MathDB

4

Part of 2015 ASDAN Math Tournament

Problems(5)

2015 Advanced #4

Source:

7/8/2022
Given a positive integer x>1x>1 with nn divisors, define f(x)f(x) to be the product of the smallest ⌈n2⌉\lceil\tfrac{n}{2}\rceil divisors of xx. Let aa be the least value of xx such that f(x)f(x) is a multiple of XX, and bb be the least value of nn such that f(y)f(y) is a multiple of yy for some yy that has exactly nn factors. Compute a+ba+b.
2015Advanced Topics Test
2015 Algebra #4

Source:

7/1/2022
Let f(x)=(x−a)3f(x)=(x-a)^3. If the sum of all xx satisfying f(x)=f(x−a)f(x)=f(x-a) is 4242, find aa.
2015Algebra Test
2015 Guts #4

Source:

7/28/2022
Compute the number of positive integers less than or equal to 20152015 that are divisible by 55 or 1313, but not both.
2015Guts Test
2015 Geometry #4

Source:

7/1/2022
In trapezoid ABCDABCD with AD∥BCAD\parallel BC, AB=6AB=6, AD=9AD=9, and BD=12BD=12. If ∠ABD=∠DCB\angle ABD=\angle DCB, find the perimeter of the trapezoid.
2015Geometry Test
2015 Team #4

Source:

8/3/2022
Let △ABC\triangle ABC be a right triangle with hypotenuse ACAC. A square is inscribed in the triangle such that points D,ED,E are on ACAC, FF is on BCBC, and GG is on ABAB. Given that AG=2AG=2 and CF=5CF=5, what is the area of △BFG\triangle BFG?
2015team test