ASVAB Practice Exam 3

Last updated: September 28, 2026

Practice Exam 3 is a fixed set of 135 original questions in the same 10 subtests, order, and time limits as the computer ASVAB. Take it timed, one question at a time, or read through the questions below. Each answer is explained.

Pick the length

Study mode is on: each answer is explained. Switch it off inside the test for real exam conditions.
Same order, question counts, and time limits as the CAT-ASVAB
#SubtestQuestionsMinutes
1General Science GS1512
2Arithmetic Reasoning AR1555
3Word Knowledge WK159
4Paragraph Comprehension PC1027
5Mathematics Knowledge MK1531
6Electronics Information EI1510
7Auto Information AI107
8Shop Information SI106
9Mechanical Comprehension MC1522
10Assembling Objects AO1518

All 135 questions in Practice Exam 3

Taking the timed test first gives you the truest read. It serves these same questions one at a time, adjusting the order to your answers. To study instead, work through them here: each answer and explanation is folded under its question.

General Science: 15 questions

Physical, life, and earth and space science. Real test: 15 questions in 12 minutes.

  1. About how long does it take Earth to spin once on its axis?

    1. A1 hour
    2. B12 hours
    3. C24 hours
    4. D365 days
    Show answer and explanation

    Answer: C. One full rotation takes about 24 hours, which gives one day and night.

    • AWrong. In 1 hour Earth turns only about 15°, or 1/24 of a full spin.
    • BWrong. 12 hours is half a spin, about the length of daylight alone at the equinoxes.
    • CCorrect. One full rotation on its axis takes about 24 hours, which gives one day and night.
    • DWrong. About 365 days is one trip around the Sun (a revolution), not one spin.

  2. At what temperature does pure water freeze on the Celsius scale?

    1. A0° C
    2. B32° C
    3. C100° C
    4. D212° C
    Show answer and explanation

    Answer: A. Pure water freezes at 0° C and boils at 100° C at sea level.

    • ACorrect. Pure water freezes at 0° C (and boils at 100° C) at sea level.
    • BWrong. 32 is the freezing point on the Fahrenheit scale (32° F); 32° C is a hot day of about 90° F.
    • CWrong. 100° C is the boiling point of water at sea level, not its freezing point.
    • DWrong. 212 is water’s boiling point on the Fahrenheit scale (212° F); 212° C is far above boiling.

  3. A push or a pull on an object is called a

    1. Amass.
    2. Bvolume.
    3. Cdensity.
    4. Dforce.
    Show answer and explanation

    Answer: D. A force is any push or pull. Forces are measured in newtons.

    • AWrong. Mass is the amount of matter in an object, measured in kilograms; it is not a push or pull.
    • BWrong. Volume is the amount of space an object takes up.
    • CWrong. Density is the mass per unit of volume of a material, such as 1 gram per milliliter for water.
    • DCorrect. A force is any push or pull on an object; forces are measured in newtons.

  4. Which part of a plant usually takes in water from the soil?

    1. ALeaves
    2. BFlowers
    3. CRoots
    4. DSeeds
    Show answer and explanation

    Answer: C. Roots absorb water and minerals from the soil and anchor the plant.

    • AWrong. Leaves take in carbon dioxide and sunlight for photosynthesis and give off water vapor; they do not draw water from the soil.
    • BWrong. Flowers are the reproductive parts of a plant that make seeds.
    • CCorrect. Roots absorb water and minerals from the soil and anchor the plant in place.
    • DWrong. A seed holds a young plant and its food supply; it soaks up water only when it begins to sprout.

  5. Sound waves travel fastest through which of the following?

    1. AAir
    2. BWater
    3. CSteel
    4. DA vacuum
    Show answer and explanation

    Answer: C. Sound travels fastest through solids, where particles are tightly linked, so steel beats water and air.

    • AWrong. Air is the slowest of these, about 340 meters per second, because gas particles are far apart.
    • BWrong. Sound moves about 1,500 meters per second in water: faster than in air, but much slower than in steel.
    • CCorrect. In a solid such as steel the particles are tightly linked, so sound moves about 5,000 meters per second or more.
    • DWrong. Sound needs matter to travel through, so it cannot cross a vacuum at all.

  6. What is the main cause of ocean tides on Earth?

    1. AWind blowing over the ocean
    2. BEarth’s magnetic field
    3. CHeat from Earth’s core
    4. DThe Moon’s gravitational pull
    Show answer and explanation

    Answer: D. The Moon’s gravity pulls on Earth’s oceans, raising bulges of water that we see as high tides. The Sun adds a smaller pull.

    • AWrong. Wind makes waves and drives surface currents, not the regular rise and fall of the tides.
    • BWrong. Earth’s magnetic field steers compass needles and charged particles; it has no real effect on sea level.
    • CWrong. Heat from Earth’s core drives plate motion and volcanoes; it does not raise and lower the sea each day.
    • DCorrect. The Moon’s gravity pulls on Earth’s oceans, raising bulges of water that we see as high tides; the Sun adds a smaller pull.

