A decent DS question - Inequalities

A decent DS question:

Is x > 0?

(1) |x + 3| < 4

(2) |x-3| < 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

We are trying to see if x is positive. Let's look at each statement alone. For 1), this statement simplifies to -7<x<1, so from this we don't know if x is positive. For 2), this statement simplifies to -1<x<7, so again, we don't know if x is positive or negative.

Let's see if combining them helps. If you think of them on a number line, Statement 1 includes all values between -7 and 1. Statement 2 includes all values between -1 and 7.

The only overlap between those two inequalities is between -1 so when we combine the two statements, we have -1<x<1, so again, this is still insufficient because we don't know if x is positive or negative, could be both.

So the answer is E, statements together are not sufficient.