ASVAB — All Questions

A room measures 14 feet by 18 feet. Carpet is sold by the square yard. How many square yards are needed?

• a.32 square yards
• b.24 square yards
• c.36 square yards
• d.28 square yards✓

The floor is 14 x 18 = 252 square feet. One square yard is 9 square feet, so 252 / 9 = 28 square yards.

Five machines fill 300 boxes in 2 hours. At the same rate, how many boxes will 8 machines fill in 3 hours?

• a.640 boxes
• b.480 boxes
• c.900 boxes
• d.720 boxes✓

One machine fills 300 / (5 x 2) = 30 boxes per hour. Eight machines for 3 hours give 30 x 8 x 3 = 720 boxes.

What is a 15 percent tip on a bill of $46.40?

• a.$9.28
• b.$7.42
• c.$5.80
• d.$6.96✓

Ten percent of $46.40 is $4.64 and 5 percent is half of that, $2.32. Together the tip is $6.96.

A saver deposits $45 the first week and increases the deposit by $5 each following week. How much has been deposited after six weeks?

• a.$315
• b.$370
• c.$330
• d.$345✓

The deposits are 45, 50, 55, 60, 65, and 70. That is six deposits of $45 plus 5 x (1+2+3+4+5) = $75, for $345.

A car with a 16-gallon tank averages 27 miles per gallon. How far can it travel on a full tank?

• a.405 miles
• b.432 miles✓
• c.448 miles
• d.486 miles

Range equals gallons times miles per gallon: 16 x 27 = 432 miles.

Of 450 recruits, 60 percent are men, and 20 percent of the men wear glasses. How many men wear glasses?

• a.54 recruits✓
• b.108 recruits
• c.45 recruits
• d.90 recruits

There are 450 x 0.60 = 270 men, and 20 percent of 270 is 54. The second percentage applies to the men only, not to all 450.

A shipment of 1,250 items has a defect rate of 4 percent. How many items are not defective?

• a.1,200 items✓
• b.1,206 items
• c.1,150 items
• d.1,246 items

Four percent of 1,250 is 50 defective items, so 1,250 - 50 = 1,200 are good.

A driver travels 2 hours at 55 miles per hour and then 3 hours at 65 miles per hour. What was the average speed for the whole trip?

• a.63 mph
• b.61 mph✓
• c.60 mph
• d.58 mph

The distance is 110 + 195 = 305 miles over 5 hours, so 305 / 5 = 61 mph. Averaging 55 and 65 ignores that more time was spent at the faster speed.

A shopper pays with a $50 bill for items costing $12.75, $8.40, and $19.99. How much change is due?

• a.$9.16
• b.$7.86
• c.$8.86✓
• d.$8.14

The items total $41.14, and 50.00 - 41.14 = $8.86.

A batch that feeds 48 people uses 6 pounds of rice. How much rice is needed for 20 people?

• a.2.0 pounds
• b.2.5 pounds✓
• c.3.0 pounds
• d.3.5 pounds

Each person needs 6 / 48 = 0.125 pound, and 0.125 x 20 = 2.5 pounds.

An account pays 0.5 percent simple interest per month. How much interest does $500 earn in 8 months?

• a.$25.00
• b.$20.00✓
• c.$12.50
• d.$40.00

Each month earns 500 x 0.005 = $2.50, and $2.50 x 8 = $20.00.

A truck has a load limit of 2,000 pounds and is carrying 46 crates weighing 38 pounds each. How many more pounds may it carry?

• a.152 pounds
• b.232 pounds
• c.252 pounds✓
• d.348 pounds

The crates weigh 46 x 38 = 1,748 pounds, so 2,000 - 1,748 = 252 pounds remain.

Two-fifths of a class of 35 students chose the morning shift and the rest chose evenings. How many chose evenings?

• a.21 students✓
• b.25 students
• c.18 students
• d.14 students

If 2/5 chose mornings, then 3/5 chose evenings. One-fifth of 35 is 7, so 3/5 is 21 students.

A copier prints 22 pages per minute for 9 minutes, jams for 4 minutes, then prints at the same rate for 6 more minutes. How many pages are printed?

• a.264 pages
• b.330 pages✓
• c.198 pages
• d.418 pages

The copier actually prints for 9 + 6 = 15 minutes, so 22 x 15 = 330 pages. The 4-minute jam produces nothing.

After a 20 percent discount, a coat costs $96. What was the original price?

• a.$108.00
• b.$124.80
• c.$120.00✓
• d.$115.20

The sale price is 80 percent of the original, so the original is 96 / 0.80 = $120.00. Checking, 20 percent of $120 is $24, and 120 - 24 = 96.

