Let A, Band Crepresent 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 the three distinct non-zero digits be A, B, and C. The possible 3-digit numbers formed by these digits without repetition are: ABC, ACB, BAC, BCA, CAB, CBA. To find the sum 'x' of these numbers: Each digit (A, B, C) appears twice in the hundreds place, twice in the tens place, and twice in the units place. For example, in the hundreds place, A appears in ABC and ACB. So, the sum x can be calculated as: x = (A+B+C) * 100 * 2 + (A+B+C) * 10 * 2 + (A+B+C) * 1 * 2 x = 200(A+B+C) + 20(A+B+C) + 2(A+B+C) x = 222(A+B+C) Now let's analyze each statement: Statement 1: The 4-digit least value of x is 1332. To find the least value of x, the sum (A+B+C) must be minimized. Since A, B, C are distinct non-zero digits, the smallest possible digits are 1, 2, and 3. So, the minimum sum (A+B+C) = 1 + 2 + 3 = 6. Substituting this into the formula for x: x = 222 * 6 = 1332. This value (1332) is indeed a 4-digit number. Therefore, the 4-digit least value of x is 1332. Statement 1 is correct. Statement 2: The 3-digit greatest value of x is 888. For x to be a 3-digit number, x must be less than 1000. So, 222(A+B+C) < 1000 A+B+C < 1000 / 222 A+B+C < 4.504... However, A, B, and C are distinct non-zero digits. The smallest possible sum for three distinct non-zero digits is 1+2+3 = 6. Since the minimum possible sum (A+B+C) is 6, which is greater than 4.504..., it is impossible for x to be a 3-digit number. The smallest possible value of x is 1332 (a 4-digit number), as calculated in Statement 1. Therefore, there is no 3-digit value for x, and Statement 2 is incorrect. Based on the analysis, only Statement 1 is correct. The final answer is A) 1 only