Question

The average of seven consecutive prime numbers is 53. What is the difference
between the greatest and the smallest of these numbers ?
The answer is 46 but how pls solve my question ​

Answer 1

The difference  between the greatest and the smallest of these numbers = 67 - 41 = 26.

Note: The answer provided in the question is wrong.

1. There are total 20 prime numbers between 1 to 100.
2. They are

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97

    3. In the question, it is given that the average of seven consecutive prime numbers is 53. Thus, we need to find only those consecutive seven prime numbers whose average is 7.

    4. Since the average is 53 ( which itself is a prime number), we will take into account only those seven prime numbers while lie close to 53.

    5. By keeping 53 in the middle and taking 3 prime numbers both from left and right side of 53, we get the following prime numbers -

                                       41, 43, 47, 53, 59, 61, 67

    6. Taking their average, we get,

                     Average = (41+43+47+53+59+61+67)/7 = 53

    7. Now, Greatest = 67 and smallest = 41

    8. Therefore, the difference  between the greatest and the smallest of these numbers = 67-41 = 26.