Arithmetic Reasoning · Practice test 8
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 trail mix recipe uses nuts and raisins in a ratio of 4 to 1. How many pounds of nuts are needed to make 30 pounds of trail mix?
Correct answer: 24 pounds
The ratio 4 to 1 splits the mix into 4 + 1 = 5 shares, and nuts take up 4 of them. One share is 30 divided by 5, or 6 pounds, so nuts come to 4 x 6 = 24 pounds.
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Question 2Not answered
A batch of 1,500 parts costs $9,750 to manufacture. What is the cost per part?
Correct answer: $6.50
Cost per part is total cost divided by the number of parts, so 9,750 divided by 1,500 gives $6.50 per part.
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Question 3Not answered
A furniture set costs $960 and is financed over 8 equal monthly payments with $96 total interest. What is each payment?
Correct answer: $132
Add the interest to the price to find the total owed: 960 + 96 = $1,056. Dividing by the 8 payments gives 1,056 divided by 8, or $132 per month.
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Question 4Not answered
A room has four walls, each measuring 10 feet wide by 8 feet high. What is the total wall area?
Correct answer: 320 square feet
Each wall covers 10 x 8 = 80 square feet, and four of them give 320 square feet. This is the figure a painter starts from before deducting doors and windows.
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Question 5Not answered
A convoy has covered 5/6 of a 138 mile route. How many miles has it travelled?
Correct answer: 115 miles
One sixth of 138 is 23, so five sixths is 5 x 23 = 115 miles. The choice 23 is the distance still remaining.
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Question 6Not answered
A solution is mixed 3 parts water to 1 part concentrate. How much water is in 20 litres of solution?
Correct answer: 15 litres
The mixture divides into 3 + 1 = 4 parts of 5 litres each, and water is 3 of them, giving 15 litres. Using 3/3 instead of 3/4 gives the wrong denominator, which is the usual slip.
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Question 7Not answered
Coursework counts for 30 percent of a grade and the final exam counts for 70 percent. A student averages 80 on coursework and scores 92 on the final. What is the course grade?
Correct answer: 88.4
Each portion contributes according to its weight. Coursework contributes 0.30 x 80 = 24 and the final contributes 0.70 x 92 = 64.4, giving a course grade of 88.4.
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Question 8Not answered
A line graph shows a warehouse's inventory count at week's end: Week 1 500, Week 2 460, Week 3 520, Week 4 480. Between which two consecutive weeks did inventory increase the most?
Correct answer: From the second week to the third week
Compare each consecutive pair: Week 1 to 2 fell by 40, Week 2 to 3 rose by 60, and Week 3 to 4 fell by 40. The largest increase, 60 units, happened from Week 2 to Week 3.
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Question 9Not answered
A tablet originally priced at $260 goes on sale for $195. By what percent was the price reduced?
Correct answer: 25 percent
Compare the drop to the original price, not the sale price. The reduction is 260 - 195 = 65 dollars, and 65 divided by 260 is 0.25, which is 25 percent.
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Question 10Not answered
A deposit of $1,000 earns 10 percent a year, compounded annually. What is the balance after 2 years?
Correct answer: $1,210
The first year adds $100, bringing the balance to $1,100. The second year earns 10 percent of $1,100, which is $110, giving $1,210. Simple interest would have given $1,200, and the extra $10 is the interest earned on interest.
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Question 11Not answered
A rowing crew travels at 6 miles per hour with the current and 4 miles per hour against it. How much longer does a 12 mile trip take going against the current than with it?
Correct answer: 1 hour
Find the time for each direction and subtract. With the current, 12 miles at 6 mph takes 2 hours; against it, 12 miles at 4 mph takes 3 hours, a difference of 1 hour.
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Question 12Not answered
How many minutes are there in 3 1/4 hours?
Correct answer: 195 minutes
An hour is 60 minutes, so three hours is 180 minutes and a quarter hour adds 15 more, making 195 minutes.
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Question 13Not answered
A ribbon 5/6 of a yard long is cut into 5 equal pieces. How long is each piece?
Correct answer: 1/6 yard
Dividing a fraction by a whole number multiplies the denominator. 5/6 divided by 5 is 5/(6*5), which simplifies to 1/6 yard per piece.
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Question 14Not answered
A dispatcher assigns 4 trucks to carry 52 crates each and 6 trucks to carry 39 crates each. How many crates are dispatched in total?
Correct answer: 442 crates
Multiply each group of trucks by its load before adding the results. Four trucks at 52 crates give 208, and six trucks at 39 crates give 234, so together they carry 208 + 234 = 442 crates.
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Question 15Not answered
An item costing a store $80 is sold at a 35 percent markup. What is the selling price?
Correct answer: $108.00
The markup of 0.35 x 80 = $28 is added to the cost, giving $108. The choice $28 is the markup alone, and $52 subtracts it instead of adding.