A garden 20 feet by 30 feet is bordered by a walkway 3 feet wide on all sides. What is the area of the walkway alone?

• a.396 square feet
• b.276 square feet
• c.306 square feet
• d.336 square feet✓

The walkway adds 3 feet on each side, making the outer rectangle 26 by 36, or 936 square feet. Subtracting the 600-square-foot garden leaves 336.

A driver covers 60 miles at 30 miles per hour and returns over the same 60 miles at 60 miles per hour. What is the average speed for the round trip?

• a.40 mph✓
• b.45 mph
• c.36 mph
• d.48 mph

The outbound leg takes 2 hours and the return takes 1 hour, so 120 miles are covered in 3 hours, or 40 mph. Averaging 30 and 60 to get 45 ignores the unequal times.

A box holds 24 red markers, 16 blue markers, and 40 green markers. What percent of the markers are blue?

• a.25%
• b.20%✓
• c.16%
• d.18%

There are 80 markers in all, and 16 / 80 = 0.20.

Two convoys leave bases 360 miles apart at the same time and drive toward each other on the same road, one at 50 miles per hour and the other at 40 miles per hour. How long until they meet?

• a.4.5 hours
• b.8.0 hours
• c.9.0 hours
• d.4.0 hours✓

Two vehicles closing on each other shut the gap at the SUM of their speeds: 50 + 40 = 90 mph, so the time is 360 / 90 = 4.0 hours. Averaging the speeds instead of adding gives 360 / 45 = 8.0 hours, and sending each convoy half the distance at its own speed gives 180 / 40 = 4.5 hours.

A courier drives 150 miles to a depot at an average of 50 miles per hour, spends 45 minutes unloading, and returns over the same route at 60 miles per hour. How long does the entire trip take?

• a.6.75 hours
• b.5.50 hours
• c.6.25 hours✓
• d.5.75 hours

Add the two legs and the stop separately. Out: 150 / 50 = 3 hours. Back: 150 / 60 = 2.5 hours. Stop: 45 / 60 = 0.75 hour. Total = 3 + 2.5 + 0.75 = 6.25 hours. Leaving the unloading time out gives 5.50 hours, and running both legs at 50 mph gives 6.75 hours.

A supply truck leaves a base at 0700 traveling 45 miles per hour. A car leaves the same base at 0900 on the same road at 65 miles per hour. How long after the car starts does it overtake the truck?

• a.1.4 hours
• b.2.3 hours
• c.4.5 hours✓
• d.0.8 hours

First the head start: the truck has run 2 hours at 45 mph, so it is 90 miles ahead. A chaser closes a gap at the DIFFERENCE of the speeds, 65 - 45 = 20 mph, so the car needs 90 / 20 = 4.5 hours. Crediting only a one-hour head start gives 2.3 hours, and dividing 90 by the car's own 65 mph gives 1.4 hours.

A bus covers the first 60 miles of a trip at 30 miles per hour and the remaining 240 miles at 60 miles per hour. What is its average speed for the whole trip?

• a.45 mph
• b.50 mph✓
• c.90 mph
• d.60 mph

Average speed is total distance over total time, never the average of the two speeds. The legs take 60 / 30 = 2 hours and 240 / 60 = 4 hours, so 300 miles / 6 hours = 50 mph. Splitting the difference between 30 and 60 gives 45 mph, adding them gives 90 mph, and quoting the longer leg alone gives 60 mph.

A driver must cover 240 miles in 4 hours. After 2 hours he has traveled only 100 miles. What average speed must he hold over the rest of the route to arrive on time?

• a.60 mph
• b.35 mph
• c.50 mph
• d.70 mph✓

Subtract before dividing: 240 - 100 = 140 miles still to go in 4 - 2 = 2 hours left, so he needs 140 / 2 = 70 mph. Dividing the 140 remaining miles by the full 4 hours gives 35 mph, 240 / 4 = 60 mph is only the trip's overall requirement, and 100 / 2 = 50 mph is the speed already run.

A boat runs 30 miles downstream in 2 hours and the same 30 miles back upstream in 3 hours. What is the speed of the current?

• a.10.0 mph
• b.12.5 mph
• c.5.0 mph
• d.2.5 mph✓

Downstream speed is boat plus current, 30 / 2 = 15 mph; upstream is boat minus current, 30 / 3 = 10 mph. The gap between them is twice the current, so the current is (15 - 10) / 2 = 2.5 mph. Stopping at the difference gives 5.0 mph, and half the sum, 12.5 mph, is the boat's own speed in still water.

