35 th Annual Armstrong Atlantic State University High School Math Tournament Ciphering Round – Junior Varsity.

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Presentation transcript:

35 th Annual Armstrong Atlantic State University High School Math Tournament Ciphering Round – Junior Varsity

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

Question 1 - Answer

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?

Question 2 - Answer

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?

Question 3 - Answer

10 seconds left 60 seconds leftQuestion 4 30 seconds left TIME’S UP!!! A box contains 6 blue chips and 3 red chips. If two chips are randomly selected, without replacement, what is the probability that one of each color is selected?

Question 4 - Answer

10 seconds left 60 seconds leftQuestion 5 30 seconds left TIME’S UP!!! The digits of 52 are strictly descending since 5 > 2. How many 2 digit numbers have digits in strictly descending order?

Question 5 - Answer

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 50 professors eat both apples and chips, 12 eat both pretzels and chips, and 75 eat chips. How many eat only chips?

Question 6 - Answer

10 seconds left 60 seconds left 30 seconds left TIME’S UP!!! Question 7 Find the digit X such that the base three numeral 1X21 represents the same value value as the base five numeral 202.

Question 7 - Answer

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

Question 8 - Answer

10 seconds left 60 seconds leftQuestion 9 30 seconds left TIME’S UP!!! What is the sum of the prime divisors of 2013?

Question 9 - Answer

10 secs 60 seconds leftQuestion 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.

Question 10 - Answer