Deck 1: Foundations for Learning Mathematics

Question 1

Write the numbers that would be in the next row of the triangle. ​ ​

A) 4 60 80 100 80 60 4
B) 4 48 168 260 168 48 4
C) 4 40 80 120 80 40 4
D) 4 44 160 240 160 44 4
E) 4 44 164 252 164 44 4

Answer 1

4 44 164 252 164 44 4

Question 2

On a digital clock, how many times in 9 days will the numbers be consecutive digits, as they are, for example, in 1:23? ​

A) 45
B) 36
C) 72
D) 90
E) 54

Answer 2

90

Question 3

At a bicycle store, there were a bunch of bicycles and tricycles. If there were 38 seats and 88 wheels, how many bicycles and how many tricycles were there? ​

A) 24 bicycles and 26 tricycles
B) 12 bicycles and 26 tricycles
C) 14 bicycles and 24 tricycles
D) 52 bicycles and 36 tricycles
E) 26 bicycles and 12 tricycles

Answer 3

26 bicycles and 12 tricycles

Question 4

A Martian farmer looks out into the barnyard and sees tribbles (which have one head and four legs) and chalkas (which have one head and seven legs). She says to her son, "I count 135 heads and 738 feet. How many tribbles and how many chalkas are out there?" ​

A) 138 tribbles and 46 chalkas
B) 79 tribbles and 56 chalkas
C) 69 tribbles and 66 chalkas
D) 99 tribbles and 36 chalkas
E) 66 tribbles and 138 chalkas

Question 5

At the beginning of the month, Jack and Jill had $ 629 in a checking account. During the month, they wrote checks for $ 23 , $ 57 , and $ 58 . They made a withdrawal of $ 61 from the automatic teller machine, and they made deposits of $ 153 and $ 70 . How much money did they have at the end of the month? ​

A) $ 430
B) $ 644
C) $ 653
D) $ 605
E) $ 711

Question 6

The table below shows the hourly wages of four different job classifications at a small construction company: Carlos Vasquez, a plumbing contractor, hires 5 plumbers from this company at the hourly wage given in the table. If each plumber works 30 hours, what are the total wages paid by Carlos?

A) $ 4,380
B) $ 4,379
C) $ 4,370
D) $ 4,350
E) .$ 4,380

Question 7

Write the numbers that would be in the next row of the triangle. ​ ​

A) 15 22 29 36 43
B) 13 20 27 34 41
C) 13 26 47 84 153
D) 13 26 39 52 65
E) 17 26 35 44 53

Question 8

In how many different ways can you make change for $ 1.70 using only dimes and nickels? ​

A) 34
B) 36
C) 22
D) 18
E) 17

Question 9

On a digital clock, the digit '1' appears the most often in one day. How many times does the digit appear in 6 days? ​

A) 960
B) 1068
C) 1584
D) 624
E) 336

Question 10

Martha planted 13 rows of apple trees, and each row had 26 trees. If each tree yielded an average of 220 apples, how many apples grew in her orchard? ​

A) 2,860
B) 37,180
C) 148,720
D) 74,360
E) 5,720

Question 11

A special rubber ball is dropped from the top of a wall that is 652 m high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 40.75 m high. How many times did the ball bounce? ​

A) 9
B) 7
C) 8
D) 6
E) 4

Question 12

The mint currently makes million pennies a day. How many pennies does the mint make per second? ​

A) 34722
B) 58
C) 579
D) 3000
E) 5787

Question 13

John's diet allows 1900 calories per day. Thus far, he has had a glass of milk (90 calories), pancakes (150 calories), an apple (75 calories), a salad (150 calories), salad dressing (195 calories), and a piece of cake (375 calories). How many calories can John consume for dinner tonight? ​

A) 1210 calories
B) 1240 calories
C) 1090 calories
D) 865 calories
E) 1015 calories

Question 14

Palindromes are numbers whose value is the same backwards as forwards. For example, 1331 is a palindrome. Most children love explorations with palindromes because they find the patterns fun and the investigations are so mathematically rich. How many palindromes can you find between 100 and 799? ​

A) 14
B) 35
C) 70
D) 77
E) 63

Question 15

If you have a bunch of 10¢ and 5¢ stamps, and you know that there are 35 stamps and their total value is $ 1.55 , how many of each do you have? ​

A) 21 10¢ stamps and 14 5¢ stamps
B) 29 10¢ stamps and 6 5¢ stamps
C) 24 10¢ stamps and 11 5¢ stamps
D) 48 10¢ stamps and 22 5¢ stamps
E) 17 10¢ stamps and 18 5¢ stamps

Question 16

What numbers would be in the next row of the triangle? ​ ​

A) 5 14 18 21 25
B) 5 10 15 20
C) 5 10 15 20 25
D) 9 12 18 24 26
E) 10 15 20 25

Question 17

A special rubber ball is dropped from the top of a wall that is 512 feet high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 1 foot high. How many times did the ball bounce? ​

