Q. Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
Select the correct answer using the code given below:
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Correct Answer: (c) Both 1 and 2
Question from UPSC Prelims 2021 CSAT Paper
Explanation:
Sum of 3-Digit Numbers with Digits 3, 6, and 9
Given Digits: 3, 6, 9
Step 1: List all possible 3-digit combinations (without repetition)
1. 369
2. 396
3. 639
4. 693
5. 936
6. 963
Step 2: Calculate sum (S)
369 + 396 + 639 + 693 + 936 + 963 = 3996
Step 3: Verify divisibility by 74
3996 ÷ 74 = 54
Therefore, 3996 is divisible by 74
Step 4: Verify divisibility by 9
3996 ÷ 9 = 444
Therefore, 3996 is divisible by 9
