Deck 4: Math: Mathematics Intermediate

Question 1

In a school fund-raiser, 10 students in class A sold an average (arithmetic mean) of 4 boxes of cookies. In class B, 15 students sold an average of 9 boxes. What was the average number of boxes of cookies sold by the 25 students?

A)13/25
B)1
C)6-1/2
D)7
E)13-6/13

Answer 1

7

Question 2

The remainder when a number n is divided by 7 is 2. Which of the following is the remainder when 2 n + 1 is divided by 7 ?

A)1
B)2
C)3
D)4
E)5

Answer 2

5

Question 3

What are all values of x such that x2 + 7 x + 6 = 0 ?

A)-6 = x = -1
B)-6 = x = 1
C)1 = x = 6
D)x = -6 or x = -1
E)x = 1 or x = 6

Answer 3

x = -6 or x = -1

Question 4

A particular flu vaccine is effective for 90 percent of the patients who receive it. What is the probability that it will be effective for both of the next two randomly selected patients?

A) 0.54
B) 0.63
C) 0.72
D) 0.81
E) 0.90

Question 5

The number of bacteria present in a laboratory sample after t days can be represented by 500(2 t). What is the initial number of bacteria present in this sample?

A)250
B)500
C)750
D)1,000
E)2,000

Question 6

Yvonne has studied the cost of tickets over time for her favorite sports team. She has created a model to predict the cost of a ticket in the future. Let C represent the cost of a ticket in dollars and y represent the number of years in the future. Her model is as follows.C = 2.50 y + 13Based on this model, how much will the cost of a ticket increase in two years?

A)$5
B)$8
C)$13
D)$18
E)$26

Question 7

Cos 2(3 x) + sin 2(3 x) =

A)0
B)1
C)3
D)6
E)9

Question 8

The population of the United States is approximately 250 million, and the national debt is approximately 4 trillion dollars. If this debt were divided equally among the population, what would be the debt, in dollars, per person?

A)16
B)1,600
C)16,000
D)1,600,000
E)16,000,000

Question 9

A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0.40 cubic foot per minute. At this rate, how many hours will it take for the water level to drop 1 foot?

A)4
B)8
C)12
D)16
E)32

Question 10

It takes 28 minutes for a certain bacteria population to double. If there are 5,241,763 bacteria in this population at 1:00 p.m., which of the following is closest to the number of bacteria in millions at 2:30 p.m. on the same day?

A)80
B)40
C)20
D)15
E)10

Question 11

For what value of x is 8 12 = 16 x?

A)3
B)4
C)8
D)9
E)12

Question 12

What is the distance between the points (2,10) and (-4,2) in the xy-plane?

A)6
B)8
C)10
D)14
E)18

Question 13

In the xy-plane, a line parallel to the x-axis intersects the y-axis at the point (0, 4). This line also intersects a circle in two points. The circle has a radius of 5 and its center is at the origin. What are the coordinates of the two points of intersection?

A)(1, 2) and (2, 1)
B)(2, 1) and (2, -1)
C)(3, 4) and (3, -4)
D)(3, 4) and (-3, 4)
E)(5, 0) and (-5, 0)

Question 14

Suppose 4 r = 3 s = 10 t, where r, s, and t are positive integers. What is the sum of the least values of r, s, and t for which this equality is true?

A)7
B)17
C)41
D)82
E)120

Question 15

3 3 + 4(8-5) ?=

A) 6.5
B) 11
C) 27.5
D)29
E)34.16

Question 16

In a group of 1,200 adults, there are 300 vegetarians. What is the ratio of nonvegetarians to vegetarians in the group?

A)1 to 3
B)1 to 4
C)3 to 1
D)4 to 1
E)4 to 3

Question 17

A certain company keeps a list of 50 employees and their annual salaries. When the salary of the very highly paid president is added to this list, which of the following statistics is most likely to be approximately the same or nearly the same for the original list and the new list?

A)The highest salary
B)The range
C)The mean
D)The median
E)The standard deviation

Question 18

The least common multiple of 8, 12, and a third number is 120. Which of the following could be the third number?

A)15
B)16
C)24
D)32
E)48

Question 19

The length of a rectangle is 3 more than its width. If L represents the length, what is an expression for the width?

