Data Sufficiency

If \(bc \ne 0,\) what is the value of \(\dfrac{a^2-b^2-c^2}{bc}?\)

(1) \(|a| = 1, |b| = 2, |c| = 3\)
(2) \(a + b + c = 0\)

Answer: B

Source: Manhattan GMAT

$$Statement\ 1:\ \left|a\right|=1,\ \left|b\right|=2,\ \left|c\right|=3$$
$$This\ means\ that\ a=\pm1,\ b=\pm2\ and\ c=\pm3$$
$$Whether\ a,\ b\ or\ c\ is\ +\ \ or\ -,\ a^2,\ b^2\ and\ c^2\ will\ be\ positive.$$
$$Therefore,\ a^2=1,\ b^2=4\, and\ c^2=9$$
$$If\ b\ne c\ positive\ and\ c\ is\ negative,\ bc=-6$$
$$Therefore,\ \frac{1-4-9}{-6}=-\frac{12}{-6}=2$$
But if b is positive and c is positive, bc=6
$$Therefore,\ \frac{1-4-9}{-6}=-\frac{12}{6}=-2$$ $$So,\ \frac{a^2-b^2-c^2}{bc}=\pm2$$
$$Since\ the\ answer\ is\ not\ certain,\ then,\ statement\ 1\ is\ NOT\ SUFFICIENT$$

$$Statement\ 2:\ a+b+c=0$$
$$a=-b-c$$
Substitute the value of a into the equation in question stem.
$$\frac{\left(-b-c\right)^2-b^2-c^2}{bc}=>\frac{b^2+2bc+c^2-b^2-c^2}{bc}$$
$$=\frac{2bc}{bc}=2$$
Statement 2 alone is SUFFICIENT. Therefore, option B is the correct answer.