Arithmetic Reasoning Overview for ASVAB Power Practice Problems

These arithmetic reasoning practice questions are based on the actual ASVAB. Take this quiz to see how you would do if you took the exam today and to determine your strengths and weaknesses as you plan your study schedule.

Time: 36 minutes

A survey has shown that a family of four can save about $40 a week by purchasing generic items rather than brand-name ones. How much can a particular family save over six months? (one month = 4.3 weeks)
1. $1,032
2. $1,320
3. $1,310
4. $1,300
Bart's eight-ounce glass is full of water. How many ounces of water does he have?
1. ounces
2. 5 ounces
3. 6 ounces
4. ounces

Use the following pie chart to answer questions 3 and 4.

Part 2: Arithmetic Reasoning

What should be the percent label for food?
1. 12%
2. 18%
3. 28%
4. 38%
If Harold's monthly income is $2,450, how much does he spend on rent each month?
1. $686
2. $735
3. $882
4. $931

If you take recyclables to whichever recycler will pay the most, what is the greatest amount of money you could get for 2,200 pounds of aluminum, 1,400 pounds of cardboard, 3,100 pounds of glass, and 900 pounds of plastic?
1. $409
2. $440
3. $447
4. $485
Five oranges, when removed from a basket containing three more than seven times as many oranges, leaves how many in the basket?
1. 21
2. 28
3. 33
4. 38
Ribbon in a craft store costs $0.75 per yard. Vernon needs to buy yards. How much will it cost?
1. $7.33
2. $6.95
3. $5.50
4. $4.25
R.J. found a lamp on sale for 0.25 off its original price. What fraction of its original price will R.J. have to pay for the lamp?

How many -pound hamburgers can be made from six pounds of ground beef?
1. 18 hamburgers
2. hamburgers
3. 24 hamburgers
4. hamburgers
The markup on a pair of sneakers is 150%. If the sneakers originally cost $45, what is the price after the markup?
1. $22.50
2. $57.50
3. $67.50
4. $112.50
Matthew had 200 baseball cards. He sold 5% of the cards on Saturday and 10% of the remaining cards on Sunday. How many cards are left?
1. 170
2. 171
3. 175
4. 185
A teacher purchased a number of supplies to start the new school year. The costs are listed as follows: $12.98, $5.68, $20.64, and $6.76.What is the total cost?
1. $45.96
2. $46.06
3. $46.16
4. $47.16
How many hours are in five days?
1. 60 hours
2. 100 hours
3. 120 hours
4. 240 hours
A truck is carrying 1,000 television sets; each set weighs 21.48 pounds. What is the total weight, in pounds, of the entire load?
1. 214.8 pounds
2. 2,148 pounds
3. 21,480 pounds
4. 214,800 pounds
Hilga and Jerome leave from different points walking directly toward each other. Hilga walks miles per hour, and Jerome walks 4 miles per hour. If they meet in hours, how far apart were they?
1. 9 miles
2. 13 miles
3. miles
4. miles
Des Moines recently received a snowstorm that left a total of eight inches of snow. If it snowed at a consistent rate of three inches every two hours, how much snow had fallen in the first five hours of the storm?
1. 3 inches
2. 3.3 inches
3. 5 inches
4. 7.5 inches

Use the following graph to answer question 17.

