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

The given number is in hexadecimal form. A number is divisible by 15 in hexadecimal if and only if it is divisible by both 3 and 5.

For divisibility by 3, the sum of the digits must be divisible by 3. The sum of the given digits is 9 + A + 4 + 1 + 5 + 6 + B = 25 + A + B. For this to be divisible by 3, A + B must be a multiple of 3. The minimum values of A and B are 0 and 1, so the minimum value of A + B is 1.

For divisibility by 5, the last digit must be 0 or 5. Here, the last digit is B, so B must be 0 or 5.

Combining these two conditions, the minimum value of A - B is achieved when A = 1 and B = 0, which gives A - B = 1 - 0 = 1. So, the minimum value of A - B is 1.