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ASVAB: Arithmetic Reasoning
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Practice ASVAB questions and explanations for the arithmetic reasoning portion of the test.
Terms in this set (28)
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. Multiply 12 miles by $3.50 per mile:
12 × $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. x + x + 8 = 70, solve for x.
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. 144 bottles in a gross, and 144 ÷ 3 (bottles per day) = 48 days.
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. x = the unknown score. (93 + 89 + 96 + 98 + x) ÷ 5 or (376 + x) ÷ 5. Now solve for x
A waitress earns an average of 12% of the cost of the food she serves. If she serves $375 worth of food in one evening, how much money in tips will she earn on average?
(a) $37
(b) $45
(c) $42
(d) $420
B. Multiply the amount spent on drinks, $375, by 12% (or 0.12) to determine the amount of tips:
$375 × 0.12 = $45
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. To determine square footage multiply length by width
12 × 12 = 144 sq feet
Joe received an hourly wage of $8.15. His boss gave him a 7% raise. How much does Joe make per hour now?
(a) $0.57
(b) $8.90
(c) $8.72
(d) $13.85
C.To calculate the new wage first multiply $8.15 × 0.07 = $0.57. Then add that to the original wage,
$8.15 + $0.57 = $8.72
Alice leaves her house, driving east at 45 miles per hour (mph). Thirty minutes later her husband Dave notices she forgot her cell phone and sets off after her. How fast must Dave travel in order to catch up with Alice 3 hours after he leaves?
(a) 49 mph
(b) 50.5 mph
(c) 52.5 mph
(d) 54 mph
C. distance = speed × time. First find how far Alice had traveled 3½ hours at 45 mph, or 157.5 mph. Dave has three hours to cover this distance. Now find his speed. 157.5 mi ÷ 3 hr. = 52.5 mph
Miriam bought five cases of motor oil on sale. A case of motor oil normally costs $24.00, but she was able to purchase the oil for $22.50 a case. How much money did Miriam save on her entire purchase?
(a) $7.50
(b) $1.50
(c) $8.00
(d) $22.50
A. Subtract the sale price from the original price, $24.00 − $22.50 = $1.50. Now multiply that number by the amount of cases to get the final answer $1.50 × 5 = $7.50
A security guard walks the equivalent of six city blocks when he makes a circuit around the building. If he walks at a pace of eight city blocks every 30 minutes, how long will it take him to complete a circuit around the building, assuming he doesn't run into any thieves?
(a) 20.00 minutes
(b) 3.75 minutes
(c) 22.50 minutes
(d) 7.5 minutes
C. Divide 30 by 8 to determine how long it takes to walk one city block = 3.75 minutes. Then multiply by 6 the number it takes to complete the circuit. The answer is 22.5 minutes.
The population of Grand Island, Nebraska, grew by 600,000 people between 1995 and 2005, one-fifth more than the town council predicted. The town originally predicted the city;s population to grow by
(a) 400,000
(b) 500,000
(c) 300,000
(d) 100,000
B. Let x = the original number predicted. An ¹/₅ would make the population growth ⁶/₅ or 120%, of x. Express the equation as 1.2x = 600,000, solve for x. x = 500,000.
Karl is driving in Austria, where the speed limit is posted in kilometers per hour. The car's speedometer shows that he's traveling at a rate of 75 kilometers per hour. Karl knows that a kilometer is about ⁵/₈ of mile. Approximately how many miles per hour is Karl traveling?
(a) 47
(b) 120
(c) 50
(d) 53
B. Multiply 75 by ⁵/₈, 375 ÷ 46.8 = 47 mph
A carpenter earns $12.30 an hour for a 40-hour week. His overtime pay is 1¹/₂ times his base pay. If he puts in a 46-hour week, how much is his weekly pay?
(a) $602.70
(b) $492.00
(c) $565.80
(d) $110.70
A. You need to add the carpenters base pay and overtime to find his total pay for the week. First find his base pay per week: $12.30 × 40hrs = $492. Then find his overtime rate per hour, which is 1¹/₂ time the base pay: $12.30 × 1.5 = $18.45. Multiply this rate by the number of hours of overtime to find his overtime pay: $18.45 × 6 hr. = $110.70. Finally add the base pay and overtime to find the total for the week, $492 + $110.7 = $602.70
An office building has 30 employees and provides 42 square feet of work space per employee. If five more employees are hired, how much less work space will each employee have?
(a) 6 square feet
(b) 7 square feet
(c) 7.5 square feet
(d) 36 square feet
A. First find the area of the office, 42 ft. × 30 = 1260 sq ft. Then divide the space by 35 employees, each employee now has 36 sq ft of workspace, which is 6 feet less than originally.
Stan bought a monster truck for a $2,000 down payment and $450 a month for five years. What's the total cost of the monster truck?
(a) $4,250
(b) $29,000
(c) $27,000
(d) $34,000
B. Five years contains 60 months, $450 payments at 60 months = $27,000. Now add the down payment, $27,000 + $2,000 = $29,000
MIchael needs 55 gallons if paint to paint an apartment building. He would like to purchase the paint for the least amount money possible. Which of the following should he buy?
