Graph Coordinates | AMC 10A, 2015 | Question 12

Try this beautiful Problem on Graph Coordinates from coordinate geometry from AMC 10A, 2015. Graph Coordinates – AMC-10A, 2015- Problem 12 Points $(\sqrt{\pi}, a)$ and $(\sqrt{\pi}, b)$ are distinct points on the graph of $y^{2}+x^{4}=2 x^{2} y+1 .$ What is...

Length and Triangle | AIME I, 1987 | Question 9

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Length and Triangle. Length and Triangle – AIME I, 1987 Triangle ABC has right angle at B, and contains a point P for which PA=10, PB=6, and \(\angle...

Positive Integer | PRMO-2017 | Question 1

Try this beautiful Positive Integer Problem from Algebra from PRMO 2017, Question 1. Positive Integer – PRMO 2017, Question 1 How many positive integers less than 1000 have the property that the sum of the digits of each such number is divisible by 7 and the...

Distance and Spheres | AIME I, 1987 | Question 2

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Distance and Spheres. Distance and Sphere – AIME I, 1987 What is the largest possible distance between two points, one on the sphere of radius 19 with...

Arithmetic Mean | AIME I, 2015 | Question 12

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2015 based on Arithmetic Mean. Arithmetic Mean of Number Theory – AIME 2015 Consider all 1000-element subsets of the set {1, 2, 3, … , 2015}. From each such subset choose...