Consider all 3-digit numbers (without repetition of 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:
1 only
2 only
Both 1 and 2
Neither 1 nor 2
This question looks like difficult logic based but is instead calculation intensive. There are only three non-zero digits which are multiples of 3: 3, 6, and 9. Since repetition of digits is not allowed, Using these 3 digits, we can make 3P2 or 3!, i.e. 6 three-digit numbers. 369 396 639 693 936 963 So their sum, S = 369 + 396 + 639 + 693 + 936 + 963 = 3996 We can check that, S is divisible by both 74 and 9 using any division technique.
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