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:
Both 1 and 2
Given:
Digits are non-zero and multiple of 3 i.e. 3, 6, 9
Number doesn't have repetition of digits.
Calculation:
The numbers thus formed are
369, 396, 639, 693, 936, 963
Sum of these numbers = 3996 and it is divisible by both 74 as well as 9.
Hence, option 3 is correct.
Important Questions from Divisibility and Remainder
If the 8-digit number 888x53y4 is divisible by 72, then what is the value of (7x + 2y), for the maximum value of y?
If all positive divisors of 132 are arranged in descending order, then what digit will be at unit place of first divisor ?
If 3 2019 is divided by 10, then what is the remainder?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?
