Arithmetic Reasoning · Practice test 1
30 questions · 36 minutes
Answer every question, then tap Check results to see your score and the method behind each answer.
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Question 1Not answered
A model airplane is built at a scale of 1 inch to 3 feet. If the actual wingspan is 33 feet, how long is the model's wingspan?
Correct answer: 11 inches
Since each inch of the model represents 3 feet of the real plane, divide the real length by 3. That gives 33 divided by 3, or 11 inches for the model.
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Question 2Not answered
A wholesaler pays $18 for a tool and sells it for $27. What percent markup was applied?
Correct answer: 50 percent
Markup percent is measured against the cost, not the selling price. The increase is 27 - 18 = 9 dollars, and 9 divided by 18 is 0.5, or a 50 percent markup.
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Question 3Not answered
How long does it take to travel 273 miles at a steady 65 miles per hour?
Correct answer: 4.2 hours
Time equals distance divided by rate. Dividing 273 by 65 gives 4.2 hours.
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Question 4Not answered
A triangular sail has a base of 12 feet and a height of 9 feet. What is its area?
Correct answer: 54 square feet
The area of a triangle is half the base times the height. Half of 12 is 6, and 6 x 9 gives 54 square feet.
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Question 5Not answered
Pump A can fill a tank in 6 hours and pump B can fill the same tank in 3 hours. Working together, how long will they take to fill it?
Correct answer: 2 hours
Add the rates, not the times. Pump A fills 1/6 of the tank per hour and pump B fills 1/3, so together they fill 1/6 + 2/6 = 1/2 of the tank each hour. Filling the whole tank therefore takes 2 hours.
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Question 6Not answered
A triangular sail has a base of 9 feet and a height of 14 feet. What is its area?
Correct answer: 63 square feet
A triangle's area is half the base times the height, so 9 x 14 = 126 and half of that is 63 square feet. Forgetting to halve gives 126.
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Question 7Not answered
A production line makes 120 units an hour. How long will an order of 1,860 units take?
Correct answer: 15.5 hours
Divide the order by the hourly output: 1,860 / 120 = 15.5 hours.
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Question 8Not answered
A canteen starts the shift with 300 meal trays, serves 187, and then restocks with 45 more. How many trays remain?
Correct answer: 158 trays
Subtract what was served first, then add the restock. Serving 187 leaves 300 - 187 = 113 trays, and adding 45 more brings the total to 113 + 45 = 158 trays.
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Question 9Not answered
A clearance sale takes 40 percent off a $95 power drill. What is the sale price?
Correct answer: $57.00
A 40 percent discount removes 0.40 x 95 = $38, so the sale price is 95 - 38 = $57.00.
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Question 10Not answered
A caterer's bill comes to $340 before a 20 percent gratuity is added. What is the total the customer pays?
Correct answer: $408.00
The gratuity is 0.20 x 340 = $68, and the total paid is the bill plus the gratuity, 340 + 68 = $408.00.
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Question 11Not answered
A tank held 850 gallons at the start of the week. Crews drew 275 gallons on Monday and 190 gallons on Tuesday. How much remains?
Correct answer: 385 gallons
Subtract both withdrawals from the starting amount. Together the crews drew 275 + 190 = 465 gallons, and 850 - 465 leaves 385 gallons in the tank.
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Question 12Not answered
A recruiter must group 90 male applicants and 75 female applicants into identical squads with no one left over. What is the greatest number of squads that can be formed?
Correct answer: 15 squads
The squad count must divide both totals evenly, so the greatest possible number of squads is the greatest common factor of 90 and 75. Since 90 is 2 x 3 x 3 x 5 and 75 is 3 x 5 x 5, they share 3 x 5 = 15, so 15 squads can be formed.
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Question 13Not answered
A garden plot measures 18 feet by 12 feet. How much fencing is needed to enclose it completely?
Correct answer: 60 feet
Fencing runs around the perimeter, not the area. One long side plus one short side is 30 feet, and doubling that for both pairs of sides gives 60 feet. The 216 option is the area, a common trap.
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Question 14Not answered
A supervisor has 108 bolts and 144 nuts to pack into identical kits with none left over. What is the greatest number of kits that can be made?
Correct answer: 36 kits
The kit count must divide both quantities exactly, so it is the greatest common factor of 108 and 144. Since 108 is 2 x 2 x 3 x 3 x 3 and 144 is 2 x 2 x 2 x 2 x 3 x 3, they share 2 x 2 x 3 x 3 = 36, so 36 kits can be made.
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Question 15Not answered
A carpenter cuts three pieces from one board, measuring 2 3/4 feet, 3 1/2 feet, and 1 1/4 feet. What total length was cut from the board?
Correct answer: 7 1/2 feet
Add the whole feet first: 2 + 3 + 1 = 6. Then add the fractions: 3/4 + 1/2 + 1/4 equals 1 1/2. Combining the two parts gives 7 1/2 feet.