Part 2: Arithmetic Reasoning

Avi's final math grade is based on his scores on four tests. To get an A, Avi needs an average test score of 88 or higher. The graph shown here represents Avi's first three test scores. What is the lowest score Avi can get on the fourth test and still earn an A?
1. 99
2. 97
3. 95
4. 93
Joan will be twice Tom's age in three years when Tom will be 40. How old is Joan now?
1. 20
2. 80
3. 77
4. 37
Kari is running for student council. The rules restrict the candidates to four two-foot-bythree-foot posters. Kari has dozens of four-inch-by-six-inch pictures that she would like to cover the posters with. What is the maximum number of pictures she will be able to use on the four posters?
1. 144
2. 130
3. 125
4. 111
It takes five-year-old Carlos 1.6 minutes to tie the lace on his right shoe and 1.5 minutes to tie the lace on his left shoe. How many minutes does it take Carlos to tie both shoes?
1. 2.1 minutes
2. 3.0 minutes
3. 3.1 minutes
4. 4.1 minutes
Tamika is restoring an antique storage chest that is in the shape of a rectangular box. She is painting only the outside of the trunk. The trunk is four feet long, 18 inches wide, and two feet tall. There is a one-square-foot brass ornament on the outside of the trunk that will not get painteHow much paint does she need, in square feet, to cover the outside of the trunk?
1. 33 square feet
2. 34 square feet
3. 143 square feet
4. 231 square feet
2,520 seconds is equivalent to how many minutes?
1. 84 minutes
2. 42 minutes
3. 151,200 minutes
4. 126 minutes
Belinda is building a garden sheWhen she helped her neighbor build an identical shed, it took them 22 hours to complete the job together. If it would have taken her neighbor, working alone, 38 hours to build the shed, how long will it take Belinda, working alone, to build her shed?
1. 33.75 hours
2. 41.00 hours
3. 41.25 hours
4. 52.25 hours
An empty crate weighs 8.16 kg and an orange weighs 220 g. If Jon can lift 11,000 g, how many oranges can he pack in the crate before lifting it onto his truck?
1. 12
2. 13
3. 37
4. 46
Jeff was 10 minutes early for class. Dee came in four minutes after Mae, who was half as early as Jeff. How many minutes early was Dee?
1. 1 minute
2. 2 minutes
3. 2.5 minutes
4. 6 minutes
A certain radio station plays classical music during 20% of its airtime. If the station is on the air 24 hours a day, how many hours each day is the station NOT playing classical music?
1. 8.0 hours
2. 15.6 hours
3. 18.2 hours
4. 19.2 hours
Change to a mixed number.

The animal shelter is developing a new outdoorgrass area for dogs. A fence needs to bepurchased that will surround the entire grassysection. The dimensions of the area are 120 feetby 250 feet. How much fencing needs to bepurchased?
1. 740 feet
2. 30,000 square feet
3. 740 square feet
4. 30,000 feet
If it takes Danielle 22.4 minutes to walk 1.25 miles, how many minutes will it take her to walk one mile?
1. 17.92 minutes
2. 18 minutes
3. 19.9 minutes
4. 21.15 minutes
Luis is mailing two packages. One weighs 12.9 pounds, and the other weighs half as much. What is the total weight, in pounds, of the two packages?
1. 6.45 pounds
2. 12.8 pounds
3. 18.5 pounds
4. 19.35 pounds

