|x + 4| is an absolute value i.e it has no regard for negative signs
$$Statement\ 1\ =>\ x^2+8x+12=0$$
$$\ x^2+6x+2x+12=0$$
$$\left(x^2+6x\right)+\left(2x+12\right)=0$$
$$x\left(x+6\right)+2\left(x+6\right)=0$$
$$\left(x+6\right)\left(x+2\right)=0$$
$$x+6=0\ or\ x+2=0$$
$$x=-6\ or\ x=-2$$
$$\left|x+4\right|=\left|-6+4\right|or\left|-2+4\right|$$
$$=\left|-2\right|or\left|2\right|$$
$$=2\ or\ 2$$
Because absolute values have no regard for negative signs, value of the absolute value from the two solutions are the same. Statement 1 is SUFFICIENT
$$Statement\ 2\ =>\ x^2+6x=0$$
$$x\left(x+6\right)=0$$
$$x=0\ or\ x=-6$$
$$\left|x+4\right|=\left|0+4\right|or\left|-6+4\right|$$
$$\left|4\right|or\left|-2\right|$$
$$=4\ or\ 2$$
The absolute value yield 2 different answers, due to this uncertainty, the target question cannot be answered and statement 2 is NOT SUFFICIENT
Since statement 1 alone is SUFFICIENT
Answer = A
What is the value of \(|x + 4|?\)
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Source: Beat The GMAT — Data Sufficiency |
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deloitte247
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