Ordered Pairs | PRMO-2019 | Problem 18

Try this beautiful problem from PRMO, 2019, Problem 18 based on Ordered Pairs. Orderd Pairs | PRMO | Problem-18 How many ordered pairs \((a, b)\) of positive integers with \(a < b\) and \(100 \leq a\), \(b \leq 1000\) satisfy \(gcd (a, b) : lcm (a, b) = 1 : 495\) ?...

Maximum area | PRMO-2019 | Problem 23

Try this beautiful problem from PRMO, 2019 based on Maximum area Maximum area | PRMO-2019 | Problem-23 Let $\mathrm{ABCD}$ be a convex cyclic quadrilateral. Suppose $\mathrm{P}$ is a point in the plane of the quadrilateral such that the sum of its distances from the...

Ratio of Circles | AMC-10A, 2009 | Problem 21

Try this beautiful problem from Geometry based on ratio of Circles from AMC 10A, 2009, Problem 21. Ratio of Circles – AMC-10A, 2009- Problem 21 Many Gothic cathedrals have windows with portions containing a ring of congruent circles that are circumscribed by a...

Rectangle Pattern | AMC-10A, 2016 | Problem 10

Try this beautiful problem from Geometry based on Rectangle Pattern from AMC 10A, 2016, Problem 10. Rectangle Pattern- AMC-10A, 2016- Problem 10 A rug is made with three different colors as shown. The areas of the three differently colored regions form an arithmetic...

Probability in Game | AMC-10A, 2005 | Problem 18

Try this beautiful problem from AMC 10A, 2005 based on Probability in Game. Probability in Game – AMC-10A, 2005- Problem 18 Team A and team B play a series. The first team to win three games wins the series. Each team is equally likely to win each game, there...