Question

The average of the least and the greatest prime number of 2-digits is
A. 54
B. 55
C. 54.5
D. 55.5

Answer 1

Hint: Before solving this question, we should know what prime numbers are. Prime numbers are the numbers having only two factors, that is 1 and the number itself. For example, 2, 3, 5, 7, etc. Now, the smallest 2-digit prime number is 11 and the greatest 2-digit prime number is 97. So the average of the least and the greatest 2-digit prime numbers is $\dfrac{97+11}{2}$.

Complete step-by-step answer:
It is given in the question, that we have to find the average of the least and the greatest 2-digit prime numbers. Before proceeding with the question, let us first see what a prime number is. A prime number is a number that has only two factors which are 1 and the number itself. For example, 2, 3, 5, 7, etc. are prime numbers.
Now, we need to find the least 2-digit prime number. We know that the least 2-digit prime number is 10, but it is not a prime number, as it has more than 2 factors. So, we will consider the next number, that is, 11. So, 11 is a prime number because it has only two factors, which are 1 and 11.
So, we have got the least 2-digit prime number as 11.
Now, we will find the greatest 2-digit prime number. We know that the greatest 2-digit number is 99, but it is not a prime number as it has more than two factors. So, we will consider the second last greatest 2-digit number, which is 98. We know that 98 also has more than two factors, hence 98 is also not a prime number. Now, let us consider the third last greatest 2-digit number, which is 97 and it is a prime number as it has only two factors, 1 and 97.
So, we have got the greatest 2-digit prime number as 97.
Now, we will find the average of the least and the greatest 2-digit prime numbers. We know that the average of numbers can be represented as follows: $\text{Average=}\dfrac{\text{Sum of given numbers}}{\text{Total number of numbers}}$.
We get the sum of the given numbers as 11 + 97 = 108 and the total number of numbers as 2. Therefore, we can write the average of the least and the greatest 2-digit prime numbers as $\dfrac{108}{2}=54$.
Hence, the average of the least and the greatest 2-digit prime numbers is 54. Therefore, option (A) is the correct answer.

Note: Some students may misunderstand the question as, find the average of the least prime number and the greatest 2-digit prime number, which is wrong as they tend to miss the word, least 2-digit prime number. And by considering only the least prime number, they may take the value as 2, which will result in the wrong answer. Hence, the students must go through the question carefully and see what is asked.