AFOQT Practice-Arithmetic Reasoning

It costs $0.85 to make a single color copy at a

copy center. At this price, how many copies can

be purchased with $68.00?

a. 9

b. 45

c. 68

d. 72

e. 80

e. Since the price per copy is $0.85, divide 68

by .85 to find the total number that can be

purchased with $68; 68 ÷ .85 = 80 copies

that can be purchased.

An aquarium has a base length of 12 inches

and a width of 5 inches. If the aquarium is

10 inches tall, what is the total volume?

a. 480 cubic inches

b. 540 cubic inches

c. 600 cubic inches

d. 720 cubic inches

e. 920 cubic inches

c. The volume of the aquarium can be found

by using the formula V = l × w × h. Since

the length is 12 inches, the width is 5 inches

and the height is 10 inches, multiply V =

12 × 5 × 10 to get a volume of 600 cubic

inches.

A man turns a woman's handbag in to the Lost

and Found Department of a large downtown

store. The man informs the clerk in charge that

he found the handbag on the floor beside an

entranceway. The clerk estimates that the

handbag is worth approximately $150. Inside,

the clerk finds the following items: one leather

makeup case valued at $65, one vial of

perfume, unopened, valued at $75, one pair of

earrings valued at $150, and $178 in cash.

The clerk is writing a report to be submitted

along with the found property. What should he

write as the total value of the found cash and

property?

a. $468

b. $608

c. $618

d. $658

e. $718

c. The value of the handbag ($150) must be

included in the total.

Which of these can be determined from the

information given in the above passage?

a. how much it will cost a family of four to

buy movie theater tickets on Saturday

afternoon

b. the difference between the cost of two

movie theater tickets on Tuesday night and

the cost of one ticket on Sunday at 3:00 P.M.

c. how much movie theater tickets will cost

each person if he or she is part of a group

of 40 people

d. the difference between the cost of a movie

theater ticket for an adult on Friday night

and a movie theater ticket for a 13-year-old

on Saturday afternoon at 1:00 P.M.

e. none of the above

d. Both choices a and b can be ruled out

because there is no way to determine how

many tickets are for adults or for children.

Choice c can be ruled out because the price

of group tickets is not given.

Based on the passage, how much will movie

theater tickets cost for two adults, one 15-yearold

child, and one 10-year-old child at 7:00 P.M.

on a Sunday night?

a. $17.00

b. $19.50

c. $25.00

d. $27.50

e. $37.50

d. Because the 15-year-old requires an adult

ticket, there are 3 adult tickets at $7.50 each

and one child's ticket at $5.

Using the passage, how can you find the

difference in price between a movie theater

ticket for an adult and a movie theater ticket

for a child under the age of 12 if the tickets are

for a show at 3:00 P.M. on a Saturday afternoon?

a. Subtract $3 from $5.50.

b. Subtract $5 from $7.50.

c. Subtract $7.50 from $5.50.

d. Add $5.50 and $3 and divide by 2.

e. Add $7.50 and $5.50 and divide by 2.

a. The adult price on Saturday afternoon is

$5.50; the child's price is $3.00.

It takes a typist 0.50 seconds to type one word.

At this rate, how many words can be typed in

60 seconds?

a. 2.25

b. 50

c. 90

d. 120

e. 220

d. This problem is solved by dividing 60 by

0.50. 60 ÷ .50 = 120.

If the average cadet burns 8.2 calories per

minute while riding a bicycle, how many

calories will the cadet burn if he or she rides

for 35 minutes?

a. 286

b. 287

c. 387

d. 980

e. 1,080

b. This problem is solved by multiplying 35

times 8.2.

Dr. Drake charges $36 for an office visit, which

is 3/4 of what Dr. Jean charges. How much does

Dr. Jean charge?

a. $27

b. $38

c. $48

d. $57

e. $68

c. You know the ratio of Drake's charge to

Jean's charge is 3 to 4, or 3

4. To find what

Jean charges, you use the equation 3

4 = 36

x ,

or 3x = 4(36); (4)(36) = 144, which is then

divided by 3 to arrive at x = 48.

Thirty percent of the cadets at the Air Force

Academy are involved in athletics. If 15% of

the athletes play lacrosse, what percentage of

the whole academy plays lacrosse?

a. 4.5%

b. 9.0%

c. 15%

d. 30%

e. 40%

a. In this question, you need to find 15% of

the 30% of cadet athletes that play lacrosse.