A) 256
B) 10
C) 18
D) 9
E) 512

Question 18

A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1160 feet of fencing material, what should be the length and the width of the field? ​

A) length = 330 feet; width = 250 feet
B) length = 280 feet; width = 200 feet
C) length = 380 feet; width = 300 feet
D) length = 430 feet; width = 350 feet
E) length = 230 feet; width = 150 feet

Question 19

Palindromes are numbers whose value is the same backwards as forwards. For example, 1331 is a palindrome. How many palindromes can you find between 1000 and 9999 ? ​

A) 90
B) 89
C) 88
D) 91
E) 85

Question 20

On a digital clock, how many times in one day will the numbers be equal digits as they are, for example in 1:11? ​

A) 3
B) 7
C) 5
D) 4
E) 6

Question 21

The mint currently makes million pennies a day. How many pennies does the mint make per year? ​

A) 3840 billion pennies
B) 5340 billion pennies
C) 5325 billion pennies
D) 5475 billion pennies
E) 3975 billion pennies

Question 22

Examine the magic triangle below. ​ ​ Describe a pattern(s) you see in the triangle. ​

A) The smallest number of each side lies in the middle.
B) The largest number of each side lies on a corner.
C) The product of each side is 15.
D) The sum of each side is 9.
E) All of the above

Question 23

Below is a magic square. ​ ​ Describe a pattern(s) you see in this magic square. ​

A) The sum of any row is 65.
B) The sum of any row or column is 65.
C) The sum of either center diagonal is 65.
D) The sum of any column is 65.
E) All of the above

Question 24

Use the following Venn diagram to answer the question. ​ ​ Represent the set {1,2,3,4,5,6,12,15} with symbols. ​

A) A ∪ B
B) A ∩ B
C) A ∩ C
D) C ∪ B
E) A ∪ C

Question 25

A family is planning a three-week vacation for which they will drive about 8,000 miles. They have a van that gets 17 miles per gallon, and they have a sedan that gets 32 miles per gallon. If gasoline costs $ 3.10 per gallon, how much more will they pay for gasoline if they take the van? ​

A) $ 2233.82
B) $ 683.82
C) $ 2480.00
D) $ 1458.82
E) $ 775.00

Question 26

Use the following Venn diagram to answer the question. ​ ​ Represent the set { 15 } with symbols. ​

A) B ∩ C
B) B ∩ A
C) B ∪ C
D) A ∩ C
E) A ∪ C

Question 27

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem} . Convert the information from the Venn diagram into everyday English. ​ ​

A) An American non-smoking healthy female.
B) An American who does not smoke and is female or has a health problem.
C) An American female who smokes or has a health problem.
D) An American female or an American smoker.
E) An American smoking female.

Question 28

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem}. ​ Convert the following symbols into everyday English. ​ S ∩ F ∩ P ​

A) An American female who is a smoker or has a health problem.
B) An American female who is not a smoker and has a health problem.
C) An American smoker who is a female or has a health problem.
D) An American female who is a smoker and has a health problem.
E) An American female who does not have a health problem.

Question 29

Place the appropriate symbol in the blank. ​ ​

A)
B)
C)
D)
E)

Question 30

Let U = { x | x is an American}, F = { x | x is a female} , S = { x | x is a smoker} , P = { x | x has a health problem} . Represent the following description with a Venn diagram. ​ An American female or an American smoker. ​

A)
B)
C)
D)
E)

Question 31

Rob Hill owns a compact car that averages 48 miles on 1 gallon of gas. How many miles could the car travel on 10 gallons of gas? ​

A) 490
B) 440
C) 580
D) 470
E) 480

Question 32

Aunt Karen wants to hang up six pictures that are all 12 inches wide on her 128 -inch wide wall. She wants to hang them in a straight line, evenly spaced between each picture and the walls. How much spacing does she need? ​

A) 16 inches
B) 24 inches
C) 56 inches
D) 10 inches
E) 8 inches

Question 33

A farmer harvested 32,000 pounds of avocados from one grove and 16,000 pounds of avocados from another grove. The avocados were all packed in shipping boxes in the same warehouse with 16 pounds in each box. How many boxes were needed to pack the avocados? ​

A) 1,000
B) 2,375
C) 2,000
D) 2,500
E) 3,000

Question 34

In the Animal Football League, the teams can score only 3-point field goals and 7-point touchdowns; no safeties or extra-credit points are allowed. In one contest, the Anteaters scored 81 points. If they scored 3 more touchdowns than field goals, how many touchdowns and field goals did they score? ​

A) 18 touchdowns and 15 field goals
B) 10 touchdowns and 7 field goals
C) 8 touchdowns and 5 field goals
D) 9 touchdowns and 6 field goals
E) 9 touchdowns and 12 field goals

Question 35

A frog is climbing out of a well that is 28 feet deep. The frog can climb 8 feet per hour, but then it rests for an hour, during which time it slips back 4 feet. How long will it take for the frog to get out of the well? ​

