2017 Pinal County Middle School Math Competition

Team Round

Question 1

Provide an appropriate response.The three-part inequality a < x ≤ b means "a is less than x and x is less than or equal to b". Which of these inequalities is not satisfied by any real number x?

a.) −8 < 𝑥 ≤ −7

b.) −5 < 𝑥 ≤ −11

c.) 0 < 𝑥 ≤ 4

d.) −2 < 𝑥 ≤ 6

e.) None of the above.

Question 2

Find the smallest angle between the hands of a clock when it is 4 o’clock.

a.) 120°

b.) 20°

c.) 240°

d.) 95°

e.) None of the above.

Question 3

Which of the following statements regarding number systems is true?

a.) Whole numbers are a subset of the Counting numbers.

b.) Real numbers are a subset of the Rational numbers.

c.) All Whole numbers are included in the set of Integers.

d.) All Integers are included in the set of Whole numbers.

e.) None of the above.

Question 4

In a group of 50 students, 23 take math, 11 take psychology, and 7 take both math and psychology. If one student is selected at random, find the probability that the student takes math or psychology.

a.) 11/50

b.) 23/50

c.) 27/50

d.) 34/50

e.) None of the above.

Question 5

Hanif, Horace, Hilary and Hannah are students. Hanif and Horace speak Chinese, whereas the others speak Arabic. Horace and Hannah speak Albanian. Everyone except Hanif speaks Esperanto.

Who only speaks Arabic and Esperanto?

a.) Hanif

b.) Horace

c.) Hilary

d.) Hannah

e.) None of the above.

Question 6

If the radius of the circle is 5 units and AC = 13 units, find AD.

a.) 14

b.) 16

c.) 12

d.) 8

e.) None of the above.

Question 7

Which of the following choices shows equivalent values?

a.) 11

4, 1.14, 114%

b.) 21

2, 2.2, 220%

c.) 11

5, 1.2, 120%

d.) 2

3, 0.66, 66%

e.) None of the above.

Question 8

The winner of a raffle will receive a new sports utility vehicle. If 500 raffle tickets were sold and you purchased ten tickets, what are the odds against your winning the car?

a.) 1 to 49

b.) 49 to 1

c.) 1 to 50

d.) 50 to 1

e.) None of the above.

Question 9

A ride service charges a $5 pickup fee plus $0.50 for each mile of the trip. If a customer gives the driver $20 and asks for $4 change. Which of the following statements would allow us to calculate the size of the tip given to the driver?

a.) The trip was 14 miles long.

b.) The tip was 1/3 the total trip charge.

c.) The distance charge was 140% of the pickup charge.

d.) Choices a.), b.), and c.)

e.) None of the above.

Question 10

The instructions on a bottle of liquid plant insecticide call for mixing two parts of the insecticide with three parts of water. To mix the entire 16-ounce bottle of insecticide, how much water is needed, in cups?

a.) 24

b.) 16

c.) 8

d.) 3

e.) None of the above.

Question 11

A student has 6 black marbles and 2 red marble in his pocket. He selects one marble at random, looks at it and puts it back. Then he will select another marble at random. What is the probability that the student selects black marbles both times?

a.) 1

b.) 5/8

c.) 1/2

d.) 9/16

e.) None of the above.

Question 12

Consider the statement “Not all pets are animals.” Which of the following statements has exactly the same meaning?

a.) Any animal can be a pet.

b.) All pets are not animals.

c.) Some pets are not animals.

d.) Some animals are not pets.

e.) None of the above.

Question 13

Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter's age was twice the sum of Carla's & Jim's age. Find the present age of each one of them.

a.) Carla:5 years, Jim: 6 years, Peter: 19 years

b.) Carla:5 years, Jim: 7 years, Peter: 20 years

c.) Carla:5 years, Jim: 3 years, Peter: 16 years

d.) Carla:5 years, Jim: 5 years, Peter: 18 years

e.) None of the above.

Question 14

If E and F are midpoints and EF = 9, and DC = 15, find AB.

a.) 5

b.) 3

c.) 2

d.) 4

e.) None of the above.

Question 15

The average of 1, 2, 5, 9, and x is 4. The average of 2, 3 and y is 6. What is the value of 𝑥 + 𝑦?

a.) 5

b.) 10

c.) 16

d.) 17

e.) None of the above.

Question 16

Draw a valid conclusion from the given premises.if a student misses a test, then they can make it up.if a student makes up a test, then they won’t be penalized.Therefore, …

a.) if a student is penalized, then they missed a test.

b.) If a student misses a test, then they won’t be penalized.

c.) If a student doesn’t miss a test, then they will be penalized.

d.) if a student is penalized, then they didn’t miss a test.

e.) None of the above.

Question 17

If three times the smaller of two consecutive integers is added to four times the larger, the result is 123. Find the smaller integer.

a.) 16

b.) 17

c.) 18

d.) 51

e.) None of the above.

Question 18

Find the length of XZ.

a.) 30

b.) 54

c.) 40

d.) 58

e.) None of the above.

Question 19

The chart shows the results of a survey asking the current age of students in the freshman class. What percent of the students surveyed were 14 years old?

a.) 50%

b.) 60%

c.) 66%

d.) 70%

e.) None of the above.

Age Students

13 years 25

14 years 66

15 years 19

Question 20

Study the pattern in the examples to the right. Then select the equation that describes the pattern.

a.) ax # ay = ax+y+4

b.) ax # ay = ax+2y

c.) ax # ay= a2x+y

d.) ax # ay = ax∙y+2

e.) None of the above.

a4 # a6 = a14

a2 # a3 = a9

a7 # a5= a16