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 ?

(UPSC CSAT – 2022)

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

Solution: Ans.(a)

The minimum possible value of three distinct non-zero digits (A, B, C) is 1,2,3.

All possible 3-digit numbers formed by A, B, and C without repetition are 123, 132, 213, 231, 312, and 321.

So, x = 123 + 132 +213 +231 + 312 + 321 = 1332.

So the least value of x is 1332.

Statement 1: The 4-digit least value of x is 1332: Correct.

Statement 2: The 3-digit greatest value of x is 888: False, as the least value of x is 1332.

Hence, the correct answer is option (a) i.e., 1 only.