Deck 6: The Nature of Algebra

Question 1

Change the given form into the decimal form. ​ ​

A)
B)
C)
D)
E)

Answer 1

Question 2

An inlet pipe on a swimming pool can be used to fill the pool in 35 hours. The drain pipe can be used to empty the pool in 40 hours. If the pool is half filled and then the drain pipe is accidentally opened, how long will it take to fill the pool?
​
__________ hours

Answer 2

140

Question 3

Change the given form into the decimal form. ​ ​​

A)
B)
C)
D)
E)

Answer 3

Question 4

The combined area of New York and California is 204,194 square miles. The area of California is 108,530 square miles more than that of New York. Find the land area of each state.
​
CA __________ mi², NY __________ mi²

Question 5

The product of two consecutive positive even numbers is 528. What are the numbers? ​

A) 24 and 26
B) 22 and 24
C) 21 and 20
D) 22 and 23
E) 20 and 22

Question 6

An animal shelter has two purebred Labradors among the 48 dogs available for adoption. It is also known that 7/8 of the dogs are mongrels. How many of the dogs are purebreds?
​
__________ dogs

Question 7

An hourly salary of $20 is equivalent to what annual salary? Assume a 35-hour work week.
​
$__________

Question 8

A swimming pool is 15 ft by 30 ft and an average of 5 ft in depth. It takes 25 minutes longer to fill than to drain the pool. If it can be drained at a rate of 10 ft ³ /min faster than it can be filled, what is the drainage rate? Give your answer to one decimal place.
​
__________ ft ³ /min

Question 9

Jane figures that her monthly car insurance payment of $140 is equal to 30% of the amount of her monthly auto loan payment. What is her total combined monthly expense for auto loan payment and insurance (rounded to the nearest dollar)? ​

A) $607
B) $467
C) $509
D) $42
E) $612

Question 10

What is the sum of the first 101 consecutive even numbers? ​

A) 5,050
B) 10,302
C) 10,300
D) 202
E) 5,151

Question 11

The product of two consecutive positive even numbers is 288. What are the numbers?

Question 12

An inlet pipe on a swimming pool can be used to fill the pool in 45 hours. The drain pipe can be used to empty the pool in 50 hours. If the pool is half filled and then the drain pipe is accidentally opened, how long will it take to fill the pool? ​

A) 209 hours
B) 225 hours
C) 237 hours
D) 450 hours
E) 5 hours

Question 13

A canoeist rows downstream in 0.5 hours and back upstream in 3 hours. What is the rate of the current if the distance rowed is 3 miles in each direction? Give your answer to one decimal place, if required.
​
__________ mph

Question 14

An animal shelter has two purebred Labradors among the 81 dogs available for adoption. It is also known that 7/9 of the dogs are mongrels. How many of the dogs are purebreds? ​

A) 16 dogs
B) 21 dogs
C) 9 dogs
D) 18 dogs
E) 63 dogs

Question 15

A canoeist rows downstream in 0.5 hours and back upstream in 4 hours. What is the rate of the current if the distance rowed is 4 miles in each direction? ​

A) 4.5 mph
B) 3.5 mph
C) 4 mph
D) 2 mph
E) 7 mph

Question 16

The combined area of New York and California is 204,188 square miles. The area of California is 108,532 square miles more than that of New York. Find the land area of each state. ​

A) California 156,614 mi ² , New-York 47,574 mi ²
B) California 156,460 mi ² , New-York 47,728 mi ²
C) California 156,360 mi ² , New-York 47,828 mi ²
D) California 47,828 mi ² , New-York 156,360 mi ²
E) California 47,928 mi ² , New-York 156,260 mi ²

Question 17

A swimming pool is 15 ft by 30 ft and an average of 5 ft in depth. It takes 25 minutes longer to fill than to drain the pool. If it can be drained at a rate of 18 ft ³ /min faster than it can be filled, what is the drainage rate? Please give the answer to one decimal places. ​

A) 55.6 ft ³ /min
B) 50.2 ft ³ /min
C) 43.9 ft ³ /min
D) 43.0 ft ³ /min
E) 32.2 ft ³ /min

Question 18

What is the sum of the first 90 consecutive even numbers?

