Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers…
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?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
Using 3 distinct digits, 6 three-digit numbers can be formed and x = 222(A + B + C). The least 4-digit value uses the smallest digits 1, 2, 3: x = 222 x 6 = 1332, so statement 1 is correct. Statement 2 is incorrect: 888 cannot be achieved as the greatest 3-digit value of x with three distinct non-zero digits. Hence only 1.