DS Questions on probability

[knight247]

In a class, each of the students were asked to pick an integer between 1 and 20, both inclusive.
What is the probability that at least two students have picked up the same integer?
(1)There were less than 30 students.
(2)There were 30 students.
(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient to answer the question asked.
(E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

[Ian Stewart]

If there are more than 20 students, then two students must have picked the same number (since even if the first 20 students all pick a different number, the 21st student will have to pick a number which is the same as one that's already been chosen). So if there are more than 20 students, the probability is 100% that two students pick the same number. So Statement 2 is sufficient here.

That said, the question is completely illogical as a GMAT DS question. Where is it from? The Statements can't possibly both be true, so how is someone supposed to consider the two statements together?