ASVAB — All Questions

A technician earns $18.50 an hour and works 37.5 hours a week for all 52 weeks of the year. What is the yearly pay?

• a.$8,325
• b.$36,075✓
• c.$34,687
• d.$38,480

Chain the rates in order: 18.50 x 37.5 = $693.75 a week, then 693.75 x 52 = $36,075 a year. Assuming a 40-hour week instead of 37.5 gives $38,480, using 50 weeks gives $34,687, and multiplying the weekly pay by 12 months rather than 52 weeks gives $8,325.

A van averages 22 miles per gallon and fuel costs $3.60 a gallon. What is the fuel cost of a 495-mile trip?

• a.$90.00
• b.$79.20
• c.$81.00✓
• d.$137.50

Go from miles to gallons to dollars. Gallons burned = 495 / 22 = 22.5, so the cost is 22.5 x 3.60 = $81.00. Multiplying 22 x 3.60 = $79.20 prices one gallon-per-mile figure instead of the trip, dividing 495 by 3.60 gives $137.50, and rounding fuel to $4 a gallon gives $90.00.

A candidate averaged 74 on the first 4 exams of a 6-exam course. What must the last two exams average for the course average to reach 80?

• a.184
• b.80
• c.86
• d.92✓

Averages are totals in disguise. The course needs 80 x 6 = 480 points and 74 x 4 = 296 are already banked, so the last two must supply 480 - 296 = 184 points, an average of 184 / 2 = 92. Reporting 184 forgets to split those points between two exams, and 80 assumes matching the target is enough.

A course grade counts homework 40 percent, the midterm 25 percent, and the final 35 percent. A student earns 95 on homework, 72 on the midterm, and 80 on the final. What is the course grade?

• a.76.0
• b.84.0✓
• c.82.3
• d.83.2

Multiply each score by its weight, add the products, and divide by 100: (95 x 40 + 72 x 25 + 80 x 35) / 100 = (3800 + 1800 + 2800) / 100 = 84.0. Averaging the three scores as equals gives 82.3, swapping the midterm and final weights gives 83.2, and averaging just the two exams gives 76.0.

One class of 12 students averaged 88 on a test and another class of 18 students averaged 78 on the same test. What is the average for all 30 students?

• a.86
• b.84
• c.82✓
• d.83

A weighted average leans toward the larger group. Total points are 12 x 88 + 18 x 78 = 1056 + 1404 = 2460, and 2460 / 30 = 82. Averaging 88 and 78 as if the classes were the same size gives 83, and attaching each average to the other class's headcount gives 84.

The average weight of 8 boxes is 24 pounds. When one box is taken away, the remaining 7 boxes average 25 pounds. What did the box that was removed weigh?

• a.1 pound
• b.24 pounds
• c.17 pounds✓
• d.32 pounds

Turn both averages into totals and subtract: 8 x 24 = 192 pounds before and 7 x 25 = 175 pounds after, so the missing box weighed 192 - 175 = 17 pounds. It has to be below average, since removing it raised the average. Subtracting the averages gives 1 pound and swapping the counts gives 32 pounds.

A shop blends 30 pounds of coffee worth $8 a pound with 20 pounds worth $13 a pound. What must a pound of the blend sell for to bring in the same total as the two lots sold separately?

• a.$21.00
• b.$10.00✓
• c.$10.50
• d.$11.00

Total value over total weight: 30 x 8 + 20 x 13 = 240 + 260 = $500 spread over 30 + 20 = 50 pounds, so $10.00 a pound. Averaging the two prices gives $10.50 and ignores that more of the cheap lot went in, pairing each price with the other lot's weight gives $11.00, and adding the prices gives $21.00.

Six crew members averaged 42 parts a shift. After new tooling arrives, every one of them produces exactly 7 more parts a shift. What is the new average?

• a.43 parts
• b.84 parts
• c.49 parts✓
• d.42 parts

When every value in a set shifts by the same amount, the average shifts by exactly that amount: 42 + 7 = 49 parts, and the crew size is never needed. Spreading the 7 parts over six people gives about 43, and adding the crew's whole gain of 6 x 7 = 42 to the old average gives 84.

