**Question:-**

Consider the set S of the unit’s digit of all numbers which are expressible as the sum of exactly two prime numbers. How many digits do not occur in S?

**OPTIONS**

1) 0

2) 1

3) 4

4) 6

**Solution**

First, we note that we can find prime numbers ending with every possible odd digit – for example, 11, 3, 5, 7 and 19. We can add any two of these to get numbers ending with every possible even digit, so all even digits are necessarily members of S.

Now, 2 is also a prime number. By adding 2 to prime numbers ending with all possible odd digits, we will get numbers that are the sum of two prime numbers and end with all possible odd digits. Hence, all odd digits are also members of S.

Since S contains all odd and even digits, there is no digit which is not a member of S.

Hence, option 1.

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