{"status": "success", "data": {"description_md": "Nonzero real numbers $x$, $y$, $a$, and $b$ satisfy $x < a$ and $y < b$. How many of the following inequalities must be true?\n$\\textbf{(I)}\\ x+y < a+b\\qquad$\n$\\textbf{(II)}\\ x-y < a-b\\qquad$\n$\\textbf{(III)}\\ xy < ab\\qquad$\n$\\textbf{(IV)}\\ \\frac{x}{y} < \\frac{a}{b}$\n\n$\\textbf{(A)}\\ 0\\qquad\\textbf{(B)}\\ 1\\qquad\\textbf{(C)}\\ 2\\qquad\\textbf{(D)}\\ 3\\qquad\\textbf{(E)}\\ 4$", "description_html": "<p>Nonzero real numbers  <span class=\"katex--inline\">x</span> ,  <span class=\"katex--inline\">y</span> ,  <span class=\"katex--inline\">a</span> , and  <span class=\"katex--inline\">b</span>  satisfy  <span class=\"katex--inline\">x &lt; a</span>  and  <span class=\"katex--inline\">y &lt; b</span> . How many of the following inequalities must be true?<br/>\n <span class=\"katex--inline\">\\textbf{(I)}\\ x+y &lt; a+b\\qquad</span> <br/>\n <span class=\"katex--inline\">\\textbf{(II)}\\ x-y &lt; a-b\\qquad</span> <br/>\n <span class=\"katex--inline\">\\textbf{(III)}\\ xy &lt; ab\\qquad</span> <br/>\n <span class=\"katex--inline\">\\textbf{(IV)}\\ \\frac{x}{y} &lt; \\frac{a}{b}</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 0\\qquad\\textbf{(B)}\\ 1\\qquad\\textbf{(C)}\\ 2\\qquad\\textbf{(D)}\\ 3\\qquad\\textbf{(E)}\\ 4</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2014 AMC 10A Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc10A_p08", "prev": "/problem/14_amc10A_p06"}}