A hardware store marks a cordless drill at $148 and runs a sale taking 35 percent off. What does a customer pay for the drill before tax?

• a.$96.20✓
• b.$113.00
• c.$51.80
• d.$62.53

Sale price = original x (100 - discount) / 100, so $148 x 65/100 = $96.20. Taking 35 percent of $148 alone gives $51.80, which is the discount and not the price; subtracting 35 as dollars gives $113.00; applying the 35 percent cut twice gives $62.53.

A shop buys work jackets for $38 each and marks them up 60 percent of cost to set the shelf price. What is the shelf price of one jacket?

• a.$95.00
• b.$98.00
• c.$22.80
• d.$60.80✓

A markup on cost means price = cost x (100 + markup) / 100, so $38 x 160/100 = $60.80. The $22.80 figure is only the markup itself; adding 60 as dollars gives $98.00; dividing by 40 percent, as if the 60 percent were a margin on the selling price, gives $95.00.

A customer buys 3 air filters at $18.50 each and 2 quarts of oil at $7.25 each. Sales tax of 8 percent is charged on the whole purchase. What is the total paid?

• a.$75.60✓
• b.$81.65
• c.$70.00
• d.$78.00

Total the goods first, then tax the total once. 3 x $18.50 = $55.50 and 2 x $7.25 = $14.50, so the goods come to $70.00, and $70.00 x 108/100 = $75.60. Stopping at $70.00 forgets the tax, adding $8 flat gives $78.00, and taxing the taxed total again gives $81.65.

A salesperson is paid $1,600 a month plus a commission of 7 percent on everything sold. In a month with $24,000 in sales, what is the total pay?

• a.$1,680
• b.$1,792
• c.$1,768
• d.$3,280✓

Pay = base + rate x sales. Seven percent of $24,000 is $1,680, and $1,600 + $1,680 = $3,280. Reporting $1,680 alone drops the base salary, using 0.7 percent instead of 7 gives $1,768, and paying commission on sales plus base rather than sales alone gives $1,792.

Four friends split an $86.40 restaurant bill evenly, and each one adds a 20 percent tip on his own share. How much does each friend pay in all?

• a.$103.68
• b.$25.92✓
• c.$21.60
• d.$38.88

Split first, then tip the share: $86.40 / 4 = $21.60, and $21.60 x 120/100 = $25.92. The $21.60 leaves the tip off; adding 20 percent of the whole bill to one share gives $38.88; $103.68 is the entire bill with tip, which is four people's money, not one.

A shop marks up a bicycle that cost it $240 by 25 percent, then later puts that bicycle on sale at 25 percent off the marked price. What does a customer pay?

• a.$300.00
• b.$225.00✓
• c.$180.00
• d.$240.00

Percent changes multiply in sequence, they do not cancel, because the second percent is taken on a larger number. $240 x 125/100 = $300.00 marked, then $300.00 x 75/100 = $225.00 paid. Assuming the two 25 percents undo each other gives $240.00, and discounting the cost gives $180.00.

A real estate agent is paid a commission of 4 percent of the selling price. The agent earned $1,380 on one sale. What was the selling price?

• a.$3,450
• b.$34,500✓
• c.$5,520
• d.$345,000

Commission = rate x price, so price = commission / rate: $1,380 / 0.04 = $34,500. Check it by taking 4 percent of the answer. Multiplying by 4 instead of dividing gives $5,520, reading the rate as 40 percent gives $3,450, and reading it as 0.4 percent gives $345,000.

A credit union lends $7,500 at simple interest. The borrower pays $975 in interest over 2 years. What annual rate was charged?

• a.13%
• b.6.5%✓
• c.0.65%
• d.3.25%

Simple interest is I = P x r x t, so r = I / (P x t) = $975 / ($7,500 x 2) = 0.065, which is 6.5 percent a year. Dividing by the principal but not by the 2 years gives 13 percent, the two-year total rather than the annual rate, and slipping one decimal place gives 0.65 percent.

A $5,000 deposit earns 6 percent annual interest compounded semiannually. What is the balance after one year?

