Arithmetic Reasoning · Practice test 7
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 student needs an average of 82 across five tests. The first four scores are 78, 85, 80, and 88. What is needed on the fifth?
Correct answer: 79
Five tests averaging 82 need 82 x 5 = 410 points in total. The first four supply 331, so the fifth must score 410 - 331 = 79.
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Question 2Not answered
A charity receives $1,840 in donations and spends 5/8 of it on supplies. How much was spent on supplies?
Correct answer: $1,150
One eighth of $1,840 is 230, so five eighths is 5 x 230, which comes to $1,150.
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Question 3Not answered
A car uses 12 gallons of fuel to travel 336 miles. What is its fuel economy?
Correct answer: 28 miles per gallon
Fuel economy is miles divided by gallons used, so 336 divided by 12 gives 28 miles per gallon.
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Question 4Not answered
Pump A can fill a tank in 4 hours and pump B can fill it in 12 hours. How long will they take working together?
Correct answer: 3 hours
Add the rates rather than the times. Pump A fills 3/12 of the tank an hour and pump B fills 1/12, giving 4/12 or one third per hour, so the tank fills in 3 hours. Averaging the two times to get 8 is the standard trap.
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Question 5Not answered
A hardware order lists a bolt priced at $2.35, a matching nut at $0.60, and a washer at $0.15. If 40 complete sets are bought, what is the total cost?
Correct answer: $124.00
Find the cost of one complete set before scaling up. One set costs 2.35 + 0.60 + 0.15 = $3.10, and 40 sets cost 40 x 3.10 = $124.00.
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Question 6Not answered
A 1.5 ounce packet of seasoning costs $0.60 and a 4 ounce jar costs $1.44. Which is the better value per ounce?
Correct answer: 4 cents per ounce less for the jar
Reduce both containers to a price per ounce before comparing. The packet costs 0.60 divided by 1.5, or 40 cents per ounce, while the jar costs 1.44 divided by 4, or 36 cents per ounce, so the jar is cheaper by 4 cents per ounce.
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Question 7Not answered
In a class the ratio of students who pass to students who fail is 7 to 2. If 18 students failed, how many passed?
Correct answer: 63 students
Since 2 parts correspond to 18 failing students, each part equals 9 students. Passing students make up 7 parts, so 7 x 9 = 63 students passed.
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Question 8Not answered
A production run of 450 units costs $3,150. What is the cost per unit?
Correct answer: $7.00
Cost per unit is the total cost divided by the number of units, so 3,150 divided by 450 gives $7.00 each.
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Question 9Not answered
A jet cruises at 480 miles per hour for 2 hours 15 minutes. How far does it travel?
Correct answer: 1,080 miles
Convert the time to a decimal first: 2 hours 15 minutes is 2.25 hours. Multiplying rate by time, 480 x 2.25 gives 1,080 miles.
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Question 10Not answered
A trainee recorded these weekly scores: Week 1, 78. Week 2, 85. Week 3, 92. Week 4, 81. Week 5, 84. What is the mean score?
Correct answer: 84
The mean is the total divided by how many values there are. The five scores add to 420, and 420 divided by 5 is 84.
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Question 11Not answered
A conveyor moves material at 2 feet per second. How many feet per minute is that rate?
Correct answer: 120 feet per minute
Converting a rate per second to a rate per minute means multiplying by the 60 seconds in a minute, so 2 x 60 gives 120 feet per minute.
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Question 12Not answered
A pump moves 3 gallons per minute. How many gallons does it move in an hour?
Correct answer: 180 gallons
Converting a rate per minute into a rate per hour means multiplying by the 60 minutes in an hour, so 3 x 60 gives 180 gallons.
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Question 13Not answered
A backpack that regularly costs $72 is marked down by 30 percent. What is the sale price?
Correct answer: $50.40
A 30 percent discount takes off 0.30 x 72 = $21.60, so the sale price is 72 - 21.60 = $50.40. Reporting $21.60 alone gives only the savings, not the price paid.
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Question 14Not answered
A boat that seats 11 passengers must carry a group of 97 people across a lake. What is the least number of trips needed?
Correct answer: 9 trips
97 divided by 11 is 8 with 9 passengers left over. That remainder still needs a ride, so a ninth trip is required to carry everyone.
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Question 15Not answered
A student needs an average of 90 across five quizzes. The first four scores are 88, 92, 85, and 94. What score is needed on the fifth quiz?
Correct answer: 91
Work backward from the total the average requires. Five quizzes averaging 90 need 90 x 5 = 450 points, and the first four supply 359, so the fifth quiz must score 450 - 359 = 91.
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Question 16Not answered
A shuttle bus travels at a steady 38 miles per hour for 3.5 hours. How far does it travel?
