Arithmetic Reasoning Review 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

In New York City, two out of every five people surveyed bicycle to work. Out of a population sample of 200,000 people, how many bicycle to work?
1. 4,000
2. 8,000
3. 40,000
4. 80,000
Serena has to choose between two jobs. One is at Books R Us and pays $18,000 with yearly raises of $800. The other, at Readers Galore, pays $16,400 per year with yearly raises of $1,200. In how many years will the two yearly salaries be equal?
1. 6
2. 5
3. 4
4. 3

Use the following pie chart to answer questions 3 through 5.

Arithmetic Reasoning

For which item does Ricardo spend half as much as he puts in his savings account?
1. his car
2. clothes
3. housing
4. food
For which two items does Ricardo spend 50% of each budgeted dollar?
1. savings and housing
2. clothes and housing
3. car and medical
4. medical and food
Last year, Ricardo made $46,500. About how much more did he spend on housing during the year than he put away in savings?
1. $2,000
2. $2,600
3. $2,800
4. $3,000
The number of red blood corpuscles in one cubic millimeter is about 5,000,000, and the number of white blood corpuscles in one cubic millimeter is about 8,000.What, then, is the ratio of white blood corpuscles to red blood corpuscles?
1. 1:625
2. 1:40
3. 4:10
4. 5:1,250
The living room in Donna's home is 182 square feet. How many square yards of carpet should she purchase to carpet the room?
1. 9 square yards
2. 1,638 square yards
3. 61 square yards
4. 21 square yards
During a basketball game, Jack has made 20 free-throw shots out of his 50 tries. How many of his next 25 free-throw attempts is Jack most likely to make?
1. 5
2. 10
3. 15
4. 20
Twelve people entered a room. Three more than two-thirds of these people then left. How many people remain in the room?
1. 0
2. 1
3. 2
4. 7
A map of Nevada has the following scale: 0.5 inches = 15 miles. Which expression tells the actual distance, d, between points that are 5.25 inches apart on the map?

The Cougars played three basketball games last week. Monday's game lasted 113.9 minutes; Wednesday's game lasted 106.7 minutes; and Friday's game lasted 122 minutes. What is the average time, in minutes, for the three games?
1. 77.6 minutes
2. 103.2 minutes
3. 114.2 minutes
4. 115.6 minutes
A helicopter flies over a river at 6:02 A.M. and arrives at a heliport 20 miles away at 6:17 A.M. How many miles per hour was the helicopter traveling?
1. 120 miles per hour
2. 300 miles per hour
3. 30 miles per hour
4. 80 miles per hour
How many minutes are there in 12 hours?
1. 24 minutes
2. 1,440 minutes
3. 720 minutes
4. 1,200 minutes
Five people in Sonja's office are planning a party. Sonja will buy a loaf of French bread ($3 per loaf) and a platter of cold cuts ($23). Barbara will buy the soda ($1 per person) and two boxes of crackers ($2 per box). Mario and Rick will split the cost of two packages of Cheese Doodles ($1 per package). Danica will supply a package of five paper plates ($4 per package). How much more will Sonja spend than the rest of the office put together?
1. $14
2. $13
3. $12
4. $11
Kathy charges $7.50 per hour to mow a lawn. Sharon charges 1.5 times as much to do the same job. How much does Sharon charge to mow a lawn?
1. $5.00 per hour
2. $11.25 per hour
3. $10.00 per hour
4. $9.00 per hour
The height of the Eiffel Tower is 986 feet. A replica of the tower made to scale is 4 inches tall. What is the scale of the replica to the real tower?
1. 1 to 246.5
2. 1 to 3,944
3. 246.5 to 1
4. 1 to 2,958
On Sundays, Mike gives half-hour drum lessons from 10:30 A.M. to 5:30 P.M. He takes a half-hour lunch break at noon. If Mike is paid $20 for each lesson, what is the total amount he makes on Sunday?
1. $260
2. $190
3. $170
4. $140
Driving 60 miles per hour, it takes one-half hour to drive to work. How much additional time will it take to drive to work if the speed is now 40 miles per hour?
1. 1 hour
2. 2 hours
3. 15 minutes
4. 30 minutes
An 8" × 10"photograph is blown up to a billboard size that is in proportion to the original photograph. If 8" is considered the height of the photo, what would be the length of the billboard if its height is 5.6 feet?
1. 7 feet
2. 400 feet
3. 56 feet
4. 9 feet
Membership dues at Arnold's Gym are $53 per month this year, but were $50 per month last year. What was the percentage increase in the gym's prices?
1. 5.5%
2. 6.0%
3. 6.5%
4. 7.0%
Which of the following best represents the following statement? Patricia (P) has four times the number of marbles Sean (S) has.
1. P = S + 4
2. S = P – 4
3. P = 4S
4. S = 4P
A piggy bank contains $8.20 in coins. If there are an equal number of quarters, nickels, dimes, and pennies, how many of each denomination are there?
1. 10
2. 20
3. 30
4. 40
Two saline solutions are mixed. Twelve liters of 5% solution are mixed with four liters of 4% solution. What percent saline is the final solution?
1. 4.25%
2. 4.5%
3. 4.75%
4. 5%
A neighbor has three dogs. Fluffy is half the age of Muffy, who is one-third as old as Spot, who is half the neighbor's age, which is 24. How old is Fluffy?
1. 2
2. 4
3. 6
4. 12
Mario has finished 35 out of 45 of his test questions. Which of the following fractions of the test does he have left?

