If you think that way, then the all other 10 integers cannot be greater than 5, because their sum will not be equal to 50

No where in the question it is mentioned that the other 10 integers should be greater than 5. One can assume that the other 10 integers are equal to 5. The question wasnt framed properly.

Read the question properly. If all the numbers are 5, then, there will be 30 integers that do not exceed 5.

Hi Vaibhav Gupta,
In this question, it is given that among these 30 integers, there are exactly 20 which do exceed 5 which means other 10 numbers should be more than 5.
I hope this helps.

Hi Abhishek Goswami,
20 integers don't exceed 5 means that the 20 integers are less than or equal to 5.
I hope this helps.

The question is correct.Read it again

Hi harshit,
The question is asking us for the average of the 20 numbers.
Note that these 20 numbers are less than or equal to 5
Hence, through various combination of integers, we can arrive at an average scoe of 4.5
For example, 10 integers are 4 and 10 integers are 5
Hope this clarifies!

Hi Satyesh,
In this case, all the 30 numbers are equal to 5
The question says "Among these 30 integers, there are exactly 20 which do not exceed 5"
While in this case, all the 30 integers do not exceed 5 i.e. "Among these 30 integers, there are exactly 30 which do not exceed 5".
Clearly statement 2 is invalidating statement 1
Hope this clarifies:)