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3

Part of 2018 Junior Regional Olympiad - FBH

Problems(3)

Junior Regional Olympiad - FBH 2018 Grade 7 Problem 3

Source:

9/19/2018
Let aa, bb and mm be three positive real numbers and a>ba>b. Which of the numbers A=a+m−aA=\sqrt{a+m}-\sqrt{a} and B=b+m−bB=\sqrt{b+m}-\sqrt{b} is bigger:
Compareroots
Junior Regional Olympiad - FBH 2018 Grade 6 Problem 3

Source:

9/18/2018
In some primary school there were 9494 students in 77th grade. Some students are involved in extracurricular activities: spanish and german language and sports. Spanish language studies 4040 students outside school program, german 2727 students and 6060 students do sports. Out of the students doing sports, 2424 of them also goes to spanish language. 1010 students who study spanish also study german. 1212 students who study german also do sports. Only 44 students go to all three activities. How many of them does only one of the activities, and how much of them do not go to any activity?
ActivitiesSetscounting
Junior Regional Olympiad - FBH 2018 Grade 8 Problem 3

Source:

9/19/2018
Find all 44 digit number abcd‾\overline{abcd} such that 4⋅abcd‾+30=dcba‾4\cdot \overline{abcd}+30=\overline{dcba}
Digits4 digit