Data Sufficiency

BTGmoderatorDC wrote:Is x > 0 ?
(1) |x+3| < 4
(2) |x-3| < 4

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then -k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k

Target question: Is x > 0 ?

Statement 1: |x+3| < 4
From Rule #1, we can write: -4 < x + 3 < 4
Subtract 3 from all 3 sides to get: -7 < x < 1
If -7 < x < 1, then:
x could equal 0.5, in which case the answer to the target question is YES, x IS greater than 0
x could equal -0.5, in which case the answer to the target question is NO, x is NOT greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x-3| < 4
From Rule #1, we can write: -4 < x - 3 < 4
Add 3 to all 3 sides to get: -1 < x < 7
If -1 < x < 7, then:
x could equal 0.5, in which case the answer to the target question is YES, x IS greater than 0
x could equal -0.5, in which case the answer to the target question is NO, x is NOT greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
x could equal 0.5, in which case the answer to the target question is YES, x IS greater than 0
x could equal -0.5, in which case the answer to the target question is NO, x is NOT greater than 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent