If r + s = 4, is s < 0?
(1) -4 > -r
(2) r > 2s + 2

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.


(A) Statement (1) tells us that -4 > -r. When we multiply this inequality by -1, we get r > 4 (remember to switch the direction of the inequality when multiplying or dividing by a negative).

When r > 4, s must be negative, otherwise r + s would be greater than 4. So this statement alone is sufficient.

Statement (2) tells us that r > 2s + 2. We could pick numbers here, but the algebra is probably easier.

Since r = 4 – s (from the question stem) and r > 2s + 2 (from the statement), we can substitute to find the range for s:
r > 2s + 2
4 – s > 2s + 2
2 > 3s
2/3 > s.

Knowing that s is less than 2/3 does not tell us whether it is positive or negative, so Statement (2) is insufficient.

Since Statement (1) is sufficient and Statement (2) is insufficient, the correct answer is choice (A).
----------

I think you are wrong here: r > 2s + 2 being 2/3 > s is telling you that s cannot be < 0, because which also answers the question.there is no negative number that you add to 2/3 and get 4 (r + s = 4 and 2/3 + s = 4)

We have the inequality for s:
2/3 > s


It tells us that s can be less than 0, or it can be from 0 (inclusive) to 2/3 (not inclusive).

Here are the examples of r and s that fit:
s = -1 and r = 5
s = 0 and r = 4
s = 1/2 and r = 3 1/2