MathDB

10

Part of 2017 AMC 10

Problems(2)

Rodblocked (my 1000th post)

Source: 2017 AMC 10A #10/12A #6

2/8/2017
Joy has 3030 thin rods, one each of every integer length from 11 cm through 3030 cm. She places the rods with lengths 33 cm, 77 cm, and 1515 cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?
<spanclass=′latex−bold′>(A)</span>16<spanclass=′latex−bold′>(B)</span>17<spanclass=′latex−bold′>(C)</span>18<spanclass=′latex−bold′>(D)</span>19<spanclass=′latex−bold′>(E)</span>20<span class='latex-bold'>(A) </span>16\qquad<span class='latex-bold'>(B) </span>17\qquad<span class='latex-bold'>(C) </span>18\qquad<span class='latex-bold'>(D) </span>19\qquad<span class='latex-bold'>(E) </span>20
2017 AMC 10A2017 AMC 12AAMC 10AMC 12countingAMC
Lines of a b c is not as easy as 1 2 3

Source: AMC10B 2017 #10

2/16/2017
The lines with equations ax−2y=cax-2y=c and 2x+by=−c2x+by=-c are perpendicular and intersect at (1,−5)(1, -5). What is cc?
<spanclass=′latex−bold′>(A)</span>−13<spanclass=′latex−bold′>(B)</span>−8<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>13<span class='latex-bold'>(A) </span> -13\qquad <span class='latex-bold'>(B) </span> -8\qquad <span class='latex-bold'>(C) </span> 2\qquad <span class='latex-bold'>(D) </span> 8\qquad <span class='latex-bold'>(E) </span> 13
AMCAMC 10AMC 10 B2017 AMC 10Acoordinategeometry2017 AMC 10B