35th Annual
Armstrong Atlantic State University
High School Math Tournament
Ciphering Round – Junior Varsity
10 seconds left60 seconds leftQuestion 1 30 seconds left
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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
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Suppose a positive integer N is divisible by 21 and 9.
What is the smallest possible number of positive integers that divide N?
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60 seconds leftQuestion 3 30 seconds left
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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?
10 seconds left60 seconds leftQuestion 4 30 seconds left
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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?
10 seconds left60 seconds leftQuestion 5 30 seconds left
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The digits of 52 are strictly descending since 5 > 2.
How many 2 digit numbers have digits in strictly descending order?
10 seconds left60 seconds leftQuestion 6 30 seconds left
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The Venn Diagram represents snack preference among 140 Armstrong professors.
C
A P
A – applesP – pretzelsC – chips
50 professors eat both apples and chips, 12 eat both pretzels and chips, and 75 eat chips. How many eat only chips?
10
53020
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Question 7
Find the digit X such that the base three
numeral 1X21 represents the same value
value as the base five numeral 202.
10 seconds left60 seconds leftQuestion 8 30 seconds left
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Solve for x, y, and z.
215
16
9
10
8
9
zyx
10 seconds left60 seconds leftQuestion 9 30 seconds left
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What is the sum of the
prime divisors of 2013?
10 secs60 seconds leftQuestion 10 30 seconds
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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.
THGIR
GNORW
GNORW