A) 7 hours
B) 17 hours
C) 8 hours
D) 28 hours
E) 56 hours

Question 36

How many subsets does the set A = { a,b,c,d,e,f,g,h } have? ​

A) 512
B) 256
C) 1024
D) 16
E) 2048

Question 37

The Lewis and Clark expedition between 1804 and 1806 covered almost 8000 miles. If you can drive 280 miles per day, about how many days will it take you to drive the same distance? Round your answer to the nearest day. ​

A) 21 days
B) 30 days
C) 26 days
D) 34 days
E) 29 days

Question 38

A long-distance phone company advertises a plan that offers 10 cents per minute rate. However, in the fine print you learn that the company charges a $ 1.50 surcharge on every call. Determine how many cents per minute you pay for a 20 minute phone call (including the surcharge). ​

A) 25 cents per minute
B) 18 cents per minute
C) 11 cents per minute
D) 8 cents per minute
E) 9 cents per minute

Question 39

Rewrite the following statement using mathematical symbols. ​ 5 is not an element of the set C. ​

A)
B)
C)
D)
E)

Question 40

The Lewis and Clark expedition between 1804 and 1806 covered almost 8000 miles. If gasoline costs $2.75 per gallon and your car gets 27 miles per gallon, how much money would it cost you to drive the same distance? ​

A) $296.30
B) $81.48
C) $814.81
D) $1111.11
E) $687.50

Question 41

People were asked three questions: Do you support the president's economic policy? Do you support the president's foreign policy? Do you support the president's social policy? Let E, F, and S denote the sets of persons responding yes to the first, second, and third questions, respectively. The results of the survey are shown in the Venn diagram below. The numbers represent the percent of respondents. What percent of people agree with the president's social policy?

A) 58 %
B) 34 %
C) 49 %
D) 20 %
E) 16 %

Question 42

Place the appropriate symbol in the blank: ​ { 2 } ____ { 1, 2, 3, 4, 5 } ​

A)
B)
C)
D)
E)

Question 43

An advertising firm found that a certain ad that ran on both radio and TV was only heard on the radio by 17 percent of the people and was only seen on TV by 34 percent of the people. Just 15 percent of the population both heard the ad on the radio and saw it on TV. What percent of the people in the area has neither seen nor heard the ad?

A) 34 percent
B) 85 percent
C) 66 percent
D) 36 percent
E) 64 percent

Question 44

Represent the following statement as a Venn Diagram. ​ Let A represent all algebra students, and let B represent all boys. Some boys are not Algebra students. ​

A)
B)
C)
D)
E)

Question 45

Let U be the set of all colors and S be the subset {red, orange, yellow, green, blue, violet}. Place the appropriate symbol in the blank: ​ green _____ U ​

A)
B)
C)
D)
E)

Question 46

In a group of 140 students, 85 know how to use a Macintosh, 100 know how to use an IBM-compatible computer, and 10 do not know how to use either kind. How many students know how to use both kinds of computers?

A) 75
B) 40
C) 55
D) 90
E) 130

Question 47

Place the appropriate symbol in the blank: ​ ​

A)
B)
C)
D)
E)

Question 48

Let U be the set of all colors and S be the subset {red, orange, yellow, green, blue, violet}. Place the appropriate symbol in the blank: ​ {orange} _____ U ​

A)
B)
C)
D)
E)

Question 49

An elementary teacher has asked her students to place their names in the region that represents their answers to the question "Which pets live in your home?" D = the set of students who have at least one dog C = the set of students who have at least one cat O = the set of students who have a pet that is not a dog or a cat Describe the following set with a Venn diagram. Students who have at least one dog but do not have any cats.

A)
B)
C)
D)
E)

Question 50

Place the appropriate symbol in the blank: ​ ​

A)
B)
C)
D)
E)

Question 51

Rewrite the following statement using mathematical symbols. ​ The set D is a subset of the set C . ​

A) D ⊄ C
B) C ⊆ D
C) D ⊆ C
D) D ⊇ C
E) D ∈ C

Question 52

An advertising firm found that a certain ad that ran on both radio and TV was only heard on the radio by 23 percent of the people and was only seen on TV by 32 percent of the people. Just 14 percent of the population both heard the ad on the radio and saw it on TV. What percent of the people in the area only heard the ad on radio or only saw the ad on TV?

A) 73 percent
B) 9 percent
C) 27 percent
D) 18 percent
E) 86 percent

Question 53

Describe the following set using set-builder notation. ​ The set of prime numbers less than 131 . ​

A) { x | x is a number less than 131 }
B) { 2, 3, 5, 7, 11, 13,..., 131 }
C) { 2, 131 }
D) [ 0, 131 )
E) { x | x is a prime number less than 131 }

Question 54

Describe the following set using set-builder notation. ​ The set of fractions between 0 and 5 . ​

A) ( 0, 5 )
B)
C) [ 0, 5 )
D) { x | x is a number between 0 and 5 }
E) { x | x is a fraction between 0 and 5 }

Question 55

Place the appropriate symbol in the blank: ​ 2 ____ { 1, 2, 3, 4, 5 } ​

A)
B)
C)
D)
E)