D'Andre rides the first half of a bike race in two hours. If his partner, Adam, rides the return trip five miles per hour less, and it takes him three hours, how fast was D'Andre traveling?
1. 10 miles per hour
2. 15 miles per hour
3. 20 miles per hour
4. 25 miles per hour
Kate earns $26,000 a year. If she receives a 4.5% salary increase, how much will she earn?
1. $26,450
2. $27,170
3. $27,260
4. $29,200
Rudy forgot to replace his gas cap the last time he filled his car with gas. The gas is evaporating out of his 14-gallon tank at a constant rate of gallon per day. How much gas does Rudy lose in one week?

Veronica took a trip to the lake. If she drove steadily for five hours traveling 220 miles, what was her average speed for the trip?
1. 44 miles per hour
2. 55 miles per hour
3. 60 miles per hour
4. 66 miles per hour
A rectangular tract of land measures 860 feet by 560 feet. Approximately how many acres is this? (one acre = 43,560 square feet)
1. 12.8 acres
2. 11.06 acres
3. 10.5 acres
4. 8.06 acres

Answers

d. You are looking for n, and of the 200,000 sample population bicycle to work.
c. Each job will pay $21,200 after 4 years. You can see this by making a chart:

a. Ricardo spends 11% for his car, half of the 22% he saves. (You can use % for the pie chart values without doing any additional math, since the values are already out of 100.)
a. Savings and housing together make up 50% of Ricardo's budget: 22% + 28%.
c. Ricardo spent 6 cents more per dollar on housing than on food: 28 — 22 = 6. Six cents is 6% of each budgeted dollar. $46,500 × 0.06 = $2,790, which is about $2,800.
a. The unreduced ratio is 8,000:5,000,000; reduced, the ratio is 8:5,000. Now divide: 5,000 ÷ 8 = 625, for a ratio of 1:625.
d. It takes 9 square feet to make a square yard. To find out how many square yards are in 182 square feet, divide: square yards. Since Donna cannot purchase part of a square yard, she has to round up. She must purchase 21 square yards to have enough to carpet the room.
b. Jack is likely to make of his next 25 free-throw attempts.
b. Let x equal the number of people remaining in the room. You have: Thus, x = 1 person.
a. or map distance in inches/actual distance in miles.
c. This is a two-step problem involving both addition and division. First, arrange the three numbers in a column, keeping the decimal points aligned. Add: 113.9 + 106.7 + 122 = 342.6. Next, divide your answer by 3: 342.6 ÷ 3 = 114.2.
d. You want to know R = helicopter's speed in miles per hour. To solve this problem, recall that rate × time = distance. It is given that T = 6:17 – 6:02 = 15 minutes = 0.25 hour and D = 20 miles. Substitute: r × 0.25 = 20. Simplify: r = 20 ÷ 0.25. Thus, r = 80 miles per hour.
c. Multiply the number of minutes in an hour by the given number of hours. There are 60 minutes in each hour. Therefore, there are 720 minutes in 12 hours: 12 hours × 60 minutes = 720 minutes.
d. Figure the amounts by setting up the following equations: First, S = $3 + $23 = $26. Now, B = ($1 × 5) + ($2 × 2) or $5 + $4 = $9. MR = $1 × 2 = $2; and D = $4 × 1 = $4. Now, add: $9 + $2 + $4 = $15. Now subtract: $26 – $15 = $11.
b. You want to find S, the rate Sharon charges to mow a lawn in dollars per hour. You are given Kathy's rate, which is K = 7.50, and you are told that S = 1.5K. Substitute: S = 1.5(7.50). Thus, S = $11.25 per hour.
d. A scale is a ratio of model to real, keeping the units consistent. The tower is 986 feet tall, and the replica is 4 inches; 986 feet must be converted to inches, by multiplying by 12: 986 times 12 is 11,832 inches. Set up the ratio of replica to real and simplify:

