diebeatsthegmat wrote: ↑Mon Aug 29, 2011 1:39 am
If w + x < 0 , is w - y > 0 ?
1) x + y < 0
2) y < X < w
Given: w + x < 0
Target question: Is w - y > 0 ?
Statement 1: x + y < 0
Since we're given the inequality
w + x < 0, and since the inequality symbols are facing the same direction, we can ADD the inequalities to get:
2x + w + y < 0
This does not provide enough information to determine whether
w - y > 0.
So, statement 1 is NOT SUFFICIENT
If you're not convinced, consider these two conflicting cases (that satisfy the given information):
Case a: w = 0, x = -1 and y = -1. In this case, the answer to the target question is
YES, w - y > 0
Case b: w = 0, x = -1 and y = 0.5. In this case, the answer to the target question is
NO, w - y is not greater than 0
Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y < x < w
In this case, we should recognize that we can answer the
target question without even using the given information (
w + x < 0)
If
y < x < w, then we can also conclude that
y < w
From here, if we subtract y from both sides of the inequality we get:
0 < w - y
In other words, the answer to the target question is
YES, w - y > 0
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
