A book is published in three volumes, the pages being numbered from 1 onwards. The page numbers are continued from the first volume to the third. The number of pages in the second volume is 50 more than in the first volume, and the number pages in the third volume is one and a half times that in […]
Pre RMO 2018 Find the problems, discussions and relevant theoretical expositions related to Pre-RMO 2018. Problems of Pre RMO 1. A book is published in three volumes, the pages being numbered from 1 onwards. The page numbers are continued from the first volume to the third. The number of pages in the second volume is […]
Problem Suppose (a, b) are positive real numbers such that (a \sqrt{a}+b \sqrt{b}=183 . a \sqrt{b}+b \sqrt{a}=182). Find (\frac{9}{5}(a+b)). Hint 1 This problem will use the following elementary algebraic identity: $(x+y)^3=x^3+y^3+3 x^2 y+3 x y^2$ Can you identify what is x and what is y? Hint 2 background_video_pause_outside_viewport="on" tab_text_shadow_style="none" body_text_shadow_style="none"] Set $x=\sqrt{a}, y=\sqrt{b}$. Then the […]
In this post we have discussed AMC 10A 2018 problem number 13.
Cyclic Quadrilaterals are often important objects in a Geometry problem. Recognizing them can lead to a path to the solution. Pre RMO 2017 Problem 13 Solution is a part of our Pre-RMO problem solving series. Also visit: Math Olympiad Program of Cheenta
Tools in Geometry is very useful for pre regional mathematical olympiad, regional mathematical olympiad as well as I.S.I. & C.M.I entrance.
Cheenta is introducing open seminar for students interested in Advanced Mathematics and preparing for Pre-RMO and ISI Entrance Students. Know more..
The fifth problem from I.S.I. B.Stat and B.Math Entrance 2018, has a clever application of this mean value theorem. Watch the video and learn.
I.S.I 2018 Problem 2 Discussion is done based on the idea of ratio of areas of similar triangles is equal to ratio of squares on their corresponding sides.
Find all pairs ( (x,y) ) with (x,y) real, satisfying the equations $$\sin\bigg(\frac{x+y}{2}\bigg)=0~,~\vert x\vert+\vert y\vert=1$$ Discussion: Back to Problems