a. 10:30 A.M. to 5:30 P.M. is a seven-hour period. Mike can give 13 lessons, each lasting 30 minutes, if he takes 30 minutes for lunch. $20 } 13 = $260.
c. First, determine the distance to drive to work, using the formula D = R × T. Substitute known values and then multiply: so D = 30. The distance to work is 30 miles.

Now, determine the time to drive to work at a rate of 40 miles per hour, again using the formula D = R × T. Substitute known values and then divide by 40: 30 = 40 × T, so 0.75 = T. The new time is 0.75 hour, or three-quarters of an hour. The problem asks how much extra time it will take to drive. This is the difference between one-half hour and three-quarters of an hour. Subtract the fractions, after changing one-half to two-quarters: One-quarter of an hour is 15 minutes.

a. Set up a ratio of length to height. The proportion is Cross multiply to get 8 × l = 10 × 5.6. Multiply 10 times 5.6 to get 8 × l = 56. Divide 56 by 8 to get 7 feet long.
b. There has been an increase in price of $3; $3 ÷ $50 = 0.06. This is an increase of 0.06, or 6%.
c. Take the words in order and substitute the letters and numbers. Patricia has (P =), four times (4 ×) the number of marbles Sean has (S). The statement becomes P = 4 × S, which is equal to P = 4S.
b. Let x equal the unknown quantity of each denomination. You know that all the coins total $8.20 and that each denomination is multiplied by the same number, x. Therefore, 0.25x + 0.10x + 0.05x + 0.01x = 8.20. This reduces to (0.25 + 0.10 + 0.05 + 0.01)x = 8.20, or 0.41x = 8.20. Thus, x = 20 coins in each denomination.
c. 12 × 5% + 4 × 4% = x times 16; x = 4.75%.
a. You are asked to find F, Fluffy's age. Begin the solution by breaking the problem into parts: Fluffy is half the age of Muffy becomes Muffy is one-third as old as Spot becomes and Spot is half the neighbor's age becomes You know the neighbor's age is 24 or N = 24. Substitute and work backward through the problem: Thus, Fluffy is two years old.
a. Mario has finished of his test, which reduces to so he has of the test to go.
b. Let x equal D'Andre's rate. D'Andre's rate multiplied by his travel time equals the distance he travels; this equals Adam's rate multiplied by his travel time: 2x = D = 3(x – 5). Therefore, 2x = 3x – 15, or x = 15 miles per hour.
b. There are three steps involved in solving this problem. First, convert 4.5% to a decimal: 0.045. Multiply that by $26,000 to find out how much the salary increases. Finally, add the result ($1,170) to the original salary of $26,000 to find out the new salary, $27,170.
b. Let L equal the number of gallons of gas lost, which is equal to the rate of loss times the time over which it occurs, or L = RT. Substitute: gallons. Notice that the 14-gallon tank size is irrelevant information in this problem.
a. Let R equal Veronica's average speed. Recall that for uniform motion, distance = rate × time or D = RT. Substitute: 220 = R(5) or Thus, R = 44 miles per hour.
b. 860 feet × 560 feet ÷ 43,560 square feet per acre = 11.06 acres.