Explanation

We have 20 numbers, and we want to know whether they are all equal or at least partly different. On to the statements, separately first.

Statement (1) tells us the sum of the numbers is 100. In one possible case, all 20 numbers are 5, and then the answer would be "yes." But, in another possible case, 18 are 5, one is 1, and one is 9. They would still sum to 100, but they would not all be equal. We have conflicting possible answers, so Statement (1) is insufficient.

Statement (2) tells us that the sum of any 5 numbers in the list is 25. The case we just considered with a 9 and a 1 on the list, would no longer be allowed, because selecting them as part of the "any 5" would not give a sum of 25. The only possible case is that all of the numbers are 5. Therefore, Statement (2) is sufficient.

The correct answer is (B).