A)3 -]>
B)L + 3
C)L - 3

Question 20

A circle with diameter 10 centimeters is to be cut from a square of paper 10 centimeters on a side. Of the following, which is closest to the amount of paper left over after the circle is cut out?

A)9 square centimeters
B)21 square centimeters
C)24 square centimeters
D)69 square centimeters
E)84 square centimeters

Question 21

The postal rate is 25 cents for the first ounce and 20 cents for each additional ounce or part of an ounce. What would it cost to mail a package that weighs 6.8 ounces?

A)$1.25
B)$1.40
C)$1.45
D)$1.70
E)$1.75

Question 22

A savings account earns 1 percent interest per month on the sum of the initial amount deposited plus any accumulated interest. If a savings account is opened with an initial deposit of $1,000 and no other deposits or withdrawals are made, what will be the amount in this account at the end of 6 months?

A)$1,060.00
B)$1,061.52
C)$1,072.14
D)$1,600.00
E)$6,000.00

Question 23

The principal of a high school would like to determine why there has been a large decline during the year in the number of students who buy food in the school?s cafeteria. To do this, 25 students from the school will be surveyed. Which method would be the most appropriate for selecting the 25 students to participate in the survey?

A)Randomly select 25 students from the senior class.
B)Randomly select 25 students from those taking physics.
C)Randomly select 25 students from a list of all students at the school.
D)Randomly select 25 students from a list of students who eat in the cafeteria.
E)Give the survey to the first 25 students to arrive at school in the morning.

Question 24

The manager of a company has to order new engines for its delivery trucks after the trucks have been driven 150,000 miles. One of the delivery trucks currently has 119,866 miles on it. This truck has the same delivery route each week and is driven an average of 40,000 miles each year. At this rate, the manager should expect this truck to reach 150,000 miles in approximately how many months?

A)Less than 4 months
B)Between 4 and 6 months
C)Between 6 and 8 months
D)Between 8 and 10 months
E)More than 10 months

Question 25

If a 2 by 18 rectangle has the same area as a square, what is the length of a side of the square?

A)4
B)6
C)8
D)10
E)12

Question 26

If the digit in the tens place of 37,241 is increased by one and the digit in the thousands place is decreased by one, how has the number been changed?

A)The number has been decreased by 990.
B)The number has been decreased by 1,000.
C)The number has been decreased by 1,010.
D)The number has been increased by 10.
E)The number has been increased by 1,010.

Question 27

Which of the following pairs of geometric figures must be similar to each other?

A)Two equilateral triangles
B)Two isosceles triangles
C)Two right triangles
D)Two rectangles
E)Two parallelograms

Question 28

The first term in a sequence of numbers is 1/2. Each term after the first term is 1 more than twice its previous term. What is the 4th term?

A)2
B)4
C)5
D)11
E)23

Question 29

Rosa is twice as old as Byron.Fred is one year older than Byron.If Fred's age is represented by F, which of the following represents the ages of Rosa and Byron, respectively?

A)½ ( F - 1) and F - 1
B)½ ( F + 1) and F + 1
C)2 ( F - 1) and F - 1
D)2 ( F + 1) and F + 1
E)2 F and F - 1

Question 30

The town of Mayville taxes property at a rate of $42 for each $1,000 of estimated value. What is the estimated value of a property on which the owner owes $5,250 in property tax?

A)$42,000
B)$47,250
C)$125,000
D)$220,500
E)$5,250,000

Question 31

A cat lies crouched on level ground 50 feet away from the base of a tree. The cat can see a bird's nest directly above the base of the tree. The angle of elevation from the cat to the bird's nest is 40°. To the nearest foot, how far above the base of the tree is the bird's nest?

A)32
B)38
C)42
D)60
E)65

Question 32

A certain machine produces 300 nails per minute. At this rate, how long will it take the machine to produce enough nails to fill 5 boxes of nails if each box will contain 250 nails?

A)4 min
B)4 min 6 sec
C)4 min 10 sec
D)4 min 50 sec
E)5 min

Question 33

1 gallon = 4 quarts1 quart = 2 pintsThe number of pints in 10 gallons could be determined by performing which of the following operations?

A)Multiplying 10 by 2
B)Dividing 10 by 6
C)Multiplying 10 by 6
D)Dividing 40 by 2
E)Multiplying 40 by 2

Question 34

Which of the following is closest to the height of the door to your classroom?