Question 19

Jane figures that her monthly car insurance payment of $190 is equal to 30% of the amount of her monthly auto loan payment. What is her total combined monthly expense for auto loan payment and insurance (rounded to the nearest dollar)?
​
$__________

Question 20

An hourly salary of $45 is equivalent to what annual salary? Assume a 35-hour work week. ​

A) $81,850
B) $70,600
C) $81,900
D) $82,150
E) $77,900

Question 21

A certain test is worth 140 points. How many points (rounded to the nearest point) are needed to obtain a score of 85%? ​

A) 61 points
B) 119 points
C) 124 points
D) 165 points
E) 55 points

Question 22

What is 4% of $1,125?
​
$__________

Question 23

Estimate the percentages. ​ of 3,300
​

A)
B) 2,211
C)
D) 2,200
E)

Question 24

Change the given form into the decimal form. ​ ​

A) 0.0575
B) 0.0675
C) 5.75
D) 4.75
E) 0.00575

Question 25

If the property tax on a $300,000 home is $2,270, what is the tax on a $150,000 home? ​

A) $1,500
B) $1,135
C) $1,143
D) $1,125
E) $227

Question 26

Insert >, < , or = as appropriate in the expression. ​ , ​

A) >
B) =
C) <

Question 27

What number is 140% of 14? ​

A) 18.5
B) 10
C) 19.6
D) 14
E) 19.3

Question 28

If 6% of the 205 million adult Americans are unemployed, how many adult Americans are unemployed? ​

A) 34.17 million
B) 12.3 million
C) 19.07 million
D) 12 million
E) 2.93 million

Question 29

Change the given form into the fraction. ​
0)015
​

A)
B)
C)
D)
E)

Question 30

A moderately active 140-pound person will use 2,100 calories per day to maintain that body weight. How many calories per day are necessary to maintain a moderately active 145-pound person? ​

A) 2,180 calories
B) 2,185 calories
C) 21,750 calories
D) 2,175 calories
E) 2,170 calories

Question 31

Solve the proportion for the item represented by a letter. ​ ​

A)
B)
C)
D)
E)

Question 32

The pitch of a roof is the ratio of the rise to the half-span. If a roof has a rise of 16 feet and a span of 56 feet, what is the pitch? ​ ​

A)
B)
C)
D) 7
E) 28

Question 33

What is 4% of $2,225? ​

A) $109
B) $556
C) $265
D) $1,656
E) $89

Question 34

Tell whether the pair of ratios forms a proportion. ​ , ​

A) yes
B) no

Question 35

A cement mixture calls for 93 pounds of cement for 3 gallons of water. What is the ratio of water to cement? ​

A) 31 to 1
B) 1 to 31
C) 1 to 30
D) 1 to 33
E) 30 to 1

Question 36

Estimate the percentages.
​
50% of 9,795
​ of 4,200

Question 37

What number is 170% of 16? Give your answer to one decimal place, if required.

Question 38

Find , when , , and . ​ ​

A)
B)
C)
D)
E)

Question 39

A certain test is worth 125 points. How many points (rounded to the nearest point) are needed to obtain a score of 85%?
​
__________ points

Question 40

If 5.2% of the 200 million adult Americans are unemployed, how many adult Americans are unemployed?
​
Give your answer to two decimal places, if required.
​
__________ million

Question 41

The sum of three consecutive integers is 81. What are the integers? ​

A) 78, 79, 80
B) 27, 28, 29
C) 25, 27, 29
D) 26, 27, 28
E) 81, 0, 0

Question 42

Solve the proportion for the item represented by a letter.
​ ​
H = __________

Question 43

The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. ​
If you subtract fifteen from twice a number, the result is three. What is the number?
​

A) 9
B) -6
C) 6
D) -9
E) -13.5

Question 44

A cement mixture calls for 9 pounds of cement for 3 gallons of water. What is the ratio of cement to water?
​
__________ to 1

Question 45

Solve the proportion for the item represented by a letter.
​ ​ __________

Question 46

Solve the proportion for the item represented by a letter. ​ ​

A) 11
B) 18
C) 17
D) 15
E) 16

Question 47

A cement mixture calls for 3 pounds of cement for 3 gallons of water. What is the ratio of water to cement?
​
__________ to 1

Question 48

A diagonal brace is to be placed in the wall of a room. The height of the wall is 7 ft, and the wall is 15 ft long. What is the exact length of the brace? ​

A)
B)
C) 17
D)
E) 13

Question 49

To dilute a medication you can use the following formula:
​ ​
How many units of a 10% solution are needed to prepare 300 units of a 7% solution?
​
__________ units

Question 50

If you add six to twice a number, the result is sixteen. What is the number? ​

A) 10
B) 5
C) 8
D) 13
E) 2

Question 51

Tell whether the pair of ratios forms a proportion. Answer yes or no.
​ ,

Question 52

A moderately active 140-pound person will use 2100 calories per day to maintain that body weight. How many calories per day are necessary to maintain a moderately active 150-pound person?
​
__________ calories

Question 53

To dilute a medication you can use the following formula. ​ ​
How many units of a 10% solution are needed to prepare 300 units of a 6% solution?
​

