Question

Sum of the number of primes between 16 to 80 and 90 to 100 is
A. 20
B. 18
C. 17
D. 16

Answer 1

Hint: We can list all the prime numbers between 16 and 80 and count them. Then we can list the prime numbers between 90 to 100 and count them. Then we can add these numbers together to get the required sum.

Complete step by step answer:

We know that prime numbers are the numbers having no factors other than 1 and the number itself. Now we can list all the prime numbers between 16 and 80.
They are 17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79.
By counting, we can say that the number of primes between 16 and 80 is 16.
Now we can list the primes between 90 and 100. It is 97.
Therefore, the number of primes between 90 and 100 is 1.
Now we have the number of primes between 16 and 80 is 16 and the number of primes between 90 and 100 as 1.
So, to get the required sum, we can add 16 and 1.
$ \Rightarrow sum = 16 + 1$
$ \Rightarrow sum = 17$
Therefore, the required sum is 17.
So, the correct answer is option C.

Note: Prime numbers are the numbers which have factor 1 and the number itself. All the even numbers except 2 are not prime numbers. Prime numbers greater than 10 have any of the 1, 3, 7, 9 in the unit’s place. We used this property to list all the prime numbers. After listing we can recheck whether any number has any factors other than 1 and the number itself.