Answers

a. This is a two-step multiplication problem. First, multiply to find out how many weeks there are in six months:6 × 4.3 = 25.8. Then, multiply to find out how much is saved: $40 × 25.8 = $1,032.
d. In this problem, you must multiply a fraction by a whole number. First, rewrite the whole number as a fraction: . Next, multiply: . Finally, convert to a mixed number: .
a. Add each of the known sectors, and subtract the sum from 100% to get 12%.
d. Since the rent sector is labeled 38%, find 38% of $2,450: 0.38 × 2,450 = $931.
d. First, determine which recycler pays the most for each material. Recycler X pays the most for aluminum, cardboard, and plastic; recycler Y pays the most for glass. Next, multiply the amount in pounds of each material by the price per pound you determined in the first step. Then add these totals together to get your answer: 2,200 × .07 + 1,400 × .04 + 3,100 × .08 + 900 × .03 = 485.
c. Let x equal the number of oranges left in the basket. Three more than seven times as many oranges as five is 7(5) + 3 = 38. Removing five leaves x = 38 – 5 = 33 oranges.
c. Convert both the cost and the length to fractions: or , which is $5.50.
b. If the lamp is 0.25 off of its original price, then the sale price will be 0.75 (1.0 – 0.25 = 0.75). Convert 0.75 into a fraction and reduce; .
c. This is a division of fractions problem. First, change the whole number to a fraction: . Then, invert the second fraction and multiply: .
d. To find 150% of $45, change the percent to a decimal and multiply: 1.50 × 45 = 67.50. Since this is the markup of the price, add $67.50 to $45 to find the new price of $112.50.
b. This is a two-step problem involving multiplication and addition. First, determine how many cards were sold on Saturday: 0.05 × 200 = 10. That leaves 190 cards. Then, find out how many cards were sold on Sunday:0.10 × 190 = 19. Next, add the cards that were sold: 10 + 19 = 29. Finally, subtract from the original number: 200 – 29 = 171.
b. This is a simple addition problem. Be sure to align the decimal points: 12.98 + 5.68 + 20.64 + 6.76 = 46.06.
c. Multiply the number of hours in a day by the given number of days. There are 24 hours in each day. There are 120 hours in 5 days; 5 days × 24 hours = 120 hours.
c. This is a multiplication problem. To multiply a number by 1,000 quickly, move the decimal point three digits to the right— one digit for each zero. In this situation, because there are only two decimal places, add a zero.
c. Hilga and Jerome's initial distance apart equals the sum of the distance each travels in 2.5 hours. Hilga travels a distance of (2.5)(2.5) = 6.25 miles, while Jerome travels (4)(2.5) = 10 miles. This means that they were 6.25 + 10 = 16.25 miles apart.
d. Three inches every 2 hours = 1.5 inches per hour × 5 hours = 7.5 inches.
b. For the lowest score Avi needs to get an A, assume his final average is 88. Average = (90 + 80 + 85 + a) ÷ 4 = 88. To find a, multiply 88 by 4. Then subtract Avi's first three scores: 88 × 4 = 352; 352 – (90 + 80 + 85) = 352 – 255 = 97.
c. The problem is to find J, Joan's present age, in years. Begin by breaking the problem up into smaller parts: Joan will be twice Tom's age in three years becomes J + 3 = 2T; Tom will be 40 becomes T = 40. Substitute: J +3 = 2(40). Simplify: J = 80 – 3, or J = 77 years old.
a. The area of each poster is 864 square inches ( 24 inches × 36 inches ). Kari may use four posters, for a total of 3,456 square inches (864 × 4). Each picture has an area of 24 square inches (4 × 6); the total area of the posters should be divided by the area of each picture, or 3,456 ÷ 24 = 144.
c. This is a simple addition problem. Add 1.6 and 1.5, keeping the decimal points aligned: 1.6 + 1.5 = 3.1.
a. The surface area of the trunk can be found by finding the sum of the areas of each of the six faces of the trunk. Since the answer is in square feet, change 18 inches to 1.5 feet: 2(4 × 2) + 2(4 × 1.5) + 2(2 × 1.5) = 2(8) + 2(6) + 2(3) = 16 + 12 + 6 = 34. Subtract the area of the brass ornament: 34 – 1 = 33 square feet.
b. Divide the total number of seconds by the number of seconds in a minute. There are 60 seconds in a minute; 2,520 seconds is 42 minutes; 2,520 seconds ÷ 60 seconds = 42 minutes.
d. Let x equal the number of hours it takes Belinda to complete the job. In one hour, the neighbor can do of the job, while Belinda can do . Working together, they take 22 hours to complete 100% of the job or: (where 1 represents 100% of the job). Simplify: or , which reduces to .Cross multiply: 16x = (22)(38), or x = 52.25 hours.
a. The empty crate weighs 8.16 kg, or 8,160 g. If Jon can lift 11,000 g and one orange weighs 220 g, then the number of oranges that he can pack into the crate is equal to . Jon cannot pack a fraction of an orange. He can pack 12 whole oranges into the crate.
a. Let D equal the time Dee arrived before class. Choosing to represent time before class as a negative number, you have: Jeff arrived 10 minutes early means J = –10, Dee came in four minutes after Mae means D = M + 4, Mae, who was half as early as Jeff means M = J. Substitute: M = –5, so D = –5 + 4 = –1. Thus, D = 1 minute before class.
d. First, determine the percent of time that the station is NOT playing classical music. Subtract from 100%: 100 – 20 = 80. Eighty percent of the time the station does NOT play classical music. Then change thepercent to a decimal and multiply: 0.8 × 24 = 19.2.
b. Divide the numerator by the denominator to find the whole number of the mixed number. The remainder, if any, becomes the numerator of the fraction: 55 ÷ 6 = 9, remainder 1. The denominator stays the same. Therefore, the mixed number is .
a. In order to find the amount of fencing, the perimeter needs to be determined: 120 + 120 + 250 + 250 = 740 feet.
a. This is a division problem. Because there are two decimal points in 1.25, move the decimal point two places in both numbers: .
d. This is a two-step problem. Divide 12.9 by 2 to get 6.45, and then add both numbers: 12.90 + 6.45 = 19.35.