A flight covers 1200 miles. If the average ground speed is raised from 300 miles per hour to 400 miles per hour, how much time is saved?

• a.12.0 hours
• b.3.0 hours
• c.1.5 hours
• d.1.0 hours✓

Time each version of the flight, then subtract: 1200 / 300 = 4 hours at the slower speed and 1200 / 400 = 3 hours at the faster one, so the saving is 4 - 3 = 1.0 hours. Dividing the distance by the 100 mph difference in speed gives 12.0 hours, and 3.0 hours is the new flight time rather than the time saved.

A supply pipe fills an empty tank in 6 hours. A drain valve left open empties a full tank in 9 hours. With both the pipe and the valve running, how long does the empty tank take to fill?

• a.3.0 hours
• b.3.6 hours
• c.15.0 hours
• d.18.0 hours✓

Work in tanks per hour. Filling adds 1/6 and draining removes 1/9, so the net rate is 1/6 - 1/9 = 3/18 - 2/18 = 1/18 of a tank an hour, and the fill takes 18.0 hours. Adding the rates as if both filled gives 3.6 hours, and adding the two times gives 15.0 hours; times never add.

Working together, two mechanics service a truck in 4 hours. Working alone, the first mechanic would need 12 hours. How long would the second mechanic need working alone?

• a.3 hours
• b.16 hours
• c.8 hours
• d.6 hours✓

Rates add, times do not. Together the pair finishes 1/4 of the truck an hour and the first does 1/12, so the second does 1/4 - 1/12 = 3/12 - 1/12 = 1/6 an hour, which is 6 hours alone. Subtracting the two times gives 8 hours, adding them gives 16 hours, and 12 / 4 gives 3 hours; none of those are rates.

A job takes 6 workers 10 days. The contractor now needs the same job done in 4 days, with every worker keeping the same pace. How many additional workers must be hired?

• a.15 workers
• b.6 workers
• c.9 workers✓
• d.24 workers

Total effort is fixed: 6 x 10 = 60 worker-days. Finishing in 4 days needs 60 / 4 = 15 workers, and 15 - 6 = 9 of them must be hired. Answering 15 workers reports the whole crew instead of the hires, and 6 x 4 = 24 treats workers and days as directly proportional when fewer days demands more workers.

One press prints 480 flyers an hour and a second press prints 320 flyers an hour. Running both at once, how long will an order of 2000 flyers take?

• a.1.5 hours
• b.2.5 hours✓
• c.6.3 hours
• d.4.2 hours

When two machines run at once, add their rates: 480 + 320 = 800 flyers an hour, so 2000 / 800 = 2.5 hours. Using the fast press alone gives 2000 / 480 = 4.2 hours and the slow one alone gives 2000 / 320 = 6.3 hours. Both are longer than the answer, which is the check that the rates were summed.

A crew paints 2/5 of a fence in 6 hours. Working at the same steady rate, how many more hours does the crew need to finish the fence?

• a.9.0 hours✓
• b.3.6 hours
• c.10.0 hours
• d.15.0 hours

Scale the elapsed time by the ratio of the work. The 3/5 still unpainted is 3/2 of the 2/5 already done, so it takes 6 x 3/2 = 9.0 hours more. The whole fence takes 6 divided by 2/5 = 15.0 hours, which is the total job and not what remains, and multiplying 6 by 3/5 gives 3.6 hours.

One loader can fill a truck in 45 minutes. It works alone for 15 minutes, and then a second loader that would need 30 minutes by itself joins in. How many more minutes does the job take?

• a.30 minutes
• b.12 minutes✓
• c.18 minutes
• d.20 minutes

In its first 15 minutes the loader finishes 15/45 = 1/3 of the truck, leaving 2/3. Now the rates add: 1/45 + 1/30 = 2/90 + 3/90 = 1/18 of the truck a minute, so 2/3 divided by 1/18 = 12 minutes. Ignoring the head start and doing the whole truck together gives 18 minutes.

A store raises the price of a $50 tool by 20 percent, and a month later cuts the new price by 20 percent. What is the final price?

• a.$60.00
• b.$48.00✓
• c.$50.00
• d.$40.00

Percent changes multiply, and each one applies to the price in force at the time. Up: 50 x 1.20 = $60.00. Down: 60 x 0.80 = $48.00. Equal percents up and down do not cancel, because the cut is taken on the larger price; assuming they cancel gives $50.00, and cutting the original instead gives $40.00.

After a 12 percent raise, a technician earns $980 a week. What was the weekly pay before the raise?