• a.$5,618.00
• b.$5,150.00
• c.$5,300.00
• d.$5,304.50✓

Compounding semiannually splits the year into two periods that each get half the annual rate: 6/2 = 3 percent, applied twice. $5,000 x 1.03 x 1.03 = $5,304.50. Simple interest for one year gives $5,300.00, one 3 percent period alone gives $5,150.00, and applying the full 6 percent twice gives $5,618.00.

A contractor borrows $9,000 at 7 percent simple interest and repays the loan in one payment 18 months later. How much is that single payment?

• a.$10,260
• b.$9,945✓
• c.$20,340
• d.$9,630

Convert the term to years before using I = P x r x t: 18 months is 18/12 = 1.5 years. Interest is $9,000 x 0.07 x 1.5 = $945, so the payment is $9,945. Treating the term as one year gives $9,630, rounding it to two years gives $10,260, and using 18 as the number of years gives $20,340.

Marcus deposits $1,500 in an account paying 8 percent simple interest a year and adds nothing more. After how many years does the balance first reach $2,100?

• a.4 years
• b.3 years
• c.5 years✓
• d.6 years

Find the interest needed, then divide by the interest earned each year. The balance must grow by $2,100 - $1,500 = $600, and simple interest pays 8 percent of the original $1,500, or $120 every year, so $600 / $120 = 5 years. Using 8 percent of the $2,100 target, $168 a year, gives about 4 years.

An account earned $1,050 in simple interest over 5 years at an annual rate of 3.5 percent. What was the principal?

• a.$183.75
• b.$6,000✓
• c.$30,000
• d.$5,250

Rearrange I = P x r x t into P = I / (r x t). Here r x t = 0.035 x 5 = 0.175, and $1,050 / 0.175 = $6,000. Dividing by the rate but not by the 5 years gives $30,000, multiplying by the rate and the years instead of dividing gives $183.75, and $1,050 x 5 gives $5,250.

An investor splits $4,800 between two accounts, putting $3,000 in one that pays 5 percent a year and the rest in one that pays 2 percent a year. What is the total interest after one year?

• a.$336
• b.$96
• c.$240
• d.$186✓

Interest is figured on each piece separately and then added. $3,000 x 0.05 = $150, and the rest, $4,800 - $3,000 = $1,800, earns $1,800 x 0.02 = $36, for $186 total. Putting the whole $4,800 at 5 percent gives $240, all of it at 2 percent gives $96, and adding the rates into 7 percent gives $336.

A roaster blends 12 pounds of coffee that costs $9 a pound with 8 pounds that costs $14 a pound. What is the cost per pound of the blend?

• a.$11.50
• b.$12.00
• c.$11.00✓
• d.$23.00

A blend's unit cost is total cost divided by total weight, weighted toward whichever lot is larger. 12 x $9 = $108 and 8 x $14 = $112, so $220 / 20 pounds = $11.00. Averaging $9 and $14 ignores the weights and gives $11.50, swapping the weights gives $12.00, and adding the prices gives $23.00.

A 6-quart container of coolant is 20 percent antifreeze. How many quarts of pure antifreeze must be added to bring the mixture to 50 percent antifreeze?

• a.1.8 quarts
• b.4.5 quarts
• c.3.6 quarts✓
• d.3.0 quarts

Pure antifreeze adds to the antifreeze and to the total, so set (1.2 + x) / (6 + x) = 0.50. Then 1.2 + x = 3 + 0.5x, so 0.5x = 1.8 and x = 3.6 quarts. Forgetting that the total also grows gives 1.8 quarts, and half of the original 6 quarts gives 3.0.

A 15-gallon drum holds a solution that is 30 percent cleaner. How many gallons of water must be added to weaken the solution to 18 percent cleaner?

• a.9 gallons
• b.10 gallons✓
• c.25 gallons
• d.5 gallons

Adding water changes the total but not the amount of cleaner, so work from that fixed amount. The drum holds 0.30 x 15 = 4.5 gallons of cleaner, and 4.5 / 0.18 = 25 gallons of finished solution, so 25 - 15 = 10 gallons of water go in. Answering 25 gallons reports the new total, and scaling the drum by 18/30 gives 9 gallons.

A grocer wants 30 pounds of a nut mix worth $5.20 a pound, using peanuts at $4.00 a pound and cashews at $7.00 a pound. How many pounds of cashews are needed?

