{"status": "success", "data": {"description_md": "For any three real numbers $a$, $b$, and $c$, with $b\\neq c$, the operation $\\otimes$ is defined by:\n\n$$\\otimes(a,b,c)=\\frac{a}{b-c}.$$\n\nWhat is $\\otimes ( \\otimes (1,2,3), \\otimes (2,3,1), \\otimes (3,1,2))$?\n\n$\\mathrm{(A) \\ } -\\frac{1}{2}\\qquad \\mathrm{(B) \\ } -\\frac{1}{4} \\qquad \\mathrm{(C) \\ } 0 \\qquad \\mathrm{(D) \\ } \\frac{1}{4} \\qquad \\mathrm{(E) \\ } \\frac{1}{2}$", "description_html": "<p>For any three real numbers <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span>, with <span class=\"katex--inline\">b\\neq c</span>, the operation <span class=\"katex--inline\">\\otimes</span> is defined by:</p>&#10;<p><span class=\"katex--display\">\\otimes(a,b,c)=\\frac{a}{b-c}.</span></p>&#10;<p>What is <span class=\"katex--inline\">\\otimes ( \\otimes (1,2,3), \\otimes (2,3,1), \\otimes (3,1,2))</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A) \\ } -\\frac{1}{2}\\qquad \\mathrm{(B) \\ } -\\frac{1}{4} \\qquad \\mathrm{(C) \\ } 0 \\qquad \\mathrm{(D) \\ } \\frac{1}{4} \\qquad \\mathrm{(E) \\ } \\frac{1}{2}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2004 AMC 10A Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10A_p03", "prev": "/problem/04_amc10A_p01"}}