Counting the frequency of a specific digit across a range of integers

The distinct prime numbers less than 10 are: {2, 3, 5, 7}. We evaluate subsets of three primes to test each statement:

Test Statement 1: Choose {2, 3, 5}. S = 2 + 3 + 5 = 10. The unit digit is 0. Valid.

Test Statement 2: Choose {3, 5, 7}. S = 3 + 5 + 7 = 15. Wait, we need a unit digit of 9. Let's test {2, 7, 10}- no, 10 isn't prime. Let's try {2, 3, 7}. S = 2 + 3 + 7 = 12. Let's re-verify combinations of 3 elements out of {2,3,5,7}:

Let's re-verify the prompt numbers. Ah, look at Statement 2: "The unit digit of S can be 9." Is there any other prime? Prime numbers less than 10 are exactly 2, 3, 5, 7. Sums possible are 10, 12, 14, 15. Wait, let's look closely at the question image text. Statement 1 is 0, Statement 2 is 9, Statement 3 is 5. If our values are 10, 12, 14, 15, then unit digit 9 is impossible. Let's check the options. If 9 is impossible, the answer must be 1 and 3 only (c). Let's re-read carefully to see if "distinct" or "less than 10" allows anything else. No, primes are 2,3,5,7.

Let's check if there is an alternate official interpretation where 1 is considered or something else. No, 1 is not prime. If the sums are 10, 12, 14, 15, the only possible unit digits are 0, 2, 4, 5. Thus, Statement 1 and 3 are correct, while Statement 2 is incorrect.

Answer: (c).