A)1 meter
B)2 meters
C)4 meters
D)7 meters

Question 35

From a shipment of 500 batteries, a sample of 25 was selected at random and tested. If 2 batteries in the sample were found to be dead, how many dead batteries would be expected in the entire shipment?

A)10
B)20
C)30
D)40
E)50

Question 36

It takes 64 identical cubes to half fill a rectangular box. If each cube has a volume of 8 cubic centimeters, what is the volume of the box in cubic centimeters?

A)1,024
B)512
C)128
D)16
E)8

Question 37

If a measurement of a rectangular box is given as 48 cubic inches, then the measurement represents the

A)distance around the top of the box
B)length of an edge of the box
C)surface area of the box
D)volume of the box

Question 38

What percent of 175 is 7 ?

A)4%
B)12.25%
C)25%
D)40%

Question 39

Which of the following expressions is NOT equivalent to (a + b)(x+y) ?

A)(a + b)x + (a + b)y
B)a(x + y) + b(x+y)
C)(b + a)(y + x)
D)ax + by
E)ax + bx + ay + by

Question 40

Which of the following containers has the greatest liquid capacity?(1 gallon = 4 quarts = 8 pints = 128 ounces)

A)A 64-ounce orange juice container
B)A 16-pint water jug
C)A 5-quart punch bowl
D)A 2-quart cola bottle
E)A 1-gallon milk bottle

Question 41

John is going to cover an attic floor with insulation. The floor measures 25 feet by 35 feet. If one roll of insulation will cover 64 square feet, how many rolls of insulation does John need?

A)1
B)2
C)8
D)14
E)110

Question 42

The cost to mail a first-class letter is 33 cents for the first ounce. Each additional ounce costs 22 cents. (Fractions of an ounce are rounded up to the next whole ounce.) How much would it cost to mail a letter that weighs 2.7 ounces?

A)55 cents
B)66 cents
C)77 cents
D)88 cents
E)99 cents

Question 43

Easy Ride Van Company finds that about 40 percent of the time a person who makes an advance reservation for transportation does not keep the reservation. Therefore, for each of their 10-passenger vans, the Easy Ride Van Company schedules 13 persons on the basis of advance reservations.Based on the information above, about how many riders out of the 13 scheduled would not keep their reservations?

A)1
B)3
C)5
D)7
E)9

Question 44

A scale drawing of a rectangular room is 5 inches by 3 inches. If 1 inch on this scale drawing represents 3 feet, what are the dimensions of the room?

A)5 feet by 3 feet
B)5 feet by 9 feet
C)15 feet by 3 feet
D)15 feet by 5 feet
E)15 feet by 9 feet

Question 45

An election involving four candidates for mayor has been held. Of the following, which is the best way to present the percentage of votes each candidate received?

A)Circle graph
B)Line graph
C)Box plot
D)Scatterplot
E)Histogram

Question 46

Of the following, which is the best unit to use when measuring the growth of a plant every other day during a 2-week period?

A)Centimeter
B)Meter
C)Kilometer
D)Foot
E)Yard

Question 47

If each of the counting numbers from 1 through 10 is multiplied by 13, how many of the resulting numbers will be even?

A)One
B)Four
C)Five
D)Six
E)Ten

Question 48

Which of the following pieces of information would NOT be useful in deciding what type of car is the most economical to drive?

A)Median income of drivers
B)Range of insurance costs
C)Average miles per gallon
D)Typical cost of repairs per year
E)Cost of routine maintenance

Question 49

Which of the following is NOT a property of every rectangle?

A)The opposite sides are equal in length.
B)The opposite sides are parallel.
C)All angles are equal in measure.
D)All sides are equal in length.
E)The diagonals are equal in length.

Question 50

If x = -4, the value of -4 x is

A)-16
B)-8
C)8
D)16

Question 51

If k can be replaced by any number, how many different values can the expression k + 6 have?

A)None
B)One
C)Six
D)Seven
E)Infinitely many

Question 52

What is the difference between the smallest positive 3-digit number and the largest positive 2-digit number?

A)1
B)9
C)10
D)90
E)900

Question 53

Ken bought a used car for $5,375. He had to pay an additional 15 percent of the purchase price to cover both sales tax and extra fees. Of the following, which is closest to the total amount Ken paid?

