These three problems were presented during the Area Stage Competition of the 10th Philippine Mathematical Olympiad. On the average, each of them requires only a few minutes to solve, so if you find yourself working on one way too long, change techniques.
If 2A99561 is equal to the product when 3(523+A) is multiplied by itself, find the digit A.
The perimeter of a square inscribed in a circle is p. What is the area of the square that circumscibes the circle?
The sum of the first ten terms of an arithmetic sequence is 160. The sum of the next ten terms of the sequence is 340. What is the first term of the sequence?
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