Question

What is the sum of the prime numbers between 90 to 100.
[a] 188
[b] 281
[c] 376
[d] 97

Answer 1

Hint: Recall the definition of prime numbers. List all the prime numbers between 90 to 100 and hence find their sum.

Complete step-by-step answer:
Prime number: A number p is said to be prime if it has exactly two divisors. Excluding 1, any number which has 1 and itself as the only divisors is prime.
Checking 90 for primality:
Since 90 is divisible by 2, 90 is not a prime number.
Checking primality of 91:
Since 91 is divisible by 7, 91 is not a prime number
Checking primality of 92:
Since 92 is divisible by 2, 92 is not a prime number
Checking primality of 93:
Sum of digits of 93 = 9+3 = 12 which is divisible by 3. Hence, 93 is divisible by 3, and hence 93 is not a prime number.
Checking primality of 94:
Since 94 is divisible by 2, 94 is not a prime number.
Checking primality of 95:
Since the digit at units place of 95 is 5, 95 is divisible by 5, and hence 95 is not a prime number.
Checking primality of 96:
Since 96 is divisible by 2, 96 is not a prime number.
Checking primality of 97:
97 is divisible only by 1 and 97. Hence 97 is a prime number.
Checking primality of 98:
98 is divisible by 2, and hence 98 is not a prime number.
Checking primality of 99:
Sum of digits of 99 = 9+9 = 18 which is divisible by 3. Hence 99 is divisible by 3, and hence 99 is not a prime number.
Checking primality of 100:
Since 100 is divisible by 2, 100 is not a prime number.
Hence 97 is the only prime number between 90 to 100, and hence the sum of all prime numbers between 90 to 100 is 97
Hence option [d] is correct.
Note: [1] In order to be sure that a number is a prime check that the number is not divisible by any of the numbers greater than 1 but less or equal to the square root of the number. Many students do not check that and end up having incorrect results. Also, note that 1 is not a prime.