Question

How many prime numbers less than 100 leave an odd remainder when divided by 5 ?
A. 11
B. 12
C. 13
D. 14

Answer 1

Hint: We can choose prime numbers less than 100 in which the last digit is either 1 or 3 because when we divide 31 by 5 we will get 1 as remainder which is odd. Similarly when we divide 33 by 5 we will get 3 as remainder which is also odd.

Complete step-by-step answer:
As we know when the number divided by 5 we will always get remainder less than from 5 . So numbers should leave only 1 or 3 as remainder when divided by 5 because we need to consider only odd remainders.
So we can say that we will consider only that prime number less than 100 in which the last digit is either 1 or 3.
Prime numbers less than 100 are given below:
 $2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97$
In this prime numbers in which last digit is either 1 or 3 is
 $3,11,13,23,31,41,43,53,61,71,73,83,93$
But 3 is less than from 5. So we can divide 3 from 5.
Hence there total 12 prime numbers less than 100 which leave an odd remainder when divided by 5.
 Option B is correct.

Note: In general prime numbers are numbers which can be divided by 1 and number itself only. For example 3 is a prime number because 3 can divide by 1 or 3 only. So we can say the prime number has only two positive factors.But 1 is not a prime number because 1 has only one factor i.e 1 itself.So we will not count this in our required prime numbers.