• a.18 pounds
• b.12 pounds✓
• c.10 pounds
• d.15 pounds

Price the whole batch, then see how far the cheap nut falls short. The mix must be worth 30 x $5.20 = $156, while 30 pounds of peanuts is only $120; each pound of cashews swapped in adds $7.00 - $4.00 = $3.00, so $36 / $3.00 = 12 pounds. The remaining 18 pounds are the peanuts, and 15 assumes an even split.

A feed dealer blends 200 pounds of feed that is 12 percent protein with 300 pounds of feed that is 22 percent protein. How many pounds of protein are in the blend?

• a.90 pounds✓
• b.170 pounds
• c.34 pounds
• d.85 pounds

Take the protein out of each lot and add the two amounts: 200 x 0.12 = 24 pounds and 300 x 0.22 = 66 pounds, for 90 pounds. Averaging the percents to 17 and applying that to all 500 pounds gives 85 pounds, while adding the percents into 34 and applying that to 500 pounds gives 170 pounds.

A radiator holds 16 quarts of a mix that is 40 percent antifreeze. A mechanic drains 4 quarts of the mix and replaces them with pure antifreeze. What percent antifreeze is the radiator now?

• a.65 percent
• b.55 percent✓
• c.50 percent
• d.40 percent

Track quarts of antifreeze, not percents. Draining 4 of 16 quarts leaves 12 quarts still 40 percent, which is 4.8 quarts of antifreeze, and the 4 quarts poured back are pure, so 8.8 quarts sit in 16, or 55 percent. Adding 25 percent of the volume straight onto 40 gives 65 percent.

A map is drawn so that 1 inch represents 40 miles. Two bases are 260 miles apart on the ground. How far apart are they on the map?

• a.6.5 inches✓
• b.7.5 inches
• c.8.7 inches
• d.5.2 inches

Going from ground distance to map distance divides by the scale, and only the reverse trip multiplies: 260 / 40 = 6.5 inches. Check the size of the answer, since a bigger scale number means fewer inches. Using 30 miles per inch gives about 8.7 inches and using 50 miles per inch gives 5.2 inches.

A floor plan uses a scale of 1/4 inch to 1 foot. A wall measures 7 inches on the plan. How long is the actual wall?

• a.28 feet✓
• b.14 feet
• c.1.75 feet
• d.21 feet

Each 1/4 inch on the plan stands for 1 foot, so count the quarter inches in 7 inches: 7 / (1/4) = 7 x 4 = 28 feet. Dividing by a fraction smaller than 1 must make the answer larger, so multiplying by 1/4 instead and getting 1.75 feet is the wrong direction; 14 feet doubles rather than quadruples.

A model ship is built to a scale of 1 to 48. The model's mast stands 9 inches tall. How tall is the real mast in feet?

• a.18 feet
• b.36 feet✓
• c.432 feet
• d.3 feet

Scale up first, then convert the units the question asks for. The real mast is 9 x 48 = 432 inches, and 432 / 12 = 36 feet. Answering 432 feet skips the inches-to-feet step, dividing by 12 a second time gives 3 feet, and dividing by 24 instead gives 18 feet.

On a map scaled at 1 inch to 15 miles, a supply route runs 3.2 inches from the depot to a camp and then 4.8 inches from the camp to the field site. How long is the whole route on the ground?

• a.120 miles✓
• b.72 miles
• c.8 miles
• d.48 miles

Add the legs in map inches first, then convert once: 3.2 + 4.8 = 8 inches, and 8 x 15 = 120 miles. Converting only the longer leg gives 72 miles, only the shorter leg gives 48 miles, and 8 miles is the map measurement reported without ever applying the scale.

A landscape drawing uses a scale of 1 inch to 6 feet. On the drawing a garden plot measures 4 inches by 3 inches. What is the actual area of the plot?

• a.72 square feet
• b.12 square feet
• c.216 square feet
• d.432 square feet✓

Convert each side before finding area: 4 inches becomes 24 feet and 3 inches becomes 18 feet, so 24 x 18 = 432 square feet. Area scales by the square of the scale, 36 times over, so multiplying the drawing's 12 square inches by 6 gives only 72 square feet and by 18 gives 216. Reading that 12 as feet converts nothing at all.

