 or 5. Here, the last digit is B, so B must be 0 or 5.

For a number to be divisible by 3, the sum of its digits must be divisible by 3. If we add up the given digits, we get 9 + 4 + 1 + 5 + 6 = 25. If we add A and B to this sum, the total must be divisible by 3.

If B is 0, then A must be a digit such that 25 + A is divisible by 3. The smallest such digit is 1, so the smallest possible value of A - B is 1 - 0 = 1.

If B is 5, then A must be a digit such that 25 + A + 5 is divisible by 3. The smallest such digit is 2, so the smallest possible value of A - B is 2 - 5 = -3.

Therefore, the minimum value of A - B is -3. So, the correct option is 5.