1

Part of 2014 ASDAN Math Tournament

Problems(8)

2014 Advanced #1

Source:

Compute the smallest positive integer that is

3

more than a multiple of

5

, and twice a multiple of

6

2014Advanced Topics Test

2014 Advanced Tiebreaker #1

Source:

Compute the number of three digit numbers such that all three digits are distinct and in descending order, and one of the digits is a

5

2014Advanced Topics Tiebreaker

2014 Algebra #1

Source:

A college math class has

N

teaching assistants. It takes the teaching assistants

5

hours to grade homework assignments. One day, another teaching assistant joins them in grading and all homework assignments take only

4

hours to grade. Assuming everyone did the same amount of work, compute the number of hours it would take for

1

teaching assistant to grade all the homework assignments.

2014Algebra Test

2014 Algebra Tiebreaker #1

Source:

Kevin is running

1000

meters. He wants to have an average speed of

10

meters a second. He runs the first

100

meters at a speed of

4

meters a second. Compute how quickly, in meters per second, he must run the last

900

meters to attain his desired average speed of

10

meters a second.

2014Algebra Tiebreaker

2014 General #1

Source:

8

points on an exam, while his friend gets

3

times as many points as Alex. What is the average of their scores?

2014General Test

Source:

Compute the remainder when

2^{30}

1000

2014 Geometry #1

Source:

Consider a square of side length

1

and erect equilateral triangles of side length

1

on all four sides of the square such that one triangle lies inside the square and the remaining three lie outside. Going clockwise around the square, let

A

B

C

D

be the circumcenters of the four equilateral triangles. Compute the area of

ABCD

2014Geometry Test

2014 Geometry Tiebreaker #1

Source:

A

B

C

D

lie in the plane with

AB=AD=7

CB=CD=4

BD=6

. Compute the sum of all possible values of

AC

2014Geometry Tiebreaker