Data Sufficiency

Source: MGMAT

Is x > 0?

(1) |x + 3| < 4

(2) |x - 3| < 4

Answer: E

Can someone please explain the best way to look at the combined inequality? This is how MGMAT explains it:



If we combine the solutions from statements (1) and (2) we get an overlapping range of -1 < x < 1. We still can't tell whether x is positive.

IS THIS BECAUSE WE DON'T KNOW THAT X IS AN INTEGER, THEREFORE, COULD BE -1/4 OR 0 (WHICH IS NOT POS OR NEG)?

missrochelle wrote: IS THIS BECAUSE WE DON'T KNOW THAT X IS AN INTEGER, THEREFORE, COULD BE -1/4 OR 0 (WHICH IS NOT POS OR NEG)?

you are right. its because x can still be 0 or negative or positive.
Since there are more than one options, the statement is INSUFFICIENT.

Hope this helps!!

|x + 3| < 4

case 1: (x + 3 )< 4

= x <1

here X can be greater than zero or less than zero. SO Insufficient

case 2 : - ( x+3) <4
-x -3 <4
-x<7
x> -7

Here again X can be greater than Zero or less than zero.

So st 1 is insufficient.

st 2 : |x - 3| < 4

case 1 : x-3 <4
x< 7
We can have X greater than or less than 0 . Insufficient

case 2: -(x-3) <4
-x+3 <4
-x< 1
x>-1
Again we can have X greater than or lesser than 0.

Combining both the statements we have -1<x<7, the sts hold true. But again X can be greater than or less than zero
Example : X= -0.5

|x - 3| < 4

|-0.5-3| = 3.5 which is less than 4

Now X= 0.5
|0.5 -3|= 2.5 <4 YES.

Here we see , we get inconsistent answers.

so Pick E as -1<X<7