ASVAB (Arithmetic Reasoning Practice Questions)

(b) 25 Subtracting a negative number is the same as addition, so 20 - (-5) is really 20 + 5 = 25.

20 - (-5) = __. (a) -25 (b) 25 (c) 15 (d) -15

(c) 24 The exclamation mark indicates a factorial. A factorial is an integer multiplied by every smaller integer, down to the number 1, like this: 4! = 4 x 3 x 2 x 1 = 24

4! = __. (a) 4 (b) 16 (c) 24 (d) 256

(a) 6 2/3% You're asked what percent of the new solution is alcohol. The (part) is the number of ounces of alcohol; the (whole) is the total number of ounces of the new solution. There were 25 ounces originally. Then 50 ounces were added, so there are 75 ounces of new solution. How many ounces are alcohol? 20% of the original 25-ounces solution was alcohol. 20% is 1/5, so 1/5 of 25, or 5 ounces are alcohol. Now you can find the percent of alcohol in the new solution: % alcohol = alcohol/total solution x 100% = 5/75 x 100% = 20/3% = 6 2/3%

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%

(d) 192 Set up the proportion. 3/8 lb / 1 day = 72 lbs / (x) days Cross multiply. 3/8 (x) = 72 (x) = 72 x 8/3 (x) = 192

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

(d) 45 You can express the ratio of baseballs to golf balls as 2/3. Since you know the number of baseballs, you can set up a proportion: 2/3 = 30/ (x) where (x) is the number of golf balls. To solve, cross-multiply to get 2(x) = 90, or x = 45.

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) 6 When the painter and his son work together, they charge the sum of their hourly rates, $12 + $6, or $18 per hour. Their bill equals the product of this combined rate and the number of hours they worked, Therefore $108 must equal $18 per hour times the number of hours they worked. Divide $108 by $18 per hour to find the number of hours. $108 / $18 = 6.

A painter charges $12 an hour while his son charges $6 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

(c) 25% They key to this question is that while the value of the stock decreases and increases by the same amount, it doesn't decrease and increase by the same percent. When the stock first decreases, the amount of changes is part of a larger whole. If the stock were to increase to its former value, that same amount of change would be a larger percent of a smaller whole. Pick a number for the original value of the stock, such as $100. (Since it's easy to take percents of 100, it's usually best to choose 100.) The 20% decrease represents $20, so the stock decreases to a value of $80. Now in order for the stock to reach the value of $100 again, there must be a $20 increase. What percent of $80 is $20? It's $20/$80 x 100%, or 1/4 x 100%, or 25%.

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%

(b) 24 The time it takes to complete the entire exam is the sum of the time spent on the first half of the exam and the time spent on the second half. The time spent on the first half is 2/3 of the time spent on he second half. If (S) represents the time spent on the second half, then the total time spent is 2/3(S) + (S) or 5/3 (S). You know this total time is one hour, or 60 minutes. Set up a simple equation and solve for (S). 5/3(S) = 60 3/5 x 5/3(S) = 3/5 x 60 (S) = 36 So the second half takes 36 minutes. The first half takes 2/3 of this, or 24 minutes. You could also find the first half by subtracting 36 minutes from the total time, 60 minutes.

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) s4 (c) 27 (d) 36

(b) 18 First, set up the rate as a proportion, where (x) is the number of stations. 3 stations/10 minutes = (x) stations/1 hour Then, convert the units. 3 stations/10 minutes = (x) stations/60 minutes Cross multiply and solve for (x). 180 = 10(x) 18 = (x)

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

(d) 96 Be careful with a question like this one. You're given the percent decrease (25%) and the new number (72), and you're asked to reconstruct the original number. Don't just take 25% of 72 and add it on. That 25% is based not on the new number, 72, but on the original number - the number you're looking for. The best way to do a problem like this is to set up an equation: (original number) - (25% of original number) = new number (x) - 0.25(x) = 72 0.75x = 72 x = 96 Alternatively, you can use the answer choices to determine the correct answer. The original number of jelly beans has to be reducible by 25%, or 1/4. That means the original number of jelly beans has to be a multiple of 4 (or else you'd be reducing by pieces of jelly beans). Only the correct answer, 96, is a multiple of 4.

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

(c) $720 You can save valuable time by estimating on this one. Pay special attention to how much you have left and how much you've already spent. If a man spent 5/12 of his salary and was left with $420, that means that he had 7/12 left, and if the man's salary is (x) dollars, then 7/12(x) = $420 That means that $420 is a little more than half of his salary. So his salary would be little less than 2($420) = $840. Choice (c), $720 is a little less than $840. So (c) works perfectly, and it's the correct answer here.