Correct answer: 133 miles
Distance is rate multiplied by time. Travelling 38 miles per hour for 3.5 hours covers 38 x 3.5 = 133 miles.
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Question 17Not answered
A worker buys tools costing $34.75, $12.60, and $8.15. How much change is returned from $60.00?
Correct answer: $4.50
Total the purchases first, then subtract from the amount handed over. The tools come to $55.50, and $60.00 minus $55.50 leaves $4.50 in change.
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Question 18Not answered
A van carries 7 passengers. What is the smallest number of vans needed to move 45 passengers at one time?
Correct answer: 7 vans
Dividing 45 by 7 gives 6 with 3 passengers left over. Those 3 still need a ride, so the leftover forces one more vehicle and 7 vans are required.
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Question 19Not answered
A number is divisible by both 6 and 8. What is the smallest positive number greater than zero for which this is true?
Correct answer: 24
The smallest number divisible by both 6 and 8 is their least common multiple. Listing multiples of 6 gives 6, 12, 18, 24, and 24 is the first one that 8 also divides evenly.
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Question 20Not answered
A warehouse begins the week with 1,250 units, receives 380 more, and ships out 465. How many remain?
Correct answer: 1,165 units
Add what came in and subtract what went out: 1,250 + 380 = 1,630, and 1,630 - 465 = 1,165 units.
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Question 21Not answered
A circular helipad has a diameter of 20 feet. Using 3.14 for pi, what is its approximate area?
Correct answer: 314 square feet
The radius is half the diameter, or 10 feet. The area formula uses the radius squared, so 3.14 x 10 x 10 gives 314 square feet. Using the diameter instead of the radius is the usual mistake.
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Question 22Not answered
A bag holds 4 white, 6 black, and 2 red markers. If one is drawn at random, what is the probability that it is not black?
Correct answer: 1/2
Six of the twelve markers are not black, so the probability is 6/12, which simplifies to 1/2. It is quicker to note that black is also 6 of 12, and the two must add to 1.
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Question 23Not answered
A crew loads 24 crates per hour for 5 hours, then slows to 18 crates per hour for 3 more hours. How many crates were loaded in total?
Correct answer: 174 crates
Work out each stretch separately before adding. The first five hours produce 24 x 5 = 120 crates and the next three produce 18 x 3 = 54, giving 174 crates in total.
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Question 24Not answered
A crate holds 9 working bulbs and 3 defective bulbs. If one bulb is picked at random, what is the probability it is defective?
Correct answer: 1/4
Probability is defective bulbs over total bulbs. There are 3 defective out of 9 + 3 = 12 bulbs, and 3/12 simplifies to 1/4.
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Question 25Not answered
How much simple interest does $3,600 earn in 2 years at an annual rate of 4.5 percent?
Correct answer: $324
Simple interest is principal times rate times time. One year earns 3,600 x 0.045 = $162, so two years earn 2 x 162 = $324.
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Question 26Not answered
A model is built to a scale of 1 to 250. A part measuring 3 inches on the model represents what actual length?
Correct answer: 62.5 feet
The actual length is 3 x 250 = 750 inches, and converting to feet gives 750 / 12 = 62.5 feet. The choice 750 is correct in inches and stops one step early.
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Question 27Not answered
Two trains 420 miles apart travel toward each other at 70 and 50 miles per hour. How long until they meet?
Correct answer: 3.5 hours
Approaching objects close the gap at the sum of their speeds, 70 + 50 = 120 miles per hour, so 420 / 120 = 3.5 hours. Using one speed alone gives 6 or 8.4 hours.
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Question 28Not answered
A parade route is about 3.1 miles long and a marching band member takes roughly 2,000 steps per mile. Roughly how many steps does the walk take?
Correct answer: About 6,000 steps
Round 3.1 miles to 3 miles for an easy estimate. Three miles at about 2,000 steps each comes to roughly 6,000 steps, close enough for a quick estimate.
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Question 29Not answered
A buyer pays a 20 percent deposit of $340 on a used car. What is the full price of the car?
Correct answer: $1,700
Here the part is known and the whole is missing, so divide rather than multiply. Since $340 represents 20 percent of the price, the full price is 340 divided by 0.20, which is $1,700.
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Question 30Not answered
A truck averages 18 miles per gallon and has a 15 gallon tank. About how far can it travel on two thirds of a tank?
Correct answer: 180 miles
Two thirds of a 15 gallon tank is 10 gallons of fuel. At 18 miles per gallon, 10 gallons carries the truck about 18 x 10 = 180 miles.
Your result
/ 30 correct
The ASVAB has no pass mark. Arithmetic Reasoning, Word Knowledge, Paragraph Comprehension and Mathematics Knowledge make up your AFQT percentile.