A recruit owns 4 shirts, 3 pairs of trousers, and 2 pairs of boots, and any of them go together. How many different complete outfits can he put together?

• a.9 outfits
• b.18 outfits
• c.24 outfits✓
• d.12 outfits

When one item is chosen from each group, the counts multiply: 4 x 3 x 2 = 24 outfits. Each of the 12 shirt-and-trouser pairings can go with either pair of boots, which is where the doubling comes from. Adding the groups gives 9, and 12 stops after the shirts and trousers and forgets the boots.

In the dark, a person reaches into a drawer holding 8 black socks and 6 white socks and pulls them out one at a time. How many socks must be pulled out to be certain of having a matching pair?

• a.3 socks✓
• b.7 socks
• c.8 socks
• d.2 socks

Certainty means planning for the worst possible draw, not the likely one. Only two colors are in the drawer, so the first two socks could be one of each, but a third sock must match one of them: 3 socks guarantee a pair. Answering 2 relies on luck, 7 guarantees one black sock, and 8 guarantees a black pair.

A bin holds 20 batteries, 5 of which are dead. One battery is drawn at random, tested, and put back; then a second is drawn. What is the probability that both draws are dead batteries?

• a.50 percent
• b.25 percent
• c.12.5 percent
• d.6.25 percent✓

Because the first battery goes back in, the draws are independent and the probabilities multiply. Each draw is 5/20 = 25 percent, so both dead is 0.25 x 0.25 = 6.25 percent. Reporting 25 percent answers only one draw, and adding the two chances gives 50 percent, which is far too likely for a double event.

A machine has a 10 percent chance of jamming during any given shift, and the shifts are independent of one another. What is the probability that it jams at least once in 2 shifts?

• a.19 percent✓
• b.10 percent
• c.20 percent
• d.81 percent

For at-least-once, find the chance the event never happens and subtract from 100 percent. No jam on one shift is 90 percent, so no jam on both is 0.90 x 0.90 = 81 percent, leaving 100 - 81 = 19 percent. Adding 10 and 10 gives 20 percent and double counts the shift where it jams twice.

Each of the 6 members of a squad shakes hands exactly once with every other member of that squad. How many handshakes take place in all?

• a.30 handshakes
• b.12 handshakes
• c.36 handshakes
• d.15 handshakes✓

Each of the 6 people shakes with the other 5, which counts 6 x 5 = 30, but that counts every handshake once from each side, so divide by 2 to get 15. Forgetting to halve leaves 30, and 6 x 6 = 36 also lets a person shake his own hand, which the problem does not allow.

A locker code is 3 digits long, each digit chosen from 1 through 5, and a digit may be used more than once. How many different codes are possible?

• a.125 codes✓
• b.15 codes
• c.243 codes
• d.60 codes

With repeats allowed, every position is filled independently from the same 5 digits, so multiply 5 by itself once per position: 5 x 5 x 5 = 125 codes. Multiplying 5 x 3 gives 15 and counts digits rather than codes, barring repeats gives 5 x 4 x 3 = 60, and 3 x 3 x 3 x 3 x 3 reverses the roles for 243.

A cafeteria meal is one main dish, one side, and one drink, chosen from 3 main dishes, 4 sides, and 2 drinks. If the cafeteria adds one more side, how many additional meals become possible?

• a.9 additional meals
• b.30 additional meals
• c.6 additional meals✓
• d.24 additional meals

Count the meals both ways and subtract: 3 x 4 x 2 = 24 now and 3 x 5 x 2 = 30 after, so 6 more. The shortcut is that the new side pairs with each of the 3 mains and 2 drinks, which is the same 6. Reporting 30 gives the new total rather than the increase, and 24 gives the old total.

Crates are stacked so that the bottom row holds 48 crates and each row above holds 5 fewer crates than the row just below it. How many crates are in the 7th row from the bottom?

• a.33 crates
• b.18 crates✓
• c.23 crates
• d.13 crates

Count the gaps between rows, not the rows themselves: the 7th row is only 6 steps above the first, so 48 - 6 x 5 = 18 crates. Subtracting 7 x 5 is the off-by-one error and gives 13, stopping at the 6th row gives 23, and stopping at the 4th gives 33.