After spending 5/12 of his salary, a man has $420 left. What is his salary? (a) $175 (b) $245 (c) $720 (d) $1,008

(b) $1.75 Compute the cost of parking a car for 5 hours at each garage. Since the two garages have a split-rate system of charging, the cost for the first hour is different from the cost of each remaining hour. The first hour at garage (A) costs $8.75 The next 4 hours cost 4 x $1.25 = $5.00 The total cost for parking at garage (A) = $8.75 + 5.00 = $13.75 The first hour at garage (B) costs $5.50 The next 4 hours cost 4 x $2.50 = $10.00 The total cost for parking at garage (B) = $5.50 + $10.00 = $15.50 So the difference in cost = $15.50 - $13.75 = $1.75, (B).

At garage (A), it cost $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

(d) $11.25 The total cost of the taxi ride equals $36 + (25% of $36), or $36 + (.25 x $36) = $36 + $9 = $45. If four people split the cost equally, then each person paid $45/4, or $11.25 each.

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

(d) 200% Be careful with combined percent increase. You cannot just add the two percents, because they're percents of different bases. In this instance, the 100% increase is based on the 1980 population, but the 50% increase is based on the larger 1990 population. If you just added 100% and 50% to get 150%, you would have chosen the wrong answer. The best way to do a problem like this one is to pick a number for the original whole and just see what happens. The best number to pick here is 100. (That may be a small number for the population of a country, but reality is not important - all that matters is the math.) If the 1990 population was 100, then a 100% increase would put the 1990 population at 200. And a 50% increase over 200 would be 200 + 100 = 300. Since the population went from 100 to 300, that's a percent increase of 200%. 300 - 100/100 x 100% = 200/100 X 100% = 200%

From 1980 through 1990, the population of Country X increased by 100%. From 1990 to 2000, he population increased by 50%. What was the continued increase for the period 1980-2000? (a) 150% (b) 166 2/3% (c) 175% (d) 200%

(a) 225 The calculations aren't too bad on this one. The most important thing to keep in mind is that you're solving for 75% of (x) and not for (x) itself. First, you are told that 50% of (x) is 150. That means that half of (x) is 150, and that (x) is 300. So 75% of (x) = 0.75 x 300 = 225.

If 50% of (x) is 150, what is 75% of (x)? (a) 225 (b) 250 (c) 275 (d) 300

(a) 36 Find the number of seconds in an hour and then multiply this by the distance the car is traveling each second. There are 60 seconds in a minute and 60 minute in one hour; therefore, there are 60 x 60, or 3,600, seconds in an hour. In one second the car travels 1/100 kilometers; in one hour the car will travel 3,600 x 1/100 or 36 kilometers.

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

(b) 44 To learn the man's overtime rate of pay, first figure out his regular rate of pay. Divide the amount of money made, $200, by the time it took to make it, 40 hours. $200 / 40 hours = $5 per hour. That is the normal rate. The man is paid 1 1/2 times his regular rate during overtime, so when working more than 40 hours he makes 3/2 x $5 per hour = $7.50 per hour. Now figure out how long it takes the man to make $230. It takes him 40 hours to make the first $200. The last $30 are made at the overtime rate. Since it takes the man one hour to make $7.50 at this rate, you can figure out the number of extra hours by dividing $30 by $7.50 per hour. $30 / $7.50 per hour = 4 hours. The total time needed is 40 hours plus 4 hours, or 44 hours.

If a man earns $200 for his first 40 hours of work in a week and then is paid one-and-one-half times his regular rate for any additional hours, how many hours must be work to make $230 in a week? (a) 43 (b) 44 (c) 45 (d)46

(d) 20,200 If you change each digit 5 into a 7 in the number 258,546, the new number would be 278,746. The difference between these two numbers would be 278,746 - 258,546 = 20,200.

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

(c) 8 hours and 20 minutes Set up a proportion: 12 pages/1 hour = 100 pages/ (x) hours 12(x) = 100 (x) = 100/12 = 8 1/3 An hour is 60 minutes; one third of that is 20 minutes. So 8 1/3 hours is 8 hours and 20 minutes.

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

(c) 14 This is a combined work problem. Joan can shovel the whole driveway in 50 minutes, so each minute she does 1/50 of the driveway. Mary can shovel the whole driveway in 20 minutes: each minute she does 1/20 of the driveway. In one minute they do: 1/50 + 1/20 + = 2/100 + 5/100 = 7/100 If they do 7/100 of the driveway in one minute, they do the entire driveway in 100/7 minutes. (If you do 1/2 of a job in 1 minute, you do the whole job in the reciprocal of 1/2, or 2 minutes.) So all that remains is to round 100/7 off to the nearest integer. Since 100/7= 14 2/7, 100/7 is approximately 14. It takes about 14 minutes for both of them to shovel the driveway.

