There are five homes. If the median price of a home is $200,000

Statement 1:
Average price of 5 homes = $240,000. This means total price of 5 homes = 5*240000 = $1,200,000.
To keep our range minimum, we should try to keep smallest and largest values (out of these 5) as close as possible.
Our smallest value can go up to 200,000 (since thats the median), and in that case, first 3 values will be 200,000 only.

So let the price of first 3 homes be $200,000 each. This makes it $600,000. Remaining price of 2 costlier homes = 1,200,000 - 600,000 = $600,000
In this case, costliest room will get the smallest value if we assume price of 4th and 5th homes to be equal, i.e., $300,000 each.

So here we have accomplished the purpose of keeping the smallest and largest value as close as possible. And the range in this case = price of highest - price of lowest = 300,000 - 200,000 = $100,000. So when here only the range is more than $80,000 then in any other case it will definitely be more than $80,000. Sufficient.

Statement 2:
Which three homes have same price we don't know. And also this doesn't help in determining the range. So not sufficient.

Hence A answer