A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A + B + C ?

To solve this, we have the equation ABC multiplied by D equals 37DD. Since A, B, C, and D are non-zero digits, we can test values for D. If D is 1, ABC would be 3711, which is a 4-digit number. This is impossible as ABC is a 3-digit number. If D is 5, 3755 divided by 5 equals 751. Here, A is 7, B is 5, and C is 1. However, the problem states that A, B, C, and D must be different digits. Since B and D are both 5, this value is rejected. If D is 6, 3766 divided by 6 does not result in a whole number. If D is 7, 3777 divided by 7 equals 539.57, which is not an integer. If D is 8, 3788 divided by 8 equals 473.5, which is not an integer. If D is 9, 3799 divided by 9 equals 422.11, which is not an integer. Now, let us try a smaller value for D. If D is 4, 3744 divided by 4 equals 936. Here, A is 9, B is 3, C is 6, and D is 4. All digits 9, 3, 6, and 4 are different and non-zero, satisfying all conditions of the problem. The value of A + B + C is 9 + 3 + 6 which equals 18. Therefore, option A is correct.