{"status": "success", "data": {"description_md": "For how many positive integers $n \\le 1000$ is$$\\left\\lfloor \\dfrac{998}{n} \\right\\rfloor+\\left\\lfloor \\dfrac{999}{n} \\right\\rfloor+\\left\\lfloor \\dfrac{1000}{n}\\right \\rfloor$$not divisible by $3$? (Recall that $\\lfloor x \\rfloor$ is the greatest integer less than or equal to $x$.)\n\n$\\textbf{(A) } 22 \\qquad\\textbf{(B) } 23 \\qquad\\textbf{(C) } 24 \\qquad\\textbf{(D) } 25 \\qquad\\textbf{(E) } 26$", "description_html": "<p>For how many positive integers <span class=\"katex--inline\">n \\le 1000</span> is<span class=\"katex--display\">\\left\\lfloor \\dfrac{998}{n} \\right\\rfloor+\\left\\lfloor \\dfrac{999}{n} \\right\\rfloor+\\left\\lfloor \\dfrac{1000}{n}\\right \\rfloor</span>not divisible by <span class=\"katex--inline\">3</span>? (Recall that <span class=\"katex--inline\">\\lfloor x \\rfloor</span> is the greatest integer less than or equal to <span class=\"katex--inline\">x</span>.)</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A) } 22 \\qquad\\textbf{(B) } 23 \\qquad\\textbf{(C) } 24 \\qquad\\textbf{(D) } 25 \\qquad\\textbf{(E) } 26</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2020 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10A_p23", "prev": "/problem/20_amc10A_p21"}}