To find 15% of 30%, change the percents to

decimal form and multiply. Since 30% =

0.30 and 15% = 0.15, multiply (0.30)(0.15)

= 0.045. As a decimal, this is equivalent to

4.5%.

Basic cable television service, which includes

16 channels, costs $15 a month. The initial

labor fee to install the service is $25. A $65

deposit is required but will be refunded within

two years if the customer's bills are paid in full.

Other cable services may be added to the basic

service: the movie channel service is $9.40 a

month; the news channels are $7.50 a month;

the arts channels are $5 a month; the sports

channels are $4.80 a month.

A customer's cable television bill totaled $20 a

month. Using the preceding passage, what

portion of the bill was for basic cable service?

a. 25%

b. 33%

c. 50%

d. 75%

e. 85%

d. The basic cable service fee of $15 is 75%

of $20.

Basic cable television service, which includes

16 channels, costs $15 a month. The initial

labor fee to install the service is $25. A $65

deposit is required but will be refunded within

two years if the customer's bills are paid in full.

Other cable services may be added to the basic

service: the movie channel service is $9.40 a

month; the news channels are $7.50 a month;

the arts channels are $5 a month; the sports

channels are $4.80 a month.

A customer's first bill after having cable

television installed totaled $112.50. This

customer chose basic cable and one additional

cable service. Which additional service was

chosen?

a. the news channels

b. the movie channels

c. the arts channels

d. the sports channels

e. none of the above

a. The labor fee ($25) plus the deposit ($65)

plus the basic service ($15) equals $105. The

difference between the total bill, $112.50,

and $105 is $7.50, the cost of the news

channels.

Out of every 200 shoppers polled, 60 said they

buy fresh vegetables every week. How many

shoppers out of 40,000 could be expected to

buy fresh vegetables every week?

a. 3,600

b. 9,000

c. 12,000

d. 24,000

e. 36,000

c. 60 out of 200 is 30%. Thirty percent of

40,000 is 12,000.

Last year, 220 people bought cars from a

certain dealer. Of those, 60 percent reported

that they were completely satisfied with their

new cars. How many people reported being

unsatisfied with their new car?

a. 36

b. 55

c. 88

d. 132

e. 155

c. If 60% of the people were satisfied with

their new car, 40% were unsatisfied; 40% of

220 is 88.

Of 1,125 OTS candidates, 135 speak fluent

Spanish. What percentage of the candidates

speaks fluent Spanish?

a. 7.3%

b. 8.3%

c. 12%

d. 14%

e. 16%

c. Divide 135 Spanish-speaking candidates by

1,125 total number of candidates to arrive

at .12 or 12%.

The perimeter of a rectangle is 268 feet. Its two

longest sides add up to 156 feet. What is the

length of each of its two shortest sides?

a. 43 feet

b. 56 feet

c. 72 feet

d. 80 feet

e. 112 feet

b. The first step in solving the problem is to

subtract 156 from 268. 268 - 156 = 112.

The remainder, 112, is then divided by 2.

112 ÷ 2 =56.

A piece of wire 3 feet 4 inches long was divided

into 5 equal parts. How long was each part?

a. 6 inches

b. 7.5 inches

c. 8 inches

d. 10 inches

e. 1 foot 2 inches

c. Three feet 4 inches equals 40 inches; 40

divided by 5 is 8.

A middle school cafeteria has three different

options for lunch. For $2, a student can get

either a sandwich or two cookies. For $3, a

student can get a sandwich and one cookie. For

$4, a student can get either two sandwiches or a

sandwich and two cookies. If Jimae has $6 to

pay for lunch for her and her brother, which of

the following is NOT a possible combination?

a. three sandwiches and one cookie

b. two sandwiches and two cookies

c. one sandwich and four cookies

d. three sandwiches and no cookies

e. three sandwiches and two cookies

a. It will cost $3 for a sandwich and a cookie.

To get two additional sandwiches, it would

cost another $4. Therefore, it would cost $7

to get three sandwiches and a cookie. Since

she only has $6 to spend, this combination

is not possible.

A bed is 4 feet wide and 6 feet long. What is the

area of the bed?

a. 10 square feet

b. 20 square feet

c. 24 square feet

d. 30 square feet

e. 36 square feet

c. Area = width × length. In this case, 4 × 6 =

24 square feet.