  7. Antibiotics are effective against illnesses caused by

    1. Abacteria.
    2. Bviruses.
    3. Callergens.
    4. Dvitamin deficiencies.
    Show answer and explanation

    Answer: A. Antibiotics kill bacteria or stop them from multiplying. They have no effect on viruses.

    • ACorrect. Antibiotics kill bacteria or stop them from multiplying, which is why they treat illnesses such as strep throat.
    • BWrong. Viruses, such as those that cause colds and flu, lack the cell parts antibiotics attack, so antibiotics do not work on them.
    • CWrong. Allergens such as pollen trigger allergies, an immune overreaction that is treated with medicines like antihistamines, not antibiotics.
    • DWrong. A deficiency disease is treated by adding the missing nutrient to the diet, not with antibiotics.

  8. Most of the energy a cell gets from food is released in the

    1. Anucleus.
    2. Bchloroplasts.
    3. Cmitochondria.
    4. Dribosomes.
    Show answer and explanation

    Answer: C. Mitochondria carry out most of cellular respiration, releasing the energy in food as ATP.

    • AWrong. The nucleus holds the cell’s DNA and directs its activities; it does not break down food.
    • BWrong. Chloroplasts capture light energy to make sugar in plant cells; they store energy in food rather than release it.
    • CCorrect. Mitochondria carry out most of cellular respiration, releasing the energy stored in food as ATP.
    • DWrong. Ribosomes build proteins; they do not release energy from food.

  9. Which of these has the lowest pH?

    1. AHousehold ammonia
    2. BBaking soda in water
    3. CPure water
    4. DLemon juice
    Show answer and explanation

    Answer: D. The lower the pH, the more acidic the substance. Lemon juice is acidic, with a pH of about 2.

    • AWrong. Household ammonia is a strong base with a pH of about 11 to 12, near the high end of the scale.
    • BWrong. Baking soda dissolved in water is a mild base with a pH of about 8 to 9.
    • CWrong. Pure water is neutral, with a pH of 7.
    • DCorrect. Lemon juice is acidic, with a pH of about 2, and the lower the pH, the more acidic the substance.

  10. Tall (T) is dominant over short (t). What fraction of offspring from a Tt × tt cross should be tall?

    1. A1/4
    2. B1/2
    3. C3/4
    4. D1
    Show answer and explanation

    Answer: B. The Punnett square for Tt × tt gives Tt, Tt, tt, tt, so 2 of 4 offspring (1/2) are tall.

    • AWrong. 1/4 is the expected share of short (tt) offspring from a Tt × Tt cross, not the tall share here.
    • BCorrect. The Punnett square gives Tt, Tt, tt, tt, so 2 of every 4 offspring (1/2) carry T and are tall.
    • CWrong. 3/4 tall is the result of crossing two Tt plants.
    • DWrong. All offspring would be tall only if one parent were TT.

  11. A long-term lack of vitamin C in the diet causes which disease?

    1. AScurvy
    2. BRickets
    3. CBeriberi
    4. DNight blindness
    Show answer and explanation

    Answer: A. Vitamin C deficiency causes scurvy, with bleeding gums, weakness, and slow-healing wounds.

    • ACorrect. A lack of vitamin C causes scurvy, with bleeding gums, weakness, and wounds that heal slowly.
    • BWrong. Rickets comes from too little vitamin D (or calcium), which leaves children’s bones soft and bent.
    • CWrong. Beriberi comes from too little vitamin B1 (thiamine) and damages the nerves and heart.
    • DWrong. Night blindness comes from too little vitamin A, which the eye needs to see in dim light.

  12. A relationship between two species in which both species benefit is called

    1. Acommensalism.
    2. Bparasitism.
    3. Cmutualism.
    4. Dcompetition.
    Show answer and explanation

    Answer: C. In mutualism both partners gain, as when bees get nectar while carrying pollen between flowers.

    • AWrong. In commensalism one species benefits and the other is neither helped nor harmed, as with barnacles riding on a whale.
    • BWrong. In parasitism one species benefits at the other’s expense, as when a tick feeds on a dog’s blood.
    • CCorrect. In mutualism both partners gain, as when bees get nectar while carrying pollen between flowers.
    • DWrong. In competition two species need the same limited resource, such as food or space, and each loses some of it to the other.

  13. Seismic S waves cannot travel through Earth’s outer core. What does this tell scientists about the outer core?

    1. AIt is solid rock.
    2. BIt is liquid.
    3. CIt is mostly gas.
    4. DIt is hollow.
    Show answer and explanation

    Answer: B. S (shear) waves can move only through solids, so their failure to cross the outer core shows it is liquid.

    • AWrong. If the outer core were solid, S waves could pass through it; it is the inner core that is solid.
    • BCorrect. S (shear) waves can travel only through solids, so the outer core must be liquid, mostly molten iron and nickel.
    • CWrong. The pressure deep inside Earth is far too great for a gas; seismic data show the outer core is a dense liquid.
    • DWrong. Earth is not hollow; P waves pass through the core, which shows it is filled with dense material.