A)$806
B)$5,510
C)$5,760
D)$5,940
E)$6,180

Question 54

Which of the following is both a multiple of 3 and a multiple of 7?

A)7,007
B)8,192
C)21,567
D)22,287
E)40,040

Question 55

The average weight of 50 prize-winning tomatoes is 2.36 pounds. What is the combined weight, in pounds, of these 50 tomatoes?

A)0)0472
B)11.8
C)52.36
D)59
E)118

Question 56

What is the least whole number x for which 2 x > 11 ?

A)5
B)6
C)9
D)22
E)23

Question 57

What is 2/3 of 15 marbles?

A)10 marbles
B)9 marbles
C)8 marbles
D)5 marbles

Question 58

Pencils sell individually for $0.07 each or in packs of 12 for $0.79 per pack. How much is saved when 24 pencils are purchased by the pack instead of individually?

A)$0.01
B)$0.05
C)$0.10
D)$0.72
E)$1.44

Question 59

If the diameter of a circle is 30 centimeters, what is the radius of the circle?

A)10 cm
B)15 cm
C)60 cm
D)90 cm
E)180 cm

Question 60

The perimeter of a square is 36 centimeters. What is the area of the square?

A)6 square cm
B)9 square cm
C)18 square cm
D)81 square cm

Question 61

The following statement is true: "If Sally goes to the movie, Mark will go also." Which statement below could NOT be true?

A)Sally and Mark both go to the movie.
B)Sally goes to the movie and Mark does not go.
C)Mark goes to the movie and Sally does not go.
D)Neither Mark nor Sally goes to the movie.

Question 62

3 3 + 4(8-5) ?=

A) .75
B) 1.08
C) 75
D) 108

Question 63

Which of these numbers is a prime number?

A)15
B)23
C)34
D)56

Question 64

Which number is between 0.09 and 0.1 ?

A)0)95
B)0)5
C)0)095
D)0)05

Question 65

30 is what percent of 60 ?

A) 0.5%
B) 2%
C) 30%
D) 50%

Question 66

Which number is between 1.8 and 1.9 ?

A) 0.189
B) 0.198
C) 1.83
D) 1.93

Question 67

15 is 25% of what number?

A) 0.60
B) 3.75
C) 37.5
D) 60

Question 68

If a triangle is equilateral, which of the following must be true?

A)Only two sides are equal.
B)All sides are equal.
C)All angles are right angles.
D)All angles have different degree measures.

Question 69

Which of the following is true about 200% of 30 ?

A)It is 1/2 times 30.
B)It is 2 times 30.
C)It is 200 times 30.
D)It is 200 times greater than 30.

Question 70

Which of the following is true about 56% of 20 ?

A)It is less than 20.
B)It is greater than 20.
C)It is equal to 20.
D)It is more than double 20.

Question 71

Which of the following is closest to the length of a car?

A)1 foot
B)3 feet
C)10 feet
D)35 feet

Question 72

A quarter is flipped 50 times. Which of the following is most likely to be the number of times heads comes up?

A)2
B)3
C)11
D)26
E)50

Question 73

The degree measures of the angles of a rectangle are a, b, c, and d. Which of the following must be true about the rectangle?

A)a + b + c = d
B)a + b + c + d = 90
C)a + b + c + d = 180
D)a + b + c + d = 270
E)a + b + c + d = 360

Question 74

Which of the following inequalities is equivalent to 5 n + 4 < 19 ?

A)n < 3
B)n < 5
C)n > 5
D)n < 10

Question 75

Henry is older than Bill, and Bill is older than Peter. Then

A)Henry is older than Peter.
B)Henry is younger than Peter.
C)Henry is the same age as Peter.
D)there is not enough information given to tell which is true.

Question 76

Which of the following decimals represents 15%?

A) 15.
B) .15
C) 1.5
D) 1500

Question 77

Which number is between 1.2 and 1.3 ?

A) 0.123
B) 0.132
C) 1.23
D) 1.32

Question 78

Carlos' basketball team won 75% of its games last season. If they played 80 games, how many games did they win?

A)20
B)60
C)68
D)75

Question 79

2x + 3y + 4x =

A)9xy
B)9x 2y
C)5xy + 4x
D)6x + 3y