• a.$875✓
• b.$1,098
• c.$968
• d.$862

The new pay is 112 percent of the old pay, so divide rather than subtract: 980 / 1.12 = $875. Taking 12 percent off $980 gives $862, which is too small because the raise was figured on the smaller old pay; adding 12 percent instead gives $1,098, and subtracting $12 gives $968.

A gym gained 45 members this year and now has 345 members. What was the percent increase in membership?

• a.13%
• b.15%✓
• c.115%
• d.87%

Percent change always uses the ORIGINAL as the base, and here the original is 345 - 45 = 300. So 45 / 300 = 0.15, or 15%. Dividing the gain by the new total of 345 gives 13%, dividing 300 by 345 gives 87%, and 345 / 300 = 115% states the new size as a percent of the old rather than the increase.

A $240 chair is marked 25 percent off, and members take a further 10 percent off the sale price. What does a member pay?

• a.$168.00
• b.$180.00
• c.$162.00✓
• d.$156.00

Stacked discounts multiply on the running price: 240 x 0.75 = $180.00, then 180 x 0.90 = $162.00. Adding the two cuts into 35 percent off and computing 240 x 0.65 = $156.00 is the classic error, since the second cut comes off the reduced $180.00 and not off the full $240.

A store buys a jacket for $45, marks it up 60 percent, and later puts it on sale at 25 percent off the marked price. What is the sale price?

• a.$33.75
• b.$60.75
• c.$72.00
• d.$54.00✓

Apply each percent to the price then in force. Marked price: 45 x 1.60 = $72.00. Sale price: 72 x 0.75 = $54.00. Netting the two changes to plus 35 percent and computing 45 x 1.35 = $60.75 fails because the 25 percent comes off $72.00, and taking it off cost gives $33.75.

A production line's defect rate fell from 8 percent to 6 percent. By what percent did the defect rate itself fall?

• a.75%
• b.33%
• c.2%
• d.25%✓

A change measured in percentage points is not a percent change. The drop is 8 - 6 = 2 points, and as a fraction of the starting 8 that is 2 / 8 = 0.25, or 25%. Answering 2% reports the points, dividing by the new rate of 6 gives 33%, and 6 / 8 = 75% says what the rate is now relative to before.

A unit's monthly supply budget rose 20 percent this year to $960. Next year it is scheduled to fall 15 percent from the current figure. What will next year's budget be?

• a.$816✓
• b.$1,104
• c.$960
• d.$800

Only the current $960 matters, because the 20 percent rise is already inside that figure and is not applied again. Next year = 960 x 0.85 = $816. Undoing the 20 percent back to $800 answers about the wrong year, and 960 x 1.15 = $1,104 raises a budget the schedule actually cuts.

The ratio of trucks to cars in a motor pool is 3 to 7, and there are 24 more cars than trucks. How many vehicles are in the pool altogether?

• a.60 vehicles✓
• b.42 vehicles
• c.18 vehicles
• d.240 vehicles

Give the ratio units. Trucks are 3 parts and cars are 7, so the surplus of cars is 7 - 3 = 4 parts. Those 4 parts are the 24 extra cars, so one part is 24 / 4 = 6 vehicles, and the pool is 3 + 7 = 10 parts, or 60 vehicles. Answering 42 counts the cars alone and 18 counts the trucks alone.

A mix holds 8 quarts of concentrate and 20 quarts of water. How many quarts of water must be added to make the ratio of concentrate to water 1 to 4?

• a.52 quarts
• b.4 quarts
• c.32 quarts
• d.12 quarts✓

The concentrate never changes, so pin it down and solve for the water it must face: 1 to 4 means water = 4 x 8 = 32 quarts. There are already 20, so add 32 - 20 = 12 quarts. Answering 32 quarts reports the final amount of water rather than the amount poured in, and adding the two gives 52 quarts.

A concrete mix combines cement, sand, and gravel in a ratio of 1 to 3 to 4 by weight. What percent of the mix is sand?

• a.50.0%
• b.75.0%
• c.37.5%✓
• d.12.5%

Turn a ratio into a percent by putting each part over the TOTAL number of parts: 1 + 3 + 4 = 8 parts, so sand is 3/8 = 37.5%. The same method gives cement 1/8 = 12.5% and gravel 4/8 = 50.0%. Comparing sand with gravel alone gives 3/4 = 75.0%, which answers a question nobody asked.

A 60-pound alloy is mixed 3 parts copper to 2 parts zinc. How many pounds of copper must be added so that the alloy becomes 4 parts copper to 2 parts zinc?