Airman Beard's temperature is 98 degrees

Fahrenheit. Using the formula C = 5

9(F - 32),

what is his temperature in degrees Celsius?

a. 35.8

b. 36.7

c. 37.6

d. 41.1

e. 59.6

b. Use the formula beginning with the

operation in parentheses: 98 - 32 = 66.

Then multiply 66 by 5

9, first multiplying 66

by 5 to get 330; 330 divided by 9 is 36.66667,

which is rounded up to 36.7.

All of the rooms on the main floor of a

barracks are rectangular, with 8-foot high

ceilings. Captain Keira's office is 9 feet wide by

11 feet long. What is the combined surface area

of the four walls of her office, including any

windows and doors?

a. 99 square feet

b. 160 square feet

c. 320 square feet

d. 792 square feet

e. 640 square feet

c. Each 9-foot wall has an area of 9 × 8 or 72

square feet. There are two such walls, so

those two walls combined have an area of

72 × 2 or 144 square feet. Each 11-foot wall

has an area of 11 × 8 or 88 square feet, and

again there are two such walls: 88 × 2 = 176.

To find the total surface area, add 144 and

176 to get 320 square feet.

A recipe serves four people and calls for 1 1/2

cups of broth. If you want to serve six people,

how much broth do you need?

a. 2 cups

b. 2 1/4 cups

c. 2 1/3 cups

d. 2 1/2 cups

e. 2 3/4 cups

b. 1 1/2 cups equals 3/2 cups. The ratio is 6 people

to 4 people, which is equal to the ratio of x

to 3/2. By cross-multiplying, we get 6(3/2) equals

4x, or 9 equals 4x. Dividing both sides by 4,

we get 9/4, or 21/4 cups.

Fort Greenville is 120 miles west and 90 miles

north of Fort Johnson. How long is a direct

straight line route from Fort Greenville to

Fort Johnson City?

a. 100 miles

b. 125 miles

c. 150 miles

d. 180 miles

e. 195 miles

c. The distance between Fort Greenville and

Fort Johnson is the hypotenuse of a right

triangle with sides of length 90 and 120. The

length of the hypotenuse equals the square

root of the sum of the other two sides

squared. 902 + 1202= = 150

miles.

What is the estimated product when 157 and

817 are rounded to the nearest hundred and

multiplied?

a. 16,000

b. 80,000

c. 160,000

d. 180,000

e. 1,600,000

c. Round 157 to 200 and round 817 to 800:

200 × 800 = 160,000.

Mr. James Rossen is just beginning a computer

consulting firm and has purchased the

following equipment: 3 telephone sets, each

costing $125; 2 computers, each costing $1,300;

2 computer monitors, each costing $950;

1 printer, costing $600; and 1 answering

machine, costing $50. Mr. Rossen is reviewing

his finances. What should he write as the total

value of the equipment he has purchased so

far?

a. $3,025

b. $4,025

c. $5,400

d. $5,525

e. $6,525

d. It is important to remember to include all

three telephone sets ($375 total), both

computers ($2,600 total), and both

monitors ($1,900 total) in the total value.

One lap on a particular outdoor track measures

a quarter of a mile around. To run a total of

three-and-a-half miles, how many laps must

a person complete?

a. 7

b. 9

c. 10

d. 13

e. 14

e. To solve this problem, you must convert 3 1/2

to 7/2 and then divide 7/2 by 1/4. The answer, 28/4 ,is then reduced to the number 14.

5/8 × 4/7 =

a. 5/14

b. 20/8

c. 25/32

d. 9/16

e. 10

a. Cancel factors that are common to the

numerator and denominator, then multiply:

5/14

Newly hired nurses have to buy duty shoes at

the full price of $84.50, but nurses who have

served at least a year get a 15% discount. Nurses

who have served at least three years get an

additional 10% off the discounted price.

How much does a nurse who has served at

least three years have to pay for shoes?

a. $63.78

b. $64.65

c. $67.49

d. $71.83

e. $72.05

b. You cannot simply take 25% off the original

price, because the 10% discount after three

years of service is taken off the price that

has already been reduced by 15%. Figure

the problem in two steps: After the 15%

discount, the price is $71.83. Another 10%

off that gives you $64.65.

