35th Annual

Armstrong Atlantic State University

High School Math Tournament

Ciphering Round – Junior Varsity

10 seconds left60 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

24

10 seconds left60 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

63) 21, 9, 7, 3, (1,

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?

Question 3 - Answer

miles course mi,2

1 2nd mi,

2

3 1st 2

10 seconds left60 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

2

1

10 seconds left60 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

45

10 seconds left60 seconds leftQuestion 6 30 seconds left

TIME’S UP!!!

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

Question 6 - Answer

18

10 seconds left60 seconds left 30 seconds left

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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.

Question 7 - Answer

2X

10 seconds left60 seconds leftQuestion 8 30 seconds left

TIME’S UP!!!

Solve for x, y, and z.

215

16

9

10

8

9

zyx

Question 8 - Answer

2,2,3 zyx

10 seconds left60 seconds leftQuestion 9 30 seconds left

TIME’S UP!!!

What is the sum of the

prime divisors of 2013?

Question 9 - Answer

75

10 secs60 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.

THGIR

GNORW

GNORW

Question 10 - Answer

6H