A decent DS question - Inequalities

[mjsobo]

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.

[deagez]

I like to use -1, 0, 1 (or any other integer that makes the premise either false or true) for this type of problem. (usually just two of the three can quickly get you an answer)

(1) 0+3 <4 = true
1+3 <4 = false

NOT SUFF

(2) 0-3 <4 = true
7-3 <4 = false

Not SUFF

Now when it is time to combine lets use x as 0 because both equations are true. So we have to find a positive value for X that works for either (1) and (2) and disproves X>0 . X=1 is good because it works for premise (2), so you have multiple answers for X, and answer is E.

Also just to Note "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. " as written above is not true. X can not be 7 in (2)or -7 in (1)

[fireplayer]

E for me, pls post OA