ASVAB - Practice math problems fully solved.

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 (c) $128 $160 (1-.20) = 160(.8) = 128 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 (b) 18 3 stations/10 minutes = (x) stations/60 minutes Cross multiply and solve for (x). 180 = 10(x) so 18 = (x) 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 (b) 2 1/3 (3/4 )/1 = 7/4 inches / x number of miles Cross-multiply: 7/4(1) = 3/4 (x number of miles) Multiply both sides by 4 : 7 = 3x x = 7/3 = 2 1/3 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 (d) 45 Express the ratio of baseballs to golf balls as 2/3. 2/3 = 30/ (x number of golf balls) cross-multiply to get 2(x) = 90, or x = 45. 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) $11.25 Total cost of the taxi ride equals $36(1 + .25)= $45. If four people split the cost equally, then each person paid $45/4, or $11.25 each. 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) 36 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. 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 (c) $25.00 Find how many gallons are needed. 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. 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 (d) 96 You're given the percent decrease (25%) and the new number (72), and you're asked to reconstruct the original number. (original number)(1 - .25) = new number (x)(.75) = 72 x = 96. 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) 24 If (S) represents the time spent on the second half, then the total time spent is 2/3(S) + (S) or 5/3 (S). 5/3(S) = 60 multiply both sides by 3/5 (S) = 36 2/3 times 36 24 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) 6 2/3% 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% 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) 2/3 = number of red + black pens/total number of pens = (4 + 6)/ (4+6+5) = 10/15=2/3 From 1980 through 1990, the population of Country X increased by 100%. From 1990 to 2000, the population increased by 50%. What was the continued increase for the period ? (a) 150% (b) 166 2/3% (c) 175% (d) 200% (d) 200% ( x # of people)(1 + 1)(1 + .5) = x(2)(1.5) = 3x new - old / old (3x - x)/x = 2 so percent is 200% Or let 1990 population =100, then a 100% increase would put the 1990 population at 200. And a 50% increase over 200 would be 200 + 100 = 300. (300 - 100)/100 = 2 X 100 = 200% 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 he work to make $230 in a week? (a) 43 (b) 44 (c) 45 (d)46 (b) 44 First figure out his regular rate of pay. Divide the amount of $200 / 40 hours = $5 per hour. 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. 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 50% of (x) is 150, what is 75% of (x)? (a) 225 (b) 250 (c) 275 (d) 300 (a) 225 .50/150 = .75/x cross multiply .5x = 112.5 x = 225 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) $4.00 x = adult fare, .5x = child's fare 2x + (3)(.5x) = 14 2x + 1.5x = 14 3.5x = 14 x = 4 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 (c) 2 x 2 x 5 x 7 140 = 2 x 70 140 = 2 x 2 x 35 140 = 2 x 2 x 5 x 7 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 (a) 6 x = number of hours worked 12x + 6x = 108 18x = 108 108 / 18 = 6. 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 (b) $1.75 The total cost for parking at garage (A) = $8.75 + 5.00 = $13.75 The total cost for parking at garage (B) = $5.50 + $2.50(4) = $5.50 + $10.00 = $15.50 So the difference in cost = $15.50 - $13.75 = $1.75, 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) 8 hours and 20 minutes 12 pages/1 hour = 100 pages/ (x) hours 12(x) = 100 (x) = 100/12 = 8 1/3 One third of an hour is 20 minutes. So 8 1/3 hours is 8 hours and 20 minutes. 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 (d) 18 2 large/3 medium = 8 large/x medium 2x = 24, x = 12 medium 2 medium/3small = 12 medium/x small 2x =36, x = 18 small 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 (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. 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 (a) $9.63 2 1/4 pounds of lumber cost 2.25 x $4.00 = $9.00. (9.00)(1 + .07) = $9.63 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) 13 to 21 3 1/4 : 2 1/4 = 13/4: 21/4 Multiply both sides of the ratio by 4. = 13:21 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) 192 3/8 lb / 1 day = 72 lbs / (x) days Cross multiply. 3/8 (x) = 72 (x) = 72 x 8/3 (x) = 192 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 (c) $720 x = starting salary x( 1 - 5/12) = 420 x(7/12) = 420 multiply both sides by 12/7 x = 720 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% (c) 25% x = the stock price increase that you're finding (1 -.2)(1 + x ) = 1 (equals starting value) (.8)(1+x) =1 1 + x = 1.25 x = .25 or 25% 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) 14 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 (x min)(7/100) = 1 (1 stands for the finished job) x = 100/7 and 100/7= 14 2/7 rounds to 14. 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 (b) $260 If Eileen earns $280, Kelly earns $330 June earns $330 - $70 = $260 per week If a car is towed 12 miles to the repair shop and the tow charge is $3.50 per mile, how much does the tow cost? (a) $12.00 (b) $3.50 (c) $42.00 (d) $100.00 C) $42.00 Multiply 12 miles by $3.50 per mile. 12 x $3.50 = $42.00 The sum of two numbers is 70. One number is 8 more than the other. What's the smaller number? (a) 31 (b) 33 (c) 35 (d) 36 A) 31 x +( x + 8) = 70 2x + 8 = 70 x = 31 A sales manager buys antacid in bottles the gross. If he goes through 3 bottles antacid everyday, how long will the gross last? (a) 144 days (b) 3 days (c) 20 days (d) 48 days D) 48 gross = 144 3 bottles/1 day = 144 bottles/x days 3x = 144 x = 48 Jenny's test grades are 93,89, 96, and 98. If she wishes to raise her average to 95, what does she need to score on her next test? (a) 100 (b) 99 (c) 97 (d) 95 B) 99 x = the unknown score. (93 + 89 + 96 + 98 + x) / 5 =95 (376 + x) / 5 =95 376 + x = 475 x= 99 How many square feet of carpeting are needed to carpet a 12-foot × 12-foot room? (a) 24 (b) 120 (c) 48 (d) 144 D) 144 To determine sq. footage, multiply length by width. 12 x 12 = 144