MathDB

day 1

Part of 2005 Indonesia Juniors

Problems(1)

Indonesia Juniors 2005 day 1 OSN SMP

Source:

10/30/2021
p1. AA is a set of numbers. The set AA is closed to subtraction, meaning that the result of subtracting two numbers in AA will be returns a number in AA as well. If it is known that two members of AA are 44 and 99, show that: a. 0∈A0\in A b. 13∈A13 \in A c. 74∈A74 \in A d. Next, list all the members of the set AA .
p2. (2,0,4,1)(2, 0, 4, 1) is one of the solutions/answers of x1+x2+x3+x4=7x_1+x_2+x_3+x_4=7. If all solutions belong on the set of not negative integers , specify as many possible solutions/answers from x1+x2+x3+x4=7x_1+x_2+x_3+x_4=7
p3. Adi is an employee at a textile company on duty save data. One time Adi was asked by the company leadership to prepare data on production increases over five periods. After searched by Adi only found four data on the increase, namely 4%4\%, 9%9\%, 7%7\%, and 5%5\%. One more data, namely the 55th data, was not found. Investigate increase of 5th data production, if Adi only remembers that the arithmetic mean and median of the five data are the same.
p4. Find all pairs of integers (x,y)(x,y) that satisfy the system of the following equations: {x(y+1)=y2−1y(x+1)=x2−1\left\{\begin{array}{l} x(y+1)=y^2-1 \\ y(x+1)=x^2-1 \end{array} \right.
p5. Given the following image. ABCDABCD is square, and EE is any point outside the square ABCDABCD. Investigate whether the relationship AE2+CE2=BE2+DE2AE^2 + CE^2 = BE^2 +DE^2 holds in the picture below. https://cdn.artofproblemsolving.com/attachments/2/5/a339b0e4df8407f97a4df9d7e1aa47283553c1.png
algebrageometrynumber theorycombinatoricsindonesia juniors