The basal metabolic rate (BMR) is the rate at

which our bodies use calories. The BMR for a

man in his twenties is about 1,700 calories per

day. If 204 of those calories should come from

protein, about what percentage of this man's

diet should be protein?

a. 1.2%

b. 8.3%

c. 12%

d. 16%

e. 18%

c. The problem is solved by dividing 204 by

1,700. The answer, 0.12, is then converted

to a percentage—12%.

How much water must be added to one liter of

a 5% saline solution to get a 2% saline

solution?

a. .5 liter

b. 1 liter

c. 1.5 liters

d. 2 liters

e. 2.5 liters

c. Use the equation .05(1) = .02(x), where x is the total amount of water in the resulting

2% solution. Solving for x, you get 2.5.

Subtracting the 1 liter of water already

present in the 5% solution, you will find

that 1.5 liters need to be added.

All of the rooms in a building are rectangular,

with 8-foot ceilings. One room is 9 feet wide by

11 feet long. What is the combined area of the

four walls, including doors and windows?

a. 90 square feet

b. 160 square feet

c. 180 square feet

d. 280 square feet

e. 320 square feet

e. Each 9-foot wall has an area of 9(8), or

72 square feet. There are two such walls, so

those two walls combined have an area of

144 square feet. Each 11-foot wall has an

area of 11(8), or 88 square feet, and again

there are two such walls: 88(2) = 176. Finally,

add 144 and 176 to get 320 square feet.

A child has a temperature of 40° C. What is the

child's temperature in degrees Fahrenheit?

(F = 9

5C + 32)

a. 100° F

b. 101° F

c. 102° F

d. 103° F

e. 104° F

e. Substituting 40 for C in the equation yields

F = (9/5)(40) + 32 = 72 + 32 = 104.

A woman drives west at 45 miles per hour.

After half an hour, a man starts to follow her.

How fast must he drive to catch up to her

three hours after he starts?

a. 52.5 miles per hour

b. 55 miles per hour

c. 60 miles per hour

d. 65 miles per hour

e. 67.5 miles per hour

a. The woman will have traveled 3.5 hours

at 45 miles per hour for a distance of

157.5 miles. To reach her in 3 hours, the

man must travel at 157.5 miles per 3 hours,

or 52.5 mph.

Jason is six times as old as Kate. In two years,

Jason will be twice as old as Kate is then. How

old is Jason now?

a. 3 years old

b. 6 years old

c. 9 years old

d. 12 years old

e. 15 years old

a. J = 6K. J + 2 = 2(K + 2), so 6K + 2 = 2K + 4,

which means K equals 1

2. J equals 6K, or 3.

A flash drive shows 827,036 bytes free. If you

delete a file of size 542,159 bytes and create a

new file of size 489,986 bytes, how many free

bytes will the flash drive have?

a. 489,986 free bytes

b. 577,179 free bytes

c. 681,525 free bytes

d. 774,863 free bytes

e. 879,209 free bytes

e. The 827,036 bytes free on the flash drive

plus 542,159 bytes freed when the file was

deleted equals 1,369,195 bytes: 1,369,195

bytes minus 489,986 bytes put into the new

file leaves 879,209 bytes free.

On the cardiac ward, there are 7 nursing

assistants. NA Basil has 8 patients; NA Hobbes

has 5 patients; NA McGuire has 9 patients;

NA Hicks has 10 patients; NA Garcia has

10 patients; NA James has 14 patients; and

NA Davis has 7 patients. What is the average

number of patients per nursing assistant?

a. 6

b. 7

c. 8

d. 9

e. 10

d. First, add the number of patients to find

the total: 63. Then, divide the number

of patients by the number of nursing

assistants: 63 divided by 7 is 9.

A patient's hospice stay cost one-fourth as

much as his visit to the emergency room.

His home nursing cost twice as much as his

hospice stay. If his total health care bill was

$140,000, how much did his home nursing

cost?

a. $10,000

b. $20,000

c. $40,000

d. $60,000

e. $80,000

c. Let E = emergency room cost; H = hospice

cost, which is (1/4)E; N = home nursing cost,

which is 2H, or 2(1/4)E. The total bill is E + H

+ N, which is E + (1/4)E + (2/4)E = 140,000. Add

the left side of the equation to get (7/4)E =

140,000. To solve for E, multiply both sides

of the equation by (4/7)E = 140,000(4/7), or

80,000. H = (1/4)E, or 20,000, and N = 2H,

or 40,000.

