turkey-yks 2015 Q11

turkey-yks · Other · lys1-math Inequalities Ordering and Sign Analysis from Inequality Constraints

Let $a , b , c$ be real numbers and $a \cdot b \cdot c > 0$ such that
$$\begin{aligned} & a \cdot b = - 2 | a | \\ & \frac { b } { c } = 3 | b | \end{aligned}$$
Given that $\mathbf { a } + \mathbf { b } + \mathbf { c } = \mathbf { 0 }$, what is a?
A) $\frac { 3 } { 2 }$
B) $\frac { 5 } { 2 }$
C) $\frac { 9 } { 2 }$
D) $\frac { 7 } { 3 }$
E) $\frac { 8 } { 3 }$

Let $a , b , c$ be real numbers and $a \cdot b \cdot c > 0$ such that

$$\begin{aligned}
& a \cdot b = - 2 | a | \\
& \frac { b } { c } = 3 | b |
\end{aligned}$$

Given that $\mathbf { a } + \mathbf { b } + \mathbf { c } = \mathbf { 0 }$, what is a?\\
A) $\frac { 3 } { 2 }$\\
B) $\frac { 5 } { 2 }$\\
C) $\frac { 9 } { 2 }$\\
D) $\frac { 7 } { 3 }$\\
E) $\frac { 8 } { 3 }$

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