Consider the following statements in respect of the sum $S = x + y + z$, where x, y and z are distinct prime…
Consider the following statements in respect of the sum $S = x + y + z$, where x, y and z are distinct prime numbers each less than 10:
1. The unit digit of S can be 0.
2. The unit digit of S can be 9.
3. The unit digit of S can be 5.
Which of the statements given above are correct?
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
Solution
Distinct primes less than 10 are 2, 3, 5, 7. Choosing $S = 2 + 3 + 5 = 10$ gives unit digit 0 (statement 1 correct). Choosing $S = 3 + 5 + 7 = 15$ gives unit digit 5 (statement 3 correct). No combination gives unit digit 9, so statement 2 is incorrect. Hence statements 1 and 3 only are correct.