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ASVAB Practice > Arithmetic Reasoning > Flashcards

Arithmetic Reasoning Flashcards

1
Q

John bough a camera on sale that normally costs $160. If the price was reduced 20% during the sale, what was the sale price of the camera?

A.) $120
B.) $124
C.) $128
D.) $140

A

C.) $128

Determine the amount of the price reduction:
160 (.20) = $32

Subtract the price reduction from the original price:
160 - 32 = $128

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2
Q

A subway car passes 3 stations every 10 minutes. At this rate, how many stations will it pass in one hour?

A.) 15
B.) 18
C.) 20
D.) 30

A

B.) 18

Set up a ratio and cross multiply: (be sure to use the same units in both ratios, so change 1 hour to 60 minutes)

   3 stations / 10 minutes    =     x   stations / 60 minutes
   3 (60) = 10x
   180 = 10x
   180/10 = x
   18 stations = x
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3
Q

On a certain map, 3/4 inch represents one mile. What distance, in miles, is represented by 1 3/4 inches?

A.) 1 1/2
B.) 2 1/3
C.) 2 1/2
D.) 5 1/4

A

B.) 2 1/3

Set up a ratio and cross multiply: (change the mixed number to an improper fraction, 1 3/4 = 7/4

3/4 inches / 1 mile = 7/4 inches / x miles
3/4 x = 7/4
x = 7/4 (4/3)
x = 7/3 = 2 1/3 miles

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4
Q

A certain box contains baseballs and golf balls. If the ratio of baseballs to golf balls is 2:3 and there are 30 baseballs in the box, how many golf balls are in the box?

A.) 18
B.) 20
C.) 36
D.) 45

A

D.) 45

Set up a ratio and cross multiply:

2 baseballs / 3 golf balls = 30 baseballs / x golf balls
2x = 90
x = 90/2 = 45 golf balls

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5
Q

Four people shared a taxi to the airport. The fare was $36.00, and they gave the driver a tip equal to 25% of the fare. If they equally shared the cost of the fare and tip, how much did each person pay?

A.) $9.75
B.) $10.25
C.) $10.75
D.) $11.25

A

D.) $11.25

Determine the amount of the tip: 36 (.25) = $9

Add the tip to the amount of the fare: 36 + 9 = $45

Divide the total price by 4 people: 45/4 = $11.25

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6
Q

If a car travels 1/100 of a kilometer each second, how many kilometers does it travel in an hour?

A.) 36
B.) 60
C.) 72
D.) 100

A

A.) 36

Find the number of seconds in an hour:
1 sec. * 60 sec/min. * 60 min/hr = 3,600 seconds

Multiply the rate and time:
1/100 (3600) = 36 kilometers

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7
Q

20 - (-5) =

A.) -25
B.) 25
C.) 15
D.) -15

A

B.) 25

Subtracting a negative number is the same as addition:
20 - (-5) = 20 + 5 = 25

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8
Q

Ms. Smith drove a total of 700 miles on a business trip. If her car averaged 35 miles per gallon of gasoline and gasoline cost $1.25 per gallon, what was the cost in dollars of the gasoline for the trip?

A.) $20
B.) $24
C.) $25
D.) $40

A

C.) $25

Determine how many gallons of gas she needs:
700 miles / 35 miles per gallon = 20 gallons

Determine the price of the gas:
20 gallons ($1.25 per gallon) = $25
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9
Q

After eating 25% of the jelly beans, Brett had 72 left. How many jelly beans did Brett have originally?

A.) 90
B.) 94
C.) 95
D.) 96

A

D.) 96

Set up an equation:
original # - 25% of the original # = # left
x - .25x = 72
.75x = 72
x = 72/.75 = 96 jellybeans originally
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10
Q

A student finishes the first half of an exam in 2/3 the time it takes him to finish the second half. If the entire exam takes him an hour, how many minutes does he spend on the first half of the exam?

A.) 20
B.) 24
C.) 27
D.) 36

A

B.) 24

Set up an equation:
first half time + second half time = entire time of test
2/3 x + x = 60 minutes
5/3 x = 60
x = 60 (3/5) = 36 minutes (Be careful! This is for the second half, the question asks you to solve for the first half.)

Solve for first half of test:
first half time + 36 minutes = 60 minutes
first half time = 60 - 36 = 24 minutes

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11
Q

A 25-ounce solution is 20% alcohol. If 50 ounces of water are added to it, what percent of the new solution is alcohol?