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

(c) $128 This question asks you to determine the sale price of a camera that normally sells at $160 and is discounted 20%. To solve, determine what 20% of $160 equals. Rewrite 20% as a decimal. 20% = 0.20. So 20% of $160 = 0.20 x $160 = $32. The sale price of the camera would be $160 - $32 = $128, choice (c)

John bought 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

(b) $260 You're told that Eileen earns $2800 per week. Kelly earns $50 more Than Eileen, so Kelly earns $280 + $50 = $330 per week. June's salary is $70 less than Kelly's, so June earns $330 - $70 = $260 per week, and (b) is correct.

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) 2/3 To find probability, determine the number of desired outcomes and divide that by the number of possible outcomes. The probability formula looks like this: Probability = # of desired outcomes/# of possible outcomes In this case, Marty is pulling one pen at random from his knapsack, and you want to determine the probability that the pen is either red or black. There are 5 blue pens, 6 black pens, and 4 red pens in the knapsack. Let's return to the probability formula: Probability = # of desired outcomes/ # of possible outcomes = number of red + black pens/number of red+ black + blue pens = 4 + 6/ 4+6+5 = 10/15=2/3

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) $9.63 Since 1 pound of lumber costs $4.00, 2 1/4 pounds of lumber cost 2.25 x $4.00 = $9.00. Then add 7% sales tax to $9.00. Find 7% of $9.00 by multiplying 0.07 x $9.00 = $0.63. Add $0.63 to $9.00 to get $9.63, choice (a).

Micheal bought 2 1/4 pounds of lumber at $4.00 per pound. If a 7% sales tax was added, how much did Micheal pay? (a) $9.63 (b) $9.98 (c) $10.70 (d) $11.77

(c) $25.00 If Ms. Smith's car average 35 miles per gallon, she can go 35 miles on 1 gallon. To go 700 miles she will need 700/35, or 20 gallons of gasoline. The price of gasoline was $1.25 per gallon, so she spent 20 x $1.25, or $25, for her trip.

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) $20.00 (b) $ 24.00 (c) $ 25.00 (d) $40.00

(b) 2 1/3 In this question, the ratio is implied: for every 3/4 inch of map there is 1 real mile, so the ratio of inches to the miles they represent is always 3/4 to 1. Therefore, you can set up the proportion: number of inches/ number of miles = 3/4 / 1 = 3/4 Now 1 3/4 inches = 7/4 inches. Set up a proportion: 7/4 inches 7/4 inches / number of miles = 3/4 Cross-multiply: 7/4(4) = 3 (number of miles) 7= 3(number of miles) 7/3 = number of miles or 2 1/3 = number of miles

On a certain map, 3/4 inch represents one mile. What distance, in miles, is presented by 1 3/4 inches? (a) 1 1/2 (b) 2 1/3 (c) 2 1/2 (d) 5 1/4

(d) 13 to 21 The question asks which of five ratios is equivalent to the ratio of 3 1/4 to 5 1/4. Since the ratios in the answer choices are expressed in whole numbers, turn this ratio into whole numbers. Start by turning the ratio into improper fractions: 3 1/4 : 2 1/4 = 13/4: 21/4 Multiply both sides of the ratio by 4. = 13:21

The ratio of 3 1/4 t0 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

(d) $4.00 This question where Backsolving (plugging in an answer choice to see if it's correct) can save you a lot of time. Let's start with choice (b) and see if it works. If (b) is correct, an adult's ticket would cost $3.00, and a child's ticket would cost $1.50. The total fare you're asked for is for two adults and three children. If an adult's fare was $3.00, that total fare would be 2($3.00) + 3($1.50) = $6.00 + $4.50 = $10.50. That's too low since the question states that the total fare is $14.00. Now see what happens if an adult fare was more expensive. If (d) was correct, an adult's ticket would cost $4.00 and a child's ticket would cost $2.00. The total fare would equal 2($4.00) + 3($2.00) = $8.00 + $6.00 = $14.00. That's the total fare you're looking for, so (d) is correct.

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

(d) 18 This problem sets up relationships among large, medium, and small sodas - 2 large sodas are equal to 3 medium sodas, and 2 medium sodas are equal to 3 small sodas. How many small sodas equal 8 large sodas? Well, 2 larges equal 3 mediums, so 12 mediums must equal 4 x 2 or 8 large sodas. You now can find how many small sodas represent 12 mediums. Since 2 mediums are the same as 3 small sodas, 12 mediums must equal 6 x 3 or 18 small sodas.

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

(c) 2 x 2 x 5 x 7 To find the prime factorization of a number, find one prime that will go into the number (here 2 is a good place to start). Express the number as that prime multiplied by some other number. 140 = 2 x 70 Then keep breaking down the larger factor until you are left with only prime numbers. 140 = 2 x 2 x 35 140 = 2 x 2 x 5 x 7

What is the prime factorization of 140? (a) 2 x 70 (b) 2 x 3 x 5 x 7 (c) 2 x 2 x 5 x 7 (d) 2 x 2 x 2 x 5 x 7