{"status": "success", "data": {"description_md": "Excelex and Geeks are on a $100$-day math training arcs in the hopes of qualifying for the **USAJMO**. Let $E(x)$ and $G(x)$ be the number of hours grinded in day $x$ for Excelex and Geeks, respectively.\n\nSuppose that $E(x) = 4x^2-16x+17$ and $G(x) = 3x^2+bx+c$, the domain of both functions is the set of all integers from $1$ to $100$, inclusive. Let day $a$ be the day where Excelex grinded the minimum amount of hours over all values of $x$ in his domain.\n\nCoincidentally, day $a$ is also the day where Geeks grinded his minimum amount of hours. Furthermore, Excelex and Geeks both grinded $d$ hours this day. With this information, compute $a+b+c+d$.", "description_html": "<p>Excelex and Geeks are on a <span class=\"katex--inline\">100</span>-day math training arcs in the hopes of qualifying for the <strong>USAJMO</strong>. Let <span class=\"katex--inline\">E(x)</span> and <span class=\"katex--inline\">G(x)</span> be the number of hours grinded in day <span class=\"katex--inline\">x</span> for Excelex and Geeks, respectively.</p>&#10;<p>Suppose that <span class=\"katex--inline\">E(x) = 4x^2-16x+17</span> and <span class=\"katex--inline\">G(x) = 3x^2+bx+c</span>, the domain of both functions is the set of all integers from <span class=\"katex--inline\">1</span> to <span class=\"katex--inline\">100</span>, inclusive. Let day <span class=\"katex--inline\">a</span> be the day where Excelex grinded the minimum amount of hours over all values of <span class=\"katex--inline\">x</span> in his domain.</p>&#10;<p>Coincidentally, day <span class=\"katex--inline\">a</span> is also the day where Geeks grinded his minimum amount of hours. Furthermore, Excelex and Geeks both grinded <span class=\"katex--inline\">d</span> hours this day. With this information, compute <span class=\"katex--inline\">a+b+c+d</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Christmas Contest - Team Round - Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p05", "prev": "/problem/christmas1_team-p03"}}