A.) 6 2/3%
B.) 7 1/2%
C.) 10%
D.) 13 1/3%

A

A.) 6 2/3%

Determine how many ounces total in the new solution:
25 + 50 = 75 ounces total

Determine how many ounces of alcohol in original solution: (.20)(25) = 5 ounces alcohol

Determine the % alcohol in new solution:
(# ounces of alcohol / total ounces) * 100%
(5/75)(100) = 6 2/3%

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12
Q

Marty has exactly 5 blue pens, 6 black pens, and 4 red pens in his backpack. If he pulls out one pen at random from his backpack, what is the probability that the pen is either red or black?

A.) 2/3
B.) 3/5
C.) 2/5
D.) 1/3

A

A.) 2/3

Probability = # desired outcomes / # possible outcomes

In this case:
Probability = (# of red + # black pens) / total # pens
(4 red pens + 6 black pens) / 15 pens total
10/15 = 2/3

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13
Q

From 1980 through 1990, the population of Country X increased by 100%. From 1990 to 2000, the population increased by 50%. What was the combined increase for the period 1980-2000?

A.) 150%
B.) 166 2/3%
C.) 175%
D.) 200%

A

D.) 200%

Be careful! The 100% increase is based on the 1980 population, but the 50% increase is based on the 1990 population. The best way to solve this is to pick an easy number (like 100) for your original population to see what happens.

1980 population = 100
1990 population = 100 + 1(100) = 200
2000 population = 200 + (.50)(200) = 300

Now determine your percent increase:
% increase = ((end pop. - original pop.)/orig. pop.)(100%)
% increase = ((300 - 100)/100)(100%) = 200%

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14
Q

If a worker earns $200 for the first 40 hours of work in a week and then is paid one-and-one-half times her regular rate for any additional hours, how many hours must she work to make $230 in a week?

A.) 43
B.) 44
C.) 45
D.) 46

A

B.) 44

Find her regular rate of pay: $200/40 hours = $5/hr

Find her overtime rate: ($5)(3/2) = $7.50/hr

Find the number of hours to make $230:
(40 hrs)($5/hr) + x hours ( 7.50/hr) = $230
200 + 7.5x = 230
7.5x = 230 - 200
7.5x = 30
x = 30 / 7.5 = 4 hours of overtime

Her total hours for the week are:
40 regular hours + 4 overtime hours = 44 hours

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15
Q

If 50% of x is 150, what is 75% of x?

A.) 225
B.) 250
C.) 275
D.) 300

A

A.) 225

Figure out what x is:
.5x = 150
x = 150 / .5 = 300

Figure out what 75% of x is:
.75 (300) = 225

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16
Q

The total fare for two adults and three children on an excursion boat is $14. If each child’s fare is one half of each adult’s fare, what is the adult fare?

A.) $2.00
B.) $3.00
C.) $3.50
D.) $4.00

A

D.) $4.00

Set up equations:
2 adults + 3 children = $14 and 1 child = 1/2 adult

Substitute to find adult fare:
2a + 3 (1/2 a) = $14
2a + 3/2 a = 14
7/2 a = 14
a = 14 (2/7) = $4
17
Q

What is the prime factorization of 140?

A.) 2 * 70
B.) 2 * 3 * 5 * 7
C.) 2 * 2 * 5 * 7
D.) 2 * 2 * 2 * 5 * 7

A

C.) 2 * 2 * 5 * 7

Make a factor tree:

                                            140
                                              ^
                                          70 * 2
                                           ^
                                      35 * 2
                                        ^
                                     5 * 7
18
Q

A painter charges $ an hour while his son charges $ an hour. If the father and son worked the same amount of time together on a job, how many hours did each of
them work if their combined charge for their labor was $108?

A.) 6
B.) 9
C.) 12
D.) 18

A

A.) 6

Set up an equation:
father's charge + son's charge = total charge
$12x + $6x = $108
18x = 108
x = 108 / 18 = 6 hours
19
Q

4! =

A.) 4
B.) 16
C.) 24
D.) 256

A

C.) 24

The exclamation mark indicates a factorial, which means to multiply the number by every smaller number down to 1.

4 * 3 * 2 * 1 = 24

20
Q

At garage A, it costs $8.75 to park a car for the first hour and $1.25 for each additional hour. At garage B, it costs $5.50 to park a car for the first hour and $2.50 for each additional hour. What is the difference between the cost of parking a car for 5 hours at garage A and parking it for the same length of time at garage B?