A bacteria culture doubles every 3 hours. If it starts with 250 cells, how many cells are present after 12 hours?

• a.2,000 cells
• b.4,000 cells✓
• c.8,000 cells
• d.1,000 cells

Count the doubling periods before doubling anything: 12 / 3 = 4 periods. Then 250 x 2 x 2 x 2 x 2 = 250 x 16 = 4,000 cells. Two doublings gives 1,000, three gives 2,000, and five gives 8,000, so the error is almost always in counting periods rather than in the multiplying.

A sequence begins 3, 7, 15, 31, where each term after the first is found by doubling the term before it and adding 1. What is the next term?

• a.62
• b.63✓
• c.39
• d.47

Apply the stated rule to the last term shown: 31 x 2 + 1 = 63. Test the rule on the earlier terms first, since 3 x 2 + 1 = 7 and 7 x 2 + 1 = 15, which confirms it. Doubling but forgetting the 1 gives 62, and treating the gaps of 4, 8, 16 as if 16 repeated gives 47.

A theater has 14 seats in the first row, and each row behind it has 3 more seats than the row in front of it. How many seats are in the first 8 rows together?

• a.196 seats✓
• b.112 seats
• c.168 seats
• d.280 seats

For an evenly growing list, total = number of terms x (first + last) / 2. The 8th row holds 14 + 7 x 3 = 35 seats, so the total is 8 x (14 + 35) / 2 = 196 seats. Using 14 for every row gives 112, using 35 for every row gives 280, and the true answer always lands between those two.

A sequence begins 2, 5, 7, 12, 19, where each term after the second is the sum of the two terms immediately before it. What is the 8th term?

• a.50
• b.81✓
• c.62
• d.31

There is no shortcut formula here, so extend the rule one term at a time and label each position: 12 + 19 = 31 is the 6th, 19 + 31 = 50 is the 7th, and 31 + 50 = 81 is the 8th. Stopping one term early gives 50, 31 is the 6th term, and doubling 31 gives 62.

A supply sergeant must move 338 sandbags using a cart that carries 24 sandbags at a time. How many trips does it take to move all of them?

• a.14 trips
• b.13 trips
• c.16 trips
• d.15 trips✓

Divide, then decide what the remainder needs: 338 / 24 = 14 full cart loads with 2 sandbags left over. Those 2 still have to be hauled, so the count rounds up to 15 trips. Dropping the remainder gives 14 and leaves 2 bags on the ground, while adding a trip for a remainder that has already been rounded up gives 16.

A baker bakes 5 sheets holding 32 rolls each, then packs the rolls 12 to a bag. How many rolls are left over after every full bag has been packed?

• a.8 rolls
• b.4 rolls✓
• c.13 rolls
• d.16 rolls

Total first, then divide and keep the remainder rather than the quotient: 5 x 32 = 160 rolls, and 160 / 12 = 13 bags with 4 rolls left over. The 13 answers how many bags were filled, not how many rolls remain, and 16 is what is still loose after only 12 bags, one bag short of done.

A shelf is 92 inches long. Storage boxes are 7 inches wide and must sit side by side on the shelf without hanging over the end. How many boxes fit?

• a.13 boxes✓
• b.14 boxes
• c.12 boxes
• d.15 boxes

Only whole boxes fit, so divide and throw the fraction away: 92 / 7 = 13.1, meaning 13 boxes with 1 inch of shelf left unused. Rounding 13.1 up to 14 assumes a partial box can hang over the end, which the problem forbids, and 12 leaves room for another full box.

A crew of 4 people must move 92 boxes, and each person can carry 3 boxes on a trip. How many trips must the crew make?

• a.9 trips
• b.23 trips
• c.8 trips✓
• d.7 trips

Find what the whole crew moves per trip, then round up for the leftovers: 4 x 3 = 12 boxes a trip, and 92 / 12 = 7 trips with 8 boxes still waiting, so an 8th trip is needed. Stopping at 7 strands those 8 boxes, and 23 divides the boxes among the 4 people while ignoring that each carries 3.