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Question 16Not answered
A worker buys 4 identical parts at $6.75 each and pays with $30.00. How much change is due?
Correct answer: $3.00
Four parts cost 4 x 6.75 = $27.00, so the change from $30.00 is $3.00. The last choice subtracts the price of only one part.
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Question 17Not answered
What is the median of 12, 15, 12, 18, 20, and 12?
Correct answer: 13.5
Ordered, the values run 12, 12, 12, 15, 18, 20, so the median is the average of the third and fourth, (12 + 15) / 2 = 13.5. The choice 12 is the mode, which appears three times.
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Question 18Not answered
Coursework counts for 40 percent of a grade and the final exam counts for 60 percent. A student averages 85 on coursework and scores 90 on the final. What is the course grade?
Correct answer: 88
Each score is worth its weight, so multiply before adding. Coursework contributes 0.40 x 85 = 34 and the final contributes 0.60 x 90 = 54, giving 88. A plain average of 85 and 90 would give 87.5, which ignores the heavier weight on the final.
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Question 19Not answered
Weekly production rises from 220 units to 275 units. What is the percent increase?
Correct answer: 25 percent
The rise is 275 - 220 = 55 units, and 55 divided by the original 220 is 0.25, or 25 percent. Dividing by the new figure of 275 gives 20 percent, which is the usual mistake.
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Question 20Not answered
A batch of 320 units costs $2,400 to produce. What is the cost per unit?
Correct answer: $7.50
Cost per unit is the total divided by the number of units, so 2,400 / 320 = $7.50.
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Question 21Not answered
A purchase of $240 carries a sales tax of 7.5 percent. What is the total?
Correct answer: $258.00
The tax is 0.075 x 240 = $18, so the total is 240 + 18 = $258. The choice $18 gives only the tax.
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Question 22Not answered
A bin holds 6 blue chips, 4 yellow chips, and 5 white chips. If one chip is drawn at random, what is the probability it is yellow?
Correct answer: 4/15
Probability is the favourable count divided by the total count. There are 4 yellow chips out of 6 + 4 + 5 = 15 chips in all, so the probability is 4/15.
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Question 23Not answered
A room measures 15 feet by 12 feet. Carpet is sold by the square foot. How much is needed?
Correct answer: 180 square feet
Area is length times width, so 15 x 12 = 180 square feet. The choice 54 is the perimeter.
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Question 24Not answered
A square patio measures 16 feet on each side and has a circular fountain of radius 3 feet at its center. Using 3.14 for pi, about how much patio area is not covered by the fountain?
Correct answer: 227.7 square feet
Find the full patio area, then subtract the fountain's area. The patio is 16 x 16 = 256 square feet and the fountain is 3.14 x 3 x 3, about 28.3 square feet, leaving about 227.7 square feet of open patio.
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Question 25Not answered
A department reduces its staff from 48 people to 36. What is the percent decrease?
Correct answer: 25 percent
The reduction is 12 people, and 12 divided by the original 48 is 0.25, or 25 percent. Dividing by the new figure of 36 gives 33 percent, and 75 percent is the share that remains.
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Question 26Not answered
Two patrol boats leave port together, one returning every 8 hours and the other every 10 hours. If both leave together at noon, after how many hours will they next leave together?
Correct answer: 40 hours
The boats align again at a common multiple of their cycles, and the soonest time is the least common multiple. The multiples of 8 are 8, 16, 24, 32, 40, and 40 is the first that 10 also divides, so they next leave together after 40 hours.
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Question 27Not answered
How many quarts are there in 5 1/2 gallons?
Correct answer: 22 quarts
There are 4 quarts in a gallon, so multiply by 4. That gives 5.5 x 4 = 22 quarts.
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Question 28Not answered
A crew of 6 workers finishes a wall in 10 days. Working at the same rate, how long would 4 workers take to finish the same wall?
Correct answer: 15 days
Fewer workers means more days, so the quantities are inversely related. The job takes 6 x 10 = 60 worker-days in total, and 60 divided by 4 workers gives 15 days.
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Question 29Not answered
A deposit of $90 represents 15 percent of the full price. What is the full price?
Correct answer: $600
Here the part is known and the whole is missing, so divide: 90 / 0.15 = $600. Multiplying instead gives $13.50, and the choice $1,350 comes from multiplying by 15 rather than dividing by 0.15.
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Question 30Not answered
A crew leader is told that a shipment of 247 items can be split into equal groups with none left over. Which of the following could be the group size?
Correct answer: 13
Test each option by dividing into 247. Since 247 divided by 13 equals 19 exactly with no remainder, 13 is a valid group size; the other choices all leave a remainder.
Your result
/ 30 correct
The ASVAB has no pass mark. Arithmetic Reasoning, Word Knowledge, Paragraph Comprehension and Mathematics Knowledge make up your AFQT percentile.