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 \(gcd (a, b) : lcm (a, b) = 1 : 495\) ?...

Circular Cylinder Problem | AMC-10A, 2001 | Problem 21

Try this beautiful problem from Geometry based on Circular Cylinder. Circular Cylinder Problem – AMC-10A, 2001- Problem 21 A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. The cone has diameter $10$ and...

Area of the Region Problem | AMC-10A, 2007 | Problem 24

Try this beautiful problem from Geometry: Area of the region Problem on Area of the Region – AMC-10A, 2007- Problem 24 Circle centered at \(A\) and \(B\) each have radius \(2\), as shown. Point \(O\) is the midpoint of \(\overline{AB}\), and \(OA = 2\sqrt {2}\)....

Sum of the digits | AMC-10A, 2007 | Problem 25

Try this beautiful problem from Algebra based on Sum of the digits. Sum of the digits – AMC-10A, 2007- Problem 25 For each positive integer $n$ , let $S(n)$ denote the sum of the digits of $n.$ For how many values of $n$ is \(n+s(n)+s(s(n))=2007\)...

Medians of triangle | PRMO-2018 | Problem 10

Try this beautiful problem from Geometry based on medians of triangle Medians of triangle | PRMO | Problem 10 In a triangle ABC, the medians from B to CA is perpendicular to the median from C to AB. If the median from A to BC is 30,determine \((BC^2 +AC^2+AB^2)/100\)?...