(a) two 25-gallon buckets at $550 each
(b) eleven 5-gallon buckets at $108 each
(c) six at 10-gallon buckets at $215 each
(d) fifty-five 1-gallon bucket at $23 each
B. Choice (a) doesn't have enough paint (2 ×25 gal = 50 gal) so it's wrong.
Choice (b): 11 × $108 = $1,188
Choice (c): 6 × $215 = $1,290
Choice (d): 55 × $23 = $1265
As a member of FEMA, you're required to set up a contingency plan to supply meals to residents of a town devastated by a tornado. A breakfast ration weights 12 ounces and the lunch and dinner rations weight 18 ounces each. Assuming a food truck can carry 3 tons and that each resident will receive 3 meals per day, how many residents can you feed from one truck during a 10-day period?
(a) 150 residents
(b) 200 residents
(c) 250 residents
(d) 300 residents
B. First find how many ounces each truck can hold. 2,000lb. are in a ton, so each truck can carry three times that 6,000lb. There are 16 ounces to a pound so one truck can carry 96,000 ounces ( 16oz. × 6,000lb.).
Now find the daily total for each persons three meals 12oz + 18oz + 18oz = 48oz. Now 96,000 × 48 = 2,000 daily rations. This rations need to last 10 days (2,000 ÷ 10 = 200) So 200 residents can be fed by one truck for 10 days.
A train headed south for Wichita left the station at the same time a train headed north for Des Moines left the same station. The train headed to Wichita traveled 55 miles per hour. The train headed for Des Moines traveled at 70 miles per hour. How many miles apart are the trains at the end of three hours?
(a) 210 miles
(b) 165 miles
(c) 125 miles
(d) 375 miles
D. Distance = speed × time, take the distance traveled by the Wichita train (55mph × 3hr = 165 miles) then add that to the distance traveled by the Des Moines train (70mph × 3hr = 210 miles). The trains are 375 miles apart in 3 hours. Another option: add the two trains mph then multiply by 3 hours (55 + 70) = 125 × 3 = 375 miles
A carpenter needs to cut four sections, each 3 feet, 8 inches long, from a piece of molding. If the board is only sold by the foot, what's the shortest length of board she can buy?
(a) 15 feet
(b) 14 feet
(c) 16 feet
(d) 12 feet
A. Each section is 3²/₃ feet, times that by four and you get 14²/₃ so 15 is the shortest board possible.
Kiya had only one coupon for 10% off one frozen turkey breast. The turkey breast costs $8.50 each, and Kiya wanted to buy two. How much did she pay?
(a) $16.15
(b) $17.00
(c) $15.30
(d) $7.65
A. First find the discounted turkey's price ($8.50 × .10 = $0.85, $8.50 - $0.85 = $7.35) then add another $8.50 because she needs two turkey breast. $7.35 + $8.50 = $16.15
Your car uses gasoline at a rate of 21 miles per gallon. If gasoline costs $2.82 per gallon and you drive for 7 hours at a speed of 48 miles per hour, how much will you pay for gasoline for the trip?
(a) $38.18
(b) $45.12
(c) $47.73
(d) $59.27
B. First determine the miles traveled d = st (7hr × 48mph = 336 miles), then divide by the rate per gallon, 21. So now you know you need 16 gallons at $2.82 per gallon to pay for the trip. 16 × $2.82 = $45.12
If you roll two six-sided dice, what's the probability of not rolling a five on either die?
(a) ¹/₃₆
(b) ¹/₆
(c) ⁴/₃₆
(d) ²⁵/₃₆
D. The probability of rolling a 5 is a 1 out of 6 chance, so the probability of NOT rolling a 5 is 5 out of 6. With two die the probability is ⁵/₆ × ⁵/₆ = ²⁵/₃₆
Jack loaned Bob $1,500 at an annual interest rate of 7%. After one year, how much will Bob owe Jack?
(a) $105
(b) $1,500
(c) $1,605
(d) $1,507
C. First find interest then add to the loan. $1,500 × 0.07 = 106, $106 + $1,500 = 1,605
A 2-ton truck is taxed at a rate of $0.12 per pound. How much is the total tax bill?
(a) $480
(b) $240
(c) $120
(d) $600
A. 2,000 pounds to a ton. 4,000 × .12 = 480
If ab = 10 and a² + b² = 30, solve for y in the equation y = (a+b)².
(a) 40
(b) 45
(c) 50
(d) 55
C. First expand the equation (a+b)² or (a+b)(a=b) into y = a² + b² +2ab. You already know ab = 10 and a² + b² = 30, so substitute the known values and solve for y. 30 + 2(10) = 50
A half-pint of cream is what part of a gallon?
(a) ¹/₈
(b) ¹/₄
(c) ¹/₁₆
(d) ¹/₆
C. 2 pints in a quart, 4 quarts to a gallon. Therefore 8 pints are to a gallon or 16 half-pints, ¹/₁₆.
The cost of a protein bar increased from $2.50 to $2.80. The percent increase to the $2.80 rate was how much?
(a) 16%
(b) 10%
(c) 15%
(d) 12%
D. Find the difference then use that number to divide the original cost $2.50 ÷ $0.30 = 0.12 or 12%
An aircraft flies over Boondock Air Force Base at 10:20 a.m. At 10:32 a.m., the plane passes over Sea Side Naval Air Station, 120 miles away. How fast is the aircraft traveling?
(a) 400 mph
(b) 500 mph
(c) 600 mph
(d) 700 mph
C. The plane traveled 120 miles in 12 minutes or ¹/₅ of an hour. d=st, 120 = ¹/₅x or 120 × 5 = 600 mph
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