MathDB

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Part of 2015 ASDAN Math Tournament

Problems(8)

2015 Advanced #1

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7/8/2022
How many integers between 22 and 100100 have only odd numbers in their prime factorizations?
2015Advanced Topics Test
2015 Advanced Tiebreaker #1

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7/8/2022
Rachel has 33 children, all of which are at least 22 years old. The ages of the children are all pairwise relatively prime, but Rachel’s age is a multiple of each of her children’s ages. What is Rachel’s minimum possible age?
2015Advanced Topics Tiebreaker
2015 Algebra #1

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7/1/2022
Given that xy+x+y=5xy+x+y=5 and x+1=2x+1=2, compute y+1y+1.
2015Algebra Test
2015 Guts #1

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7/25/2022
Rio likes fruit, and one day she decides to pick persimmons. She picks a total of 1212 persimmons from the first 55 trees she sees. Rio has 55 more trees to pick persimmons from. If she wants to pick an average of 44 persimmons per tree overall, what is the average number of persimmons that she must pick from each of the last 55 trees for her goal?
2015Guts Test
2015 Algebra Tiebreaker #1

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7/1/2022
Let ana_n be a sequence defined as a1=1a_1=1, a2=2a_2=2, and an=an−1−an−2a_n=a_{n-1}-a_{n-2}. Compute a2015a_{2015}.
2015Algebra Tiebreaker
2015 Geometry #1

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7/1/2022
Four unit circles are placed on a square of side length 22, with each circle centered on one of the four corners of the square. Compute the area of the square which is not contained within any of the four circles.
2015Geometry Test
2015 Geometry Tiebreaker #1

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7/19/2022
A rectangle ABCDABCD is split into four smaller non-overlapping rectangles by two perpendicular line segments, whose endpoints are on the sides of ABCDABCD. If the smallest three rectangles have areas of 4848, 1818, and 1212, what is the area of ABCDABCD?
2015Geometry Tiebreaker
2015 Team #1

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8/2/2022
In his spare time, Thomas likes making rectangular windows. He builds windows by taking four 30 cm×20 cm30\text{ cm}\times20\text{ cm} rectangles of glass and arranging them in a larger rectangle in wood. The window has an x cmx\text{ cm} wide strip of wood between adjacent glass pieces and an x cmx\text{ cm} wide strip of wood between each glass piece and the adjacent edge of the window. Given that the total area of the glass is equivalent to the total area of the wood, what is xx?
2015team test