2009 AMC 12B Problem 22


Parallelogram ABCDABCD has area 1,000,0001,\!000,\!000 . Vertex AA is at (0,0)(0,0) and all other vertices are in the first quadrant. Vertices BB and DD are lattice points on the lines y=xy = x and y=kxy = kx for some integer k>1k > 1 , respectively. How many such parallelograms are there?

(A) 49(B) 720(C) 784(D) 2009(E) 2048\textbf{(A)}\ 49\qquad \textbf{(B)}\ 720\qquad \textbf{(C)}\ 784\qquad \textbf{(D)}\ 2009\qquad \textbf{(E)}\ 2048


Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

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Category: AMC 12B
Points: 5
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