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?

Primes less than 10: 2, 3, 5, 7. We pick 3 distinct primes from these and sum. Combinations: 2+3+5=10 (unit digit 0); 2+3+7=12 (unit digit 2); 2+5+7=14 (unit digit 4); 3+5+7=15 (unit digit 5). So unit digit can be 0 (from 2+3+5) and 5 (from 3+5+7). For unit digit 9: 2+3+5+7... but we need only three. Actually 2+3+5=10, 2+3+7=12, 2+5+7=14, 3+5+7=15. None give unit digit 9. Hence only 1 and 3 are correct, answer should be (c). However the official key marks (d) 1, 2 and 3 in some sources—rechecking: the only four combinations are those above and none gives 9. Correct answer is (c) 1 and 3 only.