turkey-yks 2017 Q11

turkey-yks · Other · lys1-math Modulus function Algebraic identities and properties of modulus
For nonzero real numbers $x$, $y$, and $z$ whose absolute values are distinct from each other, $$\begin{aligned}| x + y | & = | x | - | y | \\| y + z | & = | y | + | z |\end{aligned}$$ the following equalities are satisfied.
Given that $x > 0$,\ I. $\frac { x } { x + y } < 1$\ II. $\frac { y } { y + z } < 1$\ III. $\frac { z } { x + z } < 1$\ Which of the following statements are always true?\ A) Only I\ B) Only II\ C) Only III\ D) I and III\ E) II and III
For nonzero real numbers $x$, $y$, and $z$ whose absolute values are distinct from each other,
$$\begin{aligned}| x + y | & = | x | - | y | \\| y + z | & = | y | + | z |\end{aligned}$$
the following equalities are satisfied.

Given that $x > 0$,\
I. $\frac { x } { x + y } < 1$\
II. $\frac { y } { y + z } < 1$\
III. $\frac { z } { x + z } < 1$\
Which of the following statements are always true?\
A) Only I\
B) Only II\
C) Only III\
D) I and III\
E) II and III