# Determine the order relation between $x$ and $y$, given $5x-2y =2y-3x$

Given: $5x-2y =2y-3x$
\begin{aligned} \text{Quantity A} && \text{Quantity B} \\ x && y \end{aligned}

$\bigcirc$ Quantity A is bigger

$\bigcirc$ Quantity B is bigger

$\bigcirc$ Two quantities are equal

$\bigcirc$ The relationship cannot be determined for the information given

The answer is $B$ according to GRE book. Simplifying I get that $2x=y$. I letting $x=0$ get $y=0$. Also let $x=1$ get $y=2$. I believe it is D but need to double check. I have read that any number in GRE is real.

• The answer is B according to book. simplifying get that $2x=y$. I letting $x=0$ get $y=0$. Also let $x=1$ get $y=2$. I belief it is D but need to double check. I have read that any number in GRE is real. – Tiger Blood Dec 20 '15 at 5:22
• B means "quantity B is bigger". D means "The relationship cannot be determined from the given information" – Tiger Blood Dec 20 '15 at 5:37

$5x-2y=2y-3x$, so $8x=4y$, so $y=2x$. There are a few possibilities. For example, $x=1$ and $y=2$, or $x=-1$ and $y=-2$, or $x=y=0$. If all we know is that $x,y$ are real, then it is not possible to know which is bigger.