Math Reasoning 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

For a science project, Stacy and Tina are measuring the length of two caterpillars. Stacy's caterpillar is 2.345 centimeters long. Tina's caterpillar is 0.0005 centimeter longer. How long is Tina's caterpillar?
1. 2.0345 centimeters
2. 2.3455 centimeters
3. 2.0345 centimeters
4. 2.845 centimeters
An elevator sign reads "Maximum weight 600 pounds." Which of the following may ride the elevator?
1. three people: one weighing 198 pounds, one weighing 185 pounds, one weighing 200 pounds
2. one person weighing 142 pounds with a load weighing 500 pounds
3. one person weighing 165 pounds with a load weighing 503 pounds
4. three people: one weighing 210 pounds, one weighing 101 pounds, one weighing 298 pounds
Laura saves at three times the rate Hazel does. If it takes Laura years to save $1,000, how many years will it take Hazel to save this amount?
1. 1
2. 3.5
3. 4.5
4. 6
On Wednesday morning, Yoder's Appliance Service had a balance of $2,354.82 in its checking account. If the bookkeeper wrote a total of $867.59 worth of checks that day, how much was left in the checking account?
1. $1,487.23
2. $1,487.33
3. $1,496.23
4. $1,587.33
At the city park, 32% of the trees are oaks. If there are 400 trees in the park, how many trees are NOT oaks?
1. 128
2. 272
3. 278
4. 312
Jake grew 0.6 inch during his senior year in high school. If he was 68.8 inches tall at the beginning of his senior year, how tall was he at the end of the year?
1. 69.0 inches
2. 69.2 inches
3. 69.4 inches
4. 74.8 inches
Phil and Alice went out to dinner and spent a total of $42.09. If they tipped the waiter $6.25 and the tip was included in their total bill, how much did their meal alone cost?
1. $35.84
2. $36.84
3. $36.74
4. $48.34

Answer question 8 on the basis of the following paragraph.

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 channels service is $9.40 a month; the news channels are $7.50 a month; the arts channels are $5.00 a month; and the sports channels are $4.80 a month.

A customer's first bill after having cable television installed totaled $110. This customer chose basic cable and one additional cable service. Which additional service was chosen?
1. the news channels
2. the movie channels
3. the arts channels
4. the sports channels
A loaf of bread has 35 slices. Ann eats eight slices, Betty eats six slices, Carl eats five slices, and Derrick eats nine slices. What fraction of the loaf is left?

The butcher at Al's Meat Market divided ground beef into eight packages. If each package weighs 0.75 pound and he has 0.04 pound of ground beef left over, how many pounds of ground beef did he start with?
1. 5.064 pounds
2. 5.64 pounds
3. 6.04 pounds
4. 6.4 pounds
While on a three-day vacation, the Wilsons spent the following amounts on motel rooms: $52.50, $47.99, and $49.32.What is the total amount they spent?
1. $139.81
2. $148.81
3. $148.83
4. $149.81
Dan rented two movies to watch last night. The first was 1 hour 40 minutes long, the second 1 hour 50 minutes long. How much time did it take for Dan to watch the two videos?
1. 4.5 hours
2. 3.5 hours
3. 2.5 hours
4. 1.5 hours
The Benton High School girls' relay team ran the mile in 6.32 minutes in April. By May, they were able to run the same race in 6.099 minutes. By how much time had their time improved?
1. 0.221 minute
2. 0.339 minute
3. 0.467 minute
4. 0.67 minute
If one pound of chicken costs $2.79 a pound, how much does 0.89 pound of chicken cost, rounded to the nearest cent?
1. $2.40
2. $2.48
3. $2.68
4. $4.72
In order to pass a certain exam, candidates must answer 70% of the test questions correctly. If there are 70 questions on the exam, how many questions must be answered correctly in order to pass?
1. 49
2. 52
3. 56
4. 60
Rashaard went fishing six days in the month of June. He caught eleven, four, zero, five, four, and six fish respectively. On the days that Rashaard fished, what was his average catch?
1. 4
2. 5
3. 6
4. 7
Ingrid has two pieces of balsa wood. Piece A is 0.724 centimeter thick. Piece B is 0.0076 centimeter thicker than Piece A. How thick is Piece B?
1. 0.7164 centimeter
2. 0.7316 centimeter
3. 0.8 centimeter
4. 0.08 centimeter
How many different meals can be ordered from a restaurant if there are three choices of soup, five choices of entrées, and two choices of dessert if a meal consists of a soup, entrée, and dessert?
1. 10
2. 15
3. 30
4. 60
If Nanette cuts a length of ribbon that is 13.5 inches long into four equal pieces, how long will each piece be?
1. 3.3075 inches
2. 3.375 inches
3. 3.385 inches
4. 3.3805 inches
Marty and Phyllis arrive late for a movie and miss 10% of it. The movie is 90 minutes long. How many minutes did they miss?
1. 10 minutes
2. 9 minutes
3. 8 minutes
4. 7 minutes
During an eight-hour workday, Bob spends two hours on the phone. What fraction of the day does he spend on the phone?

To reach his tree house, Raymond has to climb feet up a rope ladder, then feet up the tree trunk. How far does Raymond have to climb altogether?

About how many quarts of water will a 3.25-liter container hold? (one liter = 1.06 quarts)
1. 3.066 quarts
2. 3.045 quarts
3. 3.445 quarts
4. 5.2 quarts
How many ounce glasses can be completely filled from a ounce container of juice?
1. 4
2. 5
3. 6
4. 7
Lucille spent 12% of her weekly earnings on DVDs and deposited the rest into her savings account. If she spent $42 on DVDs, how much did she deposit into her savings account?
1. $42
2. $308
3. $318
4. $350
Millie is a night security guard at the art museum. Each night, she is required to walk through each gallery once. The museum contains 52 galleries. This night, Millie has walked through 16 galleries. What fraction of the total galleries has she already visited?

