20. 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. A. 1 and 2 only
2. B. 2 and 3 only
3. C. 1 and 3 only
4. D. 1, 2 and 3

Answer: C

Explanation

The distinct prime numbers less than 10 are 2, 3, 5, and 7. We need to find three distinct primes (x, y, z) from this set and check the unit digit of their sum S = x + y + z.
1. Unit digit of S can be 0: If we choose the primes (2, 3, 5), their sum S = 2 + 3 + 5 = 10. The unit digit is 0. So, statement 1 is correct.
2. Unit digit of S can be 9: Let’s test combinations: (2, 3, 7) sum is 12 (unit digit 2); (2, 5, 7) sum is 14 (unit digit 4); (3, 5, 7) sum is 15 (unit digit 5). No combination of three distinct primes less than 10 results in a sum with a unit digit of 9. So, statement 2 is incorrect.
3. Unit digit of S can be 5: If we choose the primes (3, 5, 7), their sum S = 3 + 5 + 7 = 15. The unit digit is 5. So, statement 3 is correct.
Therefore, statements 1 and 3 are correct. This question tests knowledge of prime numbers and basic arithmetic operations.