2014 AMC 10A Problems/Problem 7

Problem

Nonzero real numbers $x$ , $y$ , $a$ , and $b$ satisfy $x < a$ and $y < b$ . How many of the following inequalities must be true?

$\textbf{(I)} x+y < a+b\qquad$

$\textbf{(II)} x-y < a-b\qquad$

$\textbf{(III)} xy < ab\qquad$

$\textbf{(IV)} \frac{x}{y} < \frac{a}{b}$

$\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}}\ 3\qquad\textbf{(E)}\ 4$ (Error compiling LaTeX. Unknown error_msg)