At age six, Zack weighed 40.6 pounds. By age seven, Zack weighed 46.1 pounds. How much weight did he gain in that one year?
1. 4.5 pounds
2. 5.5 pounds
3. 5.7 pounds
4. 6.5 pounds
Michael has a $20 bill and a $5 bill in his wallet and $1.29 in change in his pocket. If he buys a half gallon of ice cream that costs $4.89, how much money will he have left?
1. $22.48
2. $22.30
3. $21.48
4. $21.40
Land consisting of a quarter section is sold for $1,850 per acre (one quarter section = 160 acres). The total sale price is
1. $296,000.
2. $592,000.
3. $1,184,000.
4. $1,850,000.
Emilio is 1 year 7 months old, and Brooke is 2 years 8 months old. How much older is Brooke than Emilio?
1. 1 year 1 month
2. 2 years
3. 1 month
4. 1 year 2 months

Answers

b. This is an addition problem. Arrange the numbers in a column so that the decimal points are aligned: 2.345 + 0.0005 = 2.3455.
a. To arrive at the answer quickly, begin by rounding off the numbers, and you will see that choice a is less than 600 pounds, whereas choices b, c, and d are all more than 600 pounds.
c. The problem is to find H, the number of years Hazel will take to save $1,000. You are told Laura saves three times faster than Hazel, a ratio of 3:1. Therefore, 3L = H. You are given L = 1.5 years. Substitute: 3(1.5) = H, or H = 4.5 years.
a. This is a basic subtraction problem. Line up the decimals and subtract: 2,354.82 – 867.59 = 1,487.23.
b. This is a two-step problem. First, determine what percent of the trees are not oaks by subtracting: 100% – 32% = 68%. Change 68% to a decimal and multiply: 0.68 ×400 = 272.
c. This is a basic addition problem. Be sure to align the decimal points before you add 68.8 + 0.6 = 69.4.
a. This is a simple subtraction problem: $42.09 – $6.25 = $35.84.
c. The labor fee ($25) plus the deposit ($65) plus the basic service ($15) equals $105. The difference between the total bill, $110, and $105 is $5.00, the cost of the arts channels.
d. Since 28 of the 35 slices have been eaten, there are 35 – 28 = 7 slices left. This means or of the loaf is left.
c. This is a two-step problem. First, multiply to determine how many pounds of beef were contained in the eight packages: 0.75 × 8 = 6. Then add: 6 + 0.04 = 6.04.
d. This is an addition problem. To add these three decimals, line them up in a column so that their decimal points are aligned: 52.50 + 47.99 + 49.32 = 149.81. Move the decimal point directly down into the answer.
b. Change the hours to minutes: 1 hour 40 minutes = 100 minutes; 1 hour 50 minutes = 110 minutes. Now add: 100 minutes + 110 minutes = 210 minutes. Now change back to hours and minutes: 210 minutes ÷ 60 minutes = 3.5 hours.
a. This is a subtraction problem. Be sure to align the decimal points: 6.32 – 6.099 = 0.221.
b. This is a multiplication problem. First, multiply 279 by 89. Then, because there are four decimal places, count off four places from the right. Your answer should be 2.4831. Because the 3 in the thousandths place is less than 5, round to 2.48.
a. First, change 70% to a decimal, which is 0.7. Then multiply: 70 ×0.7 = 49.
b. The average is the sum divided by the number of observations: (11 + 4 + 0 + 5 + 4 + 6) ÷ 6 = 5.
b. This is an addition problem. Be sure the decimal points are aligned before you add: 0.724 + 0.0076 = 0.7316.
c. The counting principle shows the number of ways an event can occur and tells you to take the total choices for each item and multiply them together: 3 ×5 ×2 = 30.
b. This is a division problem: 13.5 ÷ 4 = 3.375. Move the decimal straight up into the quotient.
b. Set up the problem this way: . If you're getting good at percentages, you may just see the answer, but if you don't, cross multiply: 10 ×90 = 100x. Solve: x = 9.
c. Change the information into a fraction: . Now, reduce the fraction: .
c. First, find the least common denominator of the fractions, which is 6. Then add:
c. This is a multiplication problem. Multiply 3.25 times 1.06. Be sure to count four decimal places from the right: 3.25×1.06 = 3.445.
c. This is a division problem with mixed numbers. First, convert the mixed numbers to fractions: . Next, invert the second fraction and multiply: . Reduce to a mixed number: . With this result, you know that only six glasses can be completely filled.
b. First, ask the question: "$42 is 12% of what number?" Change the percent to a decimal and divide $42 by 0.12. This is equal to $350, which represents the total weekly earnings. Now subtract the amount she spent on DVDs from $350: $350 – $42 = $308. She deposited $308 into her savings account.
a. Millie has completed of the total galleries.
b. This is a simple subtraction problem. Line up the decimals and subtract: 46.1 – 40.6 = 5.5.
d. This problem involves two steps: addition and subtraction. Add to determine the amount of money Michael has: $20.00 + $5.00 + $1.29 = $26.29. Then, subtract the amount spent for the ice cream: $26.29 – $4.89 = $21.40.
a. This is a multiplication problem. A quarter section contains 160 acres, so you must multiply: 160 ×$1,850 = $296,000.
a. Subtract the months first, then the years. Remember that it is best to write the problem in columns and subtract the right-most column (months) first, then the left-most column (years): 8 months – 7 months = 1 month; 2 years – 1 year = 1 year. So, Brook is 1 year 1 month older than Emilio.