A) 180 units
B) 210 units
C) 200 units
D) 170 units
E) 300 units

Question 54

A house and a lot are appraised at $224,400. If the value of the house is five times the value of the lot, how much is the house worth? ​

A) $44,880
B) $224,400
C) $37,400
D) $187,000
E) $179,520

Question 55

Find , when , , , and . Round to the nearest whole number.
​ ​ __________

Question 56

The pitch of a roof is the ratio of the rise to the half-span. If a roof has a rise of 16 feet and a span of 56 feet, what is the pitch?
​

Question 57

A cement mixture calls for 6 pounds of cement for 3 gallons of water. What is the ratio of cement to water? ​

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

Question 58

A professional gambler reported that at the end of the first race at the track he had doubled his money. He bet $33 on the second race and tripled the money he came with. He bet $60 on the third race and quadrupled his original bankroll. He bet $68 on the fourth race and lost it, but still had $64 left. With how much money did he start? ​

A) $33
B) $66
C) $165
D) $132
E) $99

Question 59

Insert >, <, or = as appropriate in the expression.
​

Question 60

If the property tax on a $200,000 home is $2,830, what is the tax on a $150,000 home? Round to the nearest dollar.
​
$__________

Question 61

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth). ​

A) 10.1, 8.1, 13.0
B) 10.1, 6.9, 13.0
C) 12.8, 10.8, 13.0
D) 11.0, 8.1, 13.0
E) 11.0, 6.9, 13.0

Question 62

The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. Carry out the first step for the following problem.
​
If you subtract fourteen from twice a number, the result is six. What is the number?

Question 63

A house and a lot are appraised at $191,700. If the value of the house is five times the value of the lot, how much is the house worth?
​
$__________

Question 64

Two joggers set out at the same time from their homes 18 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 2 mph faster than the rate of other, find the rate of each.

Question 65

The annual rate, r, compounded annually, it takes for dollar to grow to A dollars in 4 years is given by the formula . Find the rate necessary for a dollar to double in 4 years.
​
Give your answer to one decimal place, if required.
​
__________%

Question 66

A professional gambler reported that at the end of the first race at the track he had doubled his money. He bet $31 on the second race and tripled the money he came with. He bet $56 on the third race and quadrupled his original bankroll. He bet $64 on the fourth race and lost it, but still had $60 left. With how much money did he start?
​
$__________

Question 67

Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 5 meters per second. If the slower runner has a 69-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?
​
Give your answer to one decimal place, if required.
​
__________ sec

Question 68

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth).

Question 69

Two joggers set out at the same time from their homes 24 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 6 mph faster than the rate of other, find the rate of each. ​

A) 6 mph and 8 mph
B) 5 mph and 8 mph
C) 5 mph and 11 mph
D) 11 mph and 8 mph
E) 5 mph and 30 mph

Question 70

The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. Carry out the first step for the following problem.
​
A diagonal brace is to be placed in the wall of a room. The height of the wall is 8 ft, and the wall is 13 ft long. What is the exact length of the brace? __________ ft
​
What is the length of the brace to the nearest foot? __________ ft

Question 71

The sum of three consecutive integers is 99. What are the integers?

Question 72

Solve the inequality. ​ ​

A)
B)
C)
D)
E)

Question 73

Solve the inequality. ​ ​

A)
B)
C)
D)
E)

Question 74

Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 5 meters per second. If the slower runner has a 72-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time? ​

A) 10.5 sec
B) 12 sec
C) 11.5 sec
D) 13 sec
E) 14.40 sec

Question 75

Graph the solution set of the inequality. ​ ​

A)
B)
C)
D)
E)

Question 76

Rewrite the word statement using symbols: The square of negative four is equal to the four squared. Classify the equation as "true ", "false ", or open, and if it is open tell whether it is a conditional, identity, or contradiction. Find the requested number(s). Rewrite the word statement using symbols: Four added to a number is equal to the sum of the number and two. ​Classify the equation as "true ", "false ", or open, and if it is open tell whether it is a conditional, identity, or contradiction.

Question 77

The annual rate, r, compounded annually, it takes for 1 dollar to grow to D dollars in 3 years is given by the formula . Find the rate necessary for a dollar to double in 3 years. ​

A) 26.0%
B) 100.0%
C) 126.0%
D) 28.7%
E) 33.3%

Question 78

If you add two to twice a number, the result is twelve. What is the number?

Question 79

Rewrite the word statement using symbols. ​
The square of negative five is equal to the opposite of five squared.
​

A)
B)
C)
D)
E)

Question 80

Graph the solution set of the inequality. ​ ​

A)
B)
C)
D)
E)