1. 35 th Annual Armstrong Atlantic State University High School Math Tournament Ciphering Round - Varsity

2. 10 seconds left 60 seconds leftQuestion 1 30 seconds left TIME’S UP!!! Triangle ABC is a right triangle with edge lengths AB = 50, BC = 40 and CA = 30. The perpendicular from C to AB meets AB at D as shown. What is the length of DC? B A C D

3. Question 1 - Answer

4. 10 seconds left 60 seconds leftQuestion 2 30 seconds left TIME’S UP!!! Suppose a positive integer N is divisible by 21 and 9. What is the smallest possible number of positive integers that divide N ?

5. Question 2 - Answer

6. 10 seconds left 60 seconds leftQuestion 3 30 seconds left TIME’S UP!!! The following happens at a two-person relay race: The first runner hands off the baton after having raced one half the distance plus half a mile. The second runner reaches the finish line after having raced one third of the remaining distance plus one third of a mile. How long was the course?

7. Question 3 - Answer

8. 10 seconds left 60 seconds leftQuestion 4 30 seconds left TIME’S UP!!! A box contains 5 blue chips, 3 red chips, and 2 white chips. If three chips are randomly selected, without replacement, what is the probability that one of each color is selected?

9. Question 4 - Answer

10. 10 seconds left 60 seconds leftQuestion 5 30 seconds left TIME’S UP!!! The digits of both 52 and 22 are non-ascending since 5 ≥ 2 and 2 ≥ 2. How many 2 digit numbers have digits in non- ascending order?

11. Question 5 - Answer

12. 10 seconds left 60 seconds leftQuestion 6 30 seconds left TIME’S UP!!! The Venn Diagram represents snack preference among 140 Armstrong professors. C A P A – apples P – pretzels C – chips 10 5 30 20 50 professors eat both apples and chips, 12 eat both pretzels and chips, and 75 eat chips. How many eat only chips?

13. Question 6 - Answer

14. 10 seconds left 60 seconds left 30 seconds left TIME’S UP!!! Question 7 Find the digits X and Y such that the base three numeral 1X21 represents the same value as the base five numeral 2Y2.

15. Question 7 - Answer

16. 10 seconds left 60 seconds leftQuestion 8 30 seconds left TIME’S UP!!! Solve for x, y, and z.

17. Question 8 - Answer

18. 10 seconds left 60 seconds leftQuestion 9 30 seconds left TIME’S UP!!! A ball is thrown into the air with a velocity of 40 ft per sec. Its height in feet after t seconds is given by the formula Determine the time when the instantaneous velocity is equal to the average velocity of the ball on its trip up. Express answer as a fraction in lowest terms.

19. Question 9 - Answer

20. 10 secs 60 seconds leftQuestion 10 30 seconds TIME’S UP!!! Two wrongs DO make a right! Each of the letters in the following sum stands for one of the digits 1, 2, …, 8. Given that R represents 5 and O represents 7, determine what digit H represents.

21. Question 10 - Answer