Question

The unit-digit of every prime number (other than 2 and 5) must necessarily
1) 1, 3 or 5
2) 1, 3, 7 or 9
3) 7 or 9
4) 1 or 7

Answer 1

Hint: Here, we will first use the fact that all even numbers are composite other than 2. Then we will exclude all the numbers, which are divisible by 2 and then compute the unit digits of the remaining numbers to find the required value.

Complete step by step solution:
We know that all the even numbers (other than 2) are composite, which ends with the digits 0, 2, 4, 6 or 8.

So, the prime numbers (other than 2) cannot have 0, 2, 4, 6, or 8 in their unit digits.

Since we have to find the units of the prime number excluding 2 and 5, we are only left with 1, 3, 7 and 9.

Thus, the unit digit of every prime number (other than 2 and 5) must necessarily be 1, 3, 7 or 9.

Hence, option B is correct.

Note: In this question, we have to know the concept of even numbers, composite numbers and prime numbers. Some students include the number 2 as a composite number, which is wrong so the unit-digit of every prime number will never have a number divisible by 2.