• a.16 pounds
• b.12 pounds✓
• c.24 pounds
• d.6 pounds

Adding copper leaves the zinc untouched, so anchor on zinc: it is 2/5 of 60 = 24 pounds, and copper starts at 3/5 of 60 = 36 pounds. A 4 to 2 ratio means copper must be twice the zinc, or 48 pounds, so add 48 - 36 = 12 pounds. Answering 24 pounds reports the zinc instead of the copper added.

A stockroom finds that 7 crates hold 168 bolts. At the same packing rate, how many crates are needed for 552 bolts?

• a.79 crates
• b.3 crates
• c.24 crates
• d.23 crates✓

Find the unit rate before scaling: 168 / 7 = 24 bolts per crate, so 552 / 24 = 23 crates. Dividing 552 by the 7 crates gives 79 and treats crates as bolts, 552 / 168 gives about 3, the number of 168-bolt lots, and 24 is the bolts per crate rather than a count of crates.

Two partners put $600 and $900 into a venture and split the $750 profit in proportion to what each invested. How much more does the larger investor receive than the smaller one?

• a.$150✓
• b.$300
• c.$75
• d.$450

Total invested is 600 + 900 = $1500, so the shares are 900/1500 and 600/1500 of the $750, which is $450 and $300. The difference is 450 - 300 = $150. Answering $450 gives the larger share itself and $300 the smaller one; an even split would be $375 each and no difference at all.

A photograph 4 inches wide and 6 inches tall is enlarged so that its width becomes 10 inches. If the shape is unchanged, how tall is the enlargement?

• a.16 inches
• b.15 inches✓
• c.24 inches
• d.12 inches

Similar shapes scale by a multiplier, not by an added amount. The width grows 10 / 4 = 2.5 times, so the height is 6 x 2.5 = 15 inches. Adding the 6 inches the width gained gives 12 inches and adding the new width to the old height gives 16 inches; both change the shape.

A conveyor belt moves at 22 feet per second. There are 5280 feet in a mile. What is the belt's speed in miles per hour?

• a.15.0 mph✓
• b.32.3 mph
• c.1.5 mph
• d.0.3 mph

Convert one unit at a time. 22 feet per second x 60 = 1320 feet per minute, x 60 again = 79200 feet per hour, and 79200 / 5280 = 15.0 mph. Using only one factor of 60 leaves 0.3 mph, and dividing by 3600 while multiplying by 5280 turns the conversion upside down and gives 32.3 mph.

A field kitchen uses 3 gallons of stock for each meal and must serve 5 meals. It has 20 quarts of stock on hand, and there are 4 quarts in a gallon. How many more quarts are needed?

• a.15 quarts
• b.40 quarts✓
• c.60 quarts
• d.10 quarts

Get both amounts into one unit before subtracting. The kitchen needs 3 x 5 = 15 gallons, which is 15 x 4 = 60 quarts, so it must find 60 - 20 = 40 quarts more. Answering 10 is the right shortfall in gallons but the wrong unit, 15 is the gallons needed, and 60 forgets the stock already on hand.

A machine completes one cycle every 45 seconds and runs without stopping through an 8-hour shift. How many complete cycles does it finish?

• a.6400 cycles
• b.640 cycles✓
• c.480 cycles
• d.107 cycles

Convert the shift into the cycle's own unit: 8 x 60 x 60 = 28800 seconds, so 28800 / 45 = 640 cycles. Stopping at minutes gives 480, which is the length of the shift and not a cycle count, and dividing those 480 minutes by 45 gives about 107. A decimal slip in 28800 / 45 gives 6400.

A truck carries 3.5 tons of gravel, which is bagged 50 pounds to a bag. A ton is 2000 pounds. How many bags does the load fill?

• a.140 bags✓
• b.700 bags
• c.70 bags
• d.280 bags

Convert to the smaller unit first, then divide: 3.5 x 2000 = 7000 pounds, and 7000 / 50 = 140 bags. Using 1000 pounds to the ton halves the load to 70 bags, dividing by 25 instead of 50 gives 280 bags, and a decimal slip in 7000 / 50 gives 700 bags.

A water heater leaks 1 cup every 4 minutes. There are 16 cups in a gallon. How many gallons leak in 24 hours?

• a.90.0 gallons
• b.1.5 gallons
• c.22.5 gallons✓
• d.360 gallons

Build the chain of units: 24 x 60 = 1440 minutes, 1440 / 4 = 360 cups, and 360 / 16 = 22.5 gallons. Answering 360 gallons stops one conversion short and reports cups, using 4 cups to the gallon gives 90.0, and dividing the 24 hours by 16 gives 1.5 while skipping the leak rate.