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

If r+s=4, s<0?

Per statement 1, -4>-r ---> r>4. Also from r+s=4 ---> 4-s>4 --> s>0. Thus provides definite answer "no" for s<0. Thus sufficient.

Per statement 2, r>2s+2 . From r+s=4 ---> 4-s>2s+2 --> s<0.67 . Now, if s =0.5 then s<0 is a "no" but if s = -1 then s<0 is a "yes". Thus this statement is not sufficient.

A is the correct answer.

Your answer is correct. But just a small correction in statement 2.

s<2/3

Given : r+s =4
1) r > 4 and s = 4 - r so s < 0 , Sufficient

2) r > 2 ( s + 1 )
If s=0 => r > 2 So r=4 and s = 0 . S is not < 0
If s=-1 => r > 0 So r=5 and s= -1 . S is < 0
Not Sufficient

So Answer is A

800score Official Solution:

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).