A.) $2.25
B.) $1.75
C.) $1.50
D.) $1.25

A

B.) $1.75

Compute the cost for 5 hours of parking at each garage:
Garage A = 8.75 + (4)(1.25) = $13.75
Garage B = 5.50 + (4)(2.50) = $15.50

Find the difference:
$15.50 - $13.75 = $1.75

21
Q

Jan types at an average rate of 12 pages per hour. At that rate, how long will it take Jan to type 100 pages?

A.) 8 hours and 10 minutes
B.) 8 hours and 15 minutes
C.) 8 hours and 20 minutes
D.) 8 hours and 30 minutes

A

C.) 8 hours and 20 minutes

Set up a ratio and cross multiply:
12 pages / 60 minutes = 100 pages / x minutes
12x = 6000
x = 6000 / 12 = 500 minutes

Convert minutes to hours:
500 / 60 = 8 hours and 20 minutes

22
Q

Two large sodas contain the same amount as three medium sodas. Two medium sodas contain the same amount as three small sodas. How many small sodas contain the same amount as eight large sodas?

A.) 24
B.) 18
C.) 16
D.) 12

A

B.) 18

Set up equations:
2 large = 3 medium
2 medium = 3 small

Figure out how many small = 8 large:
Multiply your first equation by 4 to see that 8 large = 12 medium. Multiply your second equation by 6 to see that 12 medium = 18 small

23
Q

If each digit 5 in the number 258,546 is replaced with the digit 7, by how much will the number be increased?

A.) 2,020
B.) 2,200
C.) 20,020
D.) 20,200

A

D.) 20,200

Changing the 5’s to 7’s makes the number 278,746.

Subtract to find the amount of increase:
278,746 - 258,546 = 20,200

24
Q

Michael bought 2 1/4 pounds of lumber at $4.00 per pound. If a 7% sales tax was added, how much did Michael pay?

A.) $9.63
B.) $9.98
C.) $10.70
D.) $11.77

A

A.) $9.63

price of lumber + tax = total price
(2 1/4)(4) + (.07)(2 1/4)(4) = total price
9 + (.07)(9) = total price
9 + .63 = $9.63

25
Q

The ratio of 3 1/4 to 5 1/4 is equivalent to the ratio of

A.) 3 to 5
B.) 4 to 7
C.) 8 to 13
D.) 13 to 21

A

D.) 13 to 21

Turn the ratios into improper fractions:
3 1/4 = 13/4 5 1/4 = 21/4

Multiply both ratios by 4:
(13/4)(4) = 13 (21/4)(4) = 21

26
Q

A cat is fed 3/8 of a pound of cat food every day. For how many days will 72 pounds of this cat food feed the cat?

A.) 160
B.) 172
C.) 180
D.) 192

A

D.) 192

Set up ratios and cross multiply:

3/8 lb / day = 72 lbs / x days
3/8 x = 72
x = (72)(8/3) = 192 days

27
Q

After spending 5/12 of her salary, Eva has $420 left. What is her salary?

A.) $175
B.) $245
C.) $720
D.) $1,008

A

C.) $720

Set up equation:
Whole salary - 5/12 of salary = $420
x - 5/12 x = 420
7/12 x = 420
x = (420)(12/7) = $720
28
Q

A stock decreases in value by 20%. By what percent must the stock price increase to reach its former value?

A.) 15%
B.) 20%
C.) 25%
D.) 40%

A

C.) 25%

Pick an easy number (like $100) for the original price of your stock to see what happens:

100 - (.20)(100) = $80

At this point, the stock needs to gain $20 again to get back to its original price.

Find what percentage of 80 = $20:
20/80 = .25 = 25%

29
Q

Joan can shovel a certain driveway in 50 minutes. If Mary can shovel the same driveway in 20 minutes, how long will it take them, to the nearest minute, to shovel the driveway if they work together?

A.) 12
B.) 13
C.) 14
D.) 15

A

C.) 14

Set up fractions:
Joan = 1 driveway / 50 min. Mary = 1 driveway / 20 min.

Add the fractions:
1/50 + 1/20 = 2/100 + 5/100 = 7 driveways /100 min.

Flip the fraction and divide to find the time per driveway:
100/7 = approx. 14.29 minutes = approx. 14 minutes

30
Q

June’s weekly salary is $70 less than Kelly’s, which is $50 more than Eileen’s. If Eileen earns $280 per week, how much does June earn per week?

A.) $160
B.) $260
C.) $280
D.) $300

A

B.) $260

Set up equations:
June = Kelly - $70
Kelly = Eileen + $50
Eileen = $280/wk

Substitute and solve:
Eileen = $280
Kelly = 280 + 50 = $330
June = $330 - 70 = $260

ASVAB Practice (11 decks)

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