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Question 16Not answered
A machine produces 1,260 parts in 7 hours. How many parts does it produce per hour?
Correct answer: 180 parts
A rate per hour is the total divided by the number of hours, so 1,260 divided by 7 gives 180 parts per hour.
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Question 17Not answered
How many whole numbers divide evenly into 12?
Correct answer: 6
The divisors are 1, 2, 3, 4, 6, and 12, which makes six. Forgetting that 1 and the number itself both count is the usual reason for answering 4.
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Question 18Not answered
On a map, 2 inches represents 15 miles. If two towns are 7 inches apart on the map, how far apart are they in reality?
Correct answer: 52.5 miles
Each map inch stands for 15 divided by 2, or 7.5 real miles. Multiplying the drawn distance by that scale gives 7 x 7.5 = 52.5 miles.
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Question 19Not answered
A tank receives 1 1/3 gallons in the morning and 2 5/6 gallons in the afternoon. How much was added in total?
Correct answer: 4 1/6 gallons
Convert to sixths: 1/3 becomes 2/6, so the fractions give 2/6 + 5/6 = 7/6, which is 1 1/6. Adding that to the 3 whole gallons gives 4 1/6.
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Question 20Not answered
A crate weighs 4 pounds 6 ounces. How many total ounces does it weigh?
Correct answer: 70 ounces
There are 16 ounces in a pound, so 4 pounds is 4 x 16 = 64 ounces. Adding the extra 6 ounces gives 64 + 6 = 70 ounces.
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Question 21Not answered
A machine outputs 9 units per hour. Expressed per 8 hour workday, how many units does it produce?
Correct answer: 72 units
Multiply the hourly rate by the number of hours in the shift. That gives 9 x 8 = 72 units per workday.
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Question 22Not answered
A rectangular lot measures 40 feet by 30 feet and contains a shed with a 10 foot square base. How much of the lot is left as open ground?
Correct answer: 1,100 square feet
The lot covers 40 x 30 = 1,200 square feet and the shed occupies 10 x 10 = 100, leaving 1,100 square feet. The choice 1,190 subtracts the shed's perimeter instead of its area.
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Question 23Not answered
A rectangular yard measures 40 feet by 25 feet. How much fencing is needed to enclose it completely?
Correct answer: 130 feet
Fencing runs around the outside, which is the perimeter rather than the area. Adding one long side and one short side gives 65 feet, and doubling that for both pairs gives 130 feet. The 1,000 figure is the area, a common trap.
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Question 24Not answered
Three shelves each hold 2/5 of a full stock crate. How much of a full crate is on the three shelves combined?
Correct answer: 6/5 crates
Repeated addition of a fraction is multiplication. Three shelves at 2/5 each give 3 x 2/5 = 6/5 crates.
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Question 25Not answered
One bus leaves a depot every 15 minutes and another every 25 minutes. If both leave together, after how many minutes will they next leave together?
Correct answer: 75 minutes
They coincide at the least common multiple of 15 and 25. The multiples of 25 are 25, 50, 75, and 75 is the first that 15 also divides. Multiplying the two intervals gives 375, a common multiple but not the least.
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Question 26Not answered
A pallet holds 16 cases. How many pallets are needed to move 200 cases?
Correct answer: 13 pallets
Dividing 200 by 16 gives 12 with 8 cases left over, and those still need a pallet, so 13 are required. Stopping at 12 leaves 8 cases on the floor.
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Question 27Not answered
A moving crew packs 3 trucks with 84 boxes each and 2 trucks with 97 boxes each. How many boxes were packed altogether?
Correct answer: 446 boxes
Multiply each truck size by how many trucks carried it, then add. Three trucks give 3 x 84 = 252 boxes and two trucks give 2 x 97 = 194 boxes, for a total of 446 boxes.
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Question 28Not answered
After a 15 percent pay raise, a technician's new hourly wage is $27.60. What was the wage before the raise?
Correct answer: $24.00
The new wage represents 115 percent of the old one, so divide rather than subtract a straight 15 percent. Dividing 27.60 by 1.15 gives the original wage of $24.00.
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Question 29Not answered
A jug contains 3 1/2 quarts of coolant. After 1 3/4 quarts leaks out, how much coolant remains?
Correct answer: 1 3/4 quarts
Subtracting 1 3/4 from 3 1/2 requires a common denominator: 3 1/2 becomes 3 2/4. Taking away 1 3/4 leaves 1 3/4 quarts.
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Question 30Not answered
A wall measures 12 feet by 9 feet and contains a door opening 3 feet by 7 feet. How much wall area needs paint?
Correct answer: 87 square feet
Work out the full wall, then take away the opening. The wall is 12 x 9 = 108 square feet and the door is 3 x 7 = 21 square feet, so 108 - 21 = 87 square feet needs paint.
Your result
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The ASVAB has no pass mark. Arithmetic Reasoning, Word Knowledge, Paragraph Comprehension and Mathematics Knowledge make up your AFQT percentile.