MathDB

6

Part of 2019 AMC 10

Problems(2)

Centers and Quadrilaterals

Source: 2019 AMC 10A #6

2/8/2019
For how many of the following types of quadrilaterals does there exist a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral?
[*] a square [*]a rectangle that is not a square [*] a rhombus that is not a square [*] a parallelogram that is not a rectangle or a rhombus [*] an isosceles trapezoid that is not a parallelogram
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>2<spanclass=′latex−bold′>(C)</span>3<spanclass=′latex−bold′>(D)</span>4<spanclass=′latex−bold′>(E)</span>5<span class='latex-bold'>(A) </span> 1 \qquad<span class='latex-bold'>(B) </span> 2 \qquad<span class='latex-bold'>(C) </span> 3 \qquad<span class='latex-bold'>(D) </span> 4 \qquad<span class='latex-bold'>(E) </span> 5
AMCAMC 10 A2019 AMCquadrilateral
Factorials are fun

Source: 2019 AMC 10B #6, 12B #4

2/14/2019
A positive integer nn satisfies the equation (n+1)!+(n+2)!=n!⋅440(n+1)! + (n+2)! = n! \cdot 440. What is the sum of the digits of nn?
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>5<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>12<spanclass=′latex−bold′>(E)</span>15<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>5\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>12\qquad<span class='latex-bold'>(E) </span>15
factorial2019 AMC 10B