  14. Tiny finger-like projections that absorb digested food through the wall of the small intestine are called

    1. Aalveoli.
    2. Bcilia.
    3. Cvilli.
    4. Dnephrons.
    Show answer and explanation

    Answer: C. Villi line the small intestine and greatly increase its surface area, so nutrients pass into the blood quickly.

    • AWrong. Alveoli are the tiny air sacs in the lungs where oxygen and carbon dioxide are exchanged.
    • BWrong. Cilia are tiny hairlike structures that sweep mucus and trapped particles, for example up and out of the airways.
    • CCorrect. Villi line the small intestine and greatly increase its surface area, so digested nutrients pass into the blood quickly.
    • DWrong. Nephrons are the filtering units of the kidneys that remove wastes from the blood and form urine.

  15. Elements in the same column of the periodic table behave alike chemically because they have the same number of

    1. Aouter-shell electrons.
    2. Bprotons.
    3. Cneutrons.
    4. Denergy levels.
    Show answer and explanation

    Answer: A. Outer-shell (valence) electrons decide how an atom bonds, and elements in one column (group) have the same number of them.

    • ACorrect. Outer-shell (valence) electrons decide how an atom bonds; for example, the alkali metals in the first column each have one and all react readily with water.
    • BWrong. Each element has its own number of protons, so no two elements in a column share it.
    • CWrong. The number of neutrons varies even among atoms of one element and has almost no effect on chemical behavior.
    • DWrong. Elements in the same row (period), not the same column, have the same number of occupied energy levels.

Arithmetic Reasoning: 15 questions

Word problems solved with arithmetic. No calculator; use scratch paper. Real test: 15 questions in 55 minutes.

  1. A customer buys a sandwich for $6.75 and a drink for $1.80 and pays with a $10 bill. How much change should the customer get?

    1. A$1.45
    2. B$3.25
    3. C$8.20
    4. D$8.55
    Show answer and explanation

    Answer: A. $6.75 + $1.80 = $8.55 spent, and $10.00 − $8.55 = $1.45 in change.

    • ACorrect. $6.75 + $1.80 = $8.55 spent, and $10.00 − $8.55 = $1.45 in change.
    • BWrong. $3.25 is $10.00 − $6.75, which leaves out the $1.80 drink.
    • CWrong. $8.20 is $10.00 − $1.80, which leaves out the $6.75 sandwich.
    • DWrong. $8.55 is the total spent. It still has to be subtracted from the $10.00 paid.

  2. A roofer installs 3 bundles of shingles each hour. At that rate, how many hours will it take to install 27 bundles?

    1. A9
    2. B24
    3. C30
    4. D81
    Show answer and explanation

    Answer: A. 27 bundles ÷ 3 bundles an hour = 9 hours.

    • ACorrect. 27 bundles ÷ 3 bundles an hour = 9 hours.
    • BWrong. 24 subtracts 3 from 27 instead of dividing.
    • CWrong. 30 adds 3 to 27 instead of dividing.
    • DWrong. 81 multiplies 27 by 3 instead of dividing.

  3. A 60-gallon water tank is 2/3 full. How many more gallons are needed to fill it?

    1. A20
    2. B30
    3. C40
    4. D90
    Show answer and explanation

    Answer: A. 2/3 of 60 is 40 gallons already in the tank, so 60 − 40 = 20 gallons are still needed.

    • ACorrect. 2/3 of 60 is 40 gallons already in the tank, so 60 − 40 = 20 gallons are still needed.
    • BWrong. 30 is half of 60, as if the tank were 1/2 full instead of 2/3 full.
    • CWrong. 40 is the water already in the tank, not the amount still needed.
    • DWrong. 90 divides 60 by 2/3 instead of multiplying 60 by 2/3.

  4. A 16-ounce jar of peanut butter costs $4.80. At the same price per ounce, what would a 40-ounce jar cost?

    1. A$0.30
    2. B$7.20
    3. C$12.00
    4. D$192.00
    Show answer and explanation

    Answer: C. $4.80 ÷ 16 = $0.30 an ounce, and 40 × $0.30 = $12.00.

    • AWrong. $0.30 is the price of 1 ounce. It still has to be multiplied by 40 ounces.
    • BWrong. $7.20 prices only the 24 extra ounces (24 × $0.30), not the whole 40-ounce jar.
    • CCorrect. $4.80 ÷ 16 = $0.30 an ounce, and 40 × $0.30 = $12.00.
    • DWrong. $192.00 multiplies the whole jar's price by 40. Find the price of 1 ounce first.

  5. Movie tickets cost $12.50 each, and a large popcorn costs $7. What is the total cost of 4 tickets and 2 large popcorns?

    1. A$39
    2. B$57
    3. C$64
    4. D$78
    Show answer and explanation

    Answer: C. 4 × $12.50 = $50 for tickets and 2 × $7 = $14 for popcorn. $50 + $14 = $64.

    • AWrong. $39 is 2 × ($12.50 + $7). It buys only 2 tickets instead of 4.
    • BWrong. $57 includes all 4 tickets but only 1 popcorn.
    • CCorrect. 4 × $12.50 = $50 for tickets and 2 × $