Can someone please explain how E is correct, not D?

OE


As the range of the set A containing 10 numbers is 16, we get the smallest & the highest numbers of set A the values having a gap of 16
Similarly as the range of set B containing 8 numbers is 10, the gap between the smallest & the highest numbers of the set B would be 10 only.
Now, when the two sets are combined we get a total of 10 + 8 = 18 numbers and the range of the 18 numbers would have to be at least 16.
Taking the numbers of set B within the group of the numbers of set A, we can get minimum possible range i.e. 16 of the set of 18 numbers
For example if we consider the 10 numbers of set A as 1, 2, 3, 4, 5, 6, 7, 8, 9 & 17 & the 8 numbers of set B as 1, 1, 2, 3, 4, 5, 6, & 11, we get the combined set of 18 numbers which has the lowest value 1 and the highest value 16, so the range comes minimum 17 - 1 = 16.
Note: - To maximize the range we would take the two sets value with higher gap, for example if we take set A as 1, 2, 3, 4, 5, 6, 7, 8, 9 & 17 and set B as 143, 144, 146, 147, 148, 149, 150 & 153, we get the combined set of 18 numbers which has the lowest value 1 and the highest value 153, so the range comes 153 - 1 = 152, which can go even higher.
Hence the answer is (D).

I fixed the OA also.

My Bad.

I am sorry