A five-digit number XY235 is divisible by 3 where X and Y are digits satisfying X + Y ≤ 5. What is the number of possible pairs of values of (X, Y)?
7
Divisibility by three requires X + Y + 10 to be a multiple of three. With X ≥ 1 and X + Y ≤ 5, the sum X+Y is 2 or 5. There are 2 and 5 pairs respectively, totalling 7.
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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:
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?