Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition. Consider the following statements: 1. The 4-digit least value of x is 1332. 2. The 3-digit greatest value of x is 888 Which of the above statements is/are correct?

Let A, B, C be distinct non-zero digits. The possible 3-digit numbers formed by A, B, C without repetition are: ABC = 100A + 10B + C ACB = 100A + 10C + B BAC = 100B + 10A + C BCA = 100B + 10C + A CAB = 100C + 10A + B CBA = 100C + 10B + A

The sum x of all these numbers is: x = (100A + 10B + C) + (100A + 10C + B) + (100B + 10A + C) + (100B + 10C + A) + (100C + 10A + B) + (100C + 10B + A) x = (100+100+10+1+10+1)A + (10+1+100+100+1+10)B + (1+10+1+10+100+100)C x = 222A + 222B + 222C x = 222(A + B + C)

Now let's analyze the statements:

Statement 1: The 4-digit least value of x is 1332. To find the least value of x, we must choose the smallest distinct non-zero digits for A, B, C. These are 1, 2, and 3. So, A + B + C = 1 + 2 + 3 = 6. The least value of x = 222 * 6 = 1332. This is indeed a 4-digit number. Therefore, Statement 1 is correct.

Statement 2: The 3-digit greatest value of x is 888. For x to be a 3-digit number, it must be less than 1000. x = 222(A + B + C) < 1000 A + B + C < 1000 / 222 A + B + C < 4.50... Since A, B, C are distinct non-zero digits, the smallest possible sum (A + B + C) is 1 + 2 + 3 = 6. Since 6 is not less than 4.50..., it means that x can never be a 3-digit number. The minimum value of x is 1332 (as calculated in Statement 1), which is a 4-digit number. Therefore, Statement 2 is incorrect because x can never be a 3-digit number.

Conclusion: Statement 1 is correct. Statement 2 is incorrect.

The final answer is A