{"status": "success", "data": {"description_md": "Parallelogram $ABCD$ has area $1,\\!000,\\!000$. Vertex $A$ is at $(0,0)$ and all other vertices are in the first quadrant. Vertices $B$ and $D$ are lattice points on the lines $y = x$ and $y = kx$ for some integer $k > 1$, respectively. How many such parallelograms are there?\n\n$\\textbf{(A)}\\ 49\\qquad \\textbf{(B)}\\ 720\\qquad \\textbf{(C)}\\ 784\\qquad \\textbf{(D)}\\ 2009\\qquad \\textbf{(E)}\\ 2048$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Parallelogram  <span class=\"katex--inline\">ABCD</span>  has area  <span class=\"katex--inline\">1,\\!000,\\!000</span> . Vertex  <span class=\"katex--inline\">A</span>  is at  <span class=\"katex--inline\">(0,0)</span>  and all other vertices are in the first quadrant. Vertices  <span class=\"katex--inline\">B</span>  and  <span class=\"katex--inline\">D</span>  are lattice points on the lines  <span class=\"katex--inline\">y = x</span>  and  <span class=\"katex--inline\">y = kx</span>  for some integer  <span class=\"katex--inline\">k &gt; 1</span> , respectively. How many such parallelograms are there?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 49\\qquad \\textbf{(B)}\\ 720\\qquad \\textbf{(C)}\\ 784\\qquad \\textbf{(D)}\\ 2009\\qquad \\textbf{(E)}\\ 2048</span> </p>&#10;<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": 5, "problem_name": "2009 AMC 12B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12B_p23", "prev": "/problem/09_amc12B_p21"}}