The sum of three digits x, y and z is 12 . What is the largest 3-digit number that can be found using each of the digits exactly once ?

To find the largest 3-digit number using the digits x, y, and z (where x + y + z = 12), you want to maximize the leftmost digit to make the number as large as possible.

The largest possible leftmost digit is 9, as it's the largest single-digit number. To form the largest 3-digit number, you should place 9 as the leftmost digit. Now, you need to arrange the remaining digits (x and y) in the rightmost positions to maximize the number further.

To maximize the number, you should place the next largest digit (8, if available) in the hundreds place and the remaining digit in the tens place. If 8 is not available, use the next largest available digit.

So, if we place 9 in the hundreds place, and if x and y are the remaining digits, the largest number will be 9xy.

Now, we need to find the combination of x and y that adds up to 12. The only combination that satisfies this is x = 3 and y = 0.

So, the largest 3-digit number using the digits x, y, and z (where x + y + z = 12) is 930.

Therefore, the correct answer is 930.