At a certain school, half of all the students are

female and one-twelfth of the students are

from outside the state. Half of the out-of-state

students are also female. What proportion of

the students would you expect to be females

from outside the state?

a. 1/12

b. 1/24

c. 1/8

d. 1/6

e. 1/3

b. If half the students are female, then you

would expect half of the out-of-state

students to be female. One-half of 1/12 is 1/24.

Based on the following information, estimate

the weight of a person who is 5′5″ tall.

Height Weight

5′ 110 lbs.

6′ 170 lbs.

a. 125

b. 130

c. 135

d. 140

e. 145

c. A foot in height makes a difference of

60 pounds, or 5 pounds per inch of height

over 5′. A person who is 5′5″ is (5)(5 pounds),

or 25 pounds, heavier than the person who

is 5′, so add 25 pounds to 110 pounds to get

135 pounds.

During exercise, a person's heart rate should

be between 60% and 90% of the difference

between 220 and the person's age. According

to this guideline, what should a 30-year-old

person's maximum heart rate be during

exercise?

a. 114

b. 132

c. 156

d. 171

e. 198

d. The difference between 220 and this

person's age is 190. The maximum heart

rate is 90% of this: (0.9)(190) = 171.

A certain water pollutant is unsafe at a level of

20 ppm (parts per million). A city's water

supply now contains 50 ppm of this pollutant.

What percentage of improvement will make

the water safe?

a. 20%

b. 30%

c. 40%

d. 50%

e. 60%

e. An amount equaling 30 ppm of the pollutant

would have to be removed to bring the

50 ppm down to 20 ppm (30 ppm is 60%

of 50 ppm).

A study shows that 600,000 women die each

year in pregnancy and childbirth, one-fifth

more than scientists previously estimated.

How many such deaths did the scientists

previously estimate?

a. 120,000

b. 240,000

c. 300,000

d. 480,000

e. 500,000

e. Let E = the estimate. One-fifth more than

the estimate would be 6/5, or 120%, of E, so

600,000 = (1.20)(E). Dividing both sides

by 1.2 leaves E = 500,000.

What is 250 milligrams in terms of grams?

a. 0.0250 grams

b. 0.250 grams

c. 2.50 grams

d. 25 grams

e. 250,000 grams

b. In terms of grams, 250 milligrams is

250/1000 gram, or 0.250 grams.

An Army food supply truck can carry three

tons. A breakfast ration weighs 12 ounces, and

the other two daily meals weigh 18 ounces

each. Assuming each soldier gets three meals

per day, on a 10-day trip, how many soldiers

can be supplied by one truck?

a. 100 soldiers

b. 150 soldiers

c. 200 soldiers

d. 320 soldiers

e. 270 soldiers

c. Three tons = 6,000 pounds. At 16 ounces

per pound, 6,000 pounds = 96,000 ounces

that can be carried by the truck. The total

weight of each daily ration is 12 ounces +

18 ounces + 18 ounces = 48 ounces per

soldier per day, and 96,000/48 = 2,000. So 2,000/10 days

= 200 soldiers supplied.

A train must travel 3,450 miles in six days.

How many miles must it travel each day?

a. 525

b. 550

c. 600

d. 575

e. 625

d. The total number of miles, 3,450, divided by

6 days is 575 miles.

A dormitory now houses 30 men and allows

42 square feet of space per man. If five more

men are put into this dormitory, how much

less space will each man have?

a. 5 square feet

b. 6 square feet

c. 7 square feet

d. 8 square feet

e. 9 square feet

b. The present number of men, 30, multiplied

by 42 square feet of space is 1,260 square

feet of space; 1,260 square feet divided by

35 men is 36 square feet, so each man will

have 6 square feet of space less.

Ron is half as old as Sam, who is three times

as old as Ted. The sum of their ages is 55.

How old is Ron?

a. 5 years old

b. 10 years old

c. 15 years old

d. 20 years old

e. 30 years old

c. Let T = Ted's age; S = Sam's age = 3T;

R = Ron's age = S/2 , or 3T/2 . The sum of the

ages is 55, which means T + 3T + 3T/2 = 55.

To find the common denominator (2), you

can add to the left side of the equation:

T = 10. If Ted is 10, then Sam is 30, and

Ron is 3T/2 , which is 15 years old.