Of the numbers r + s, r – s, r × s, and r/s,which is greast?

[okitar872002]

(1) r = s = 1
(2) r – s is the least of the numbers.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

The correct answer is A,but i do not know why statement(2) is not sufficient.

[Sage Pearce-Higgins]

If a statement is not sufficient on Data Sufficiency, then we should be able to prove that by testing cases. That is to say that we can find two cases which agree with the statement but that give different answers to the question. Let's see if we can do that.

Statement 2 tells us that "r – s is the least of the numbers". So If I pick r = 1 and s = 1, then r – s = 0, which is indeed smaller than the other combinations. For this case, r + s = 2, and that's the greatest. Now we're looking for another case that follows the statement, but that has a different answer to the question. Let's try r = 3 and s = 3. For this second case, r – s = 0, r + s = 6, r x s = 9, and r/s = 1. Again, r – s is the smallest (what we need to agree with the statement), but the biggest this time is r x s, showing that statement 2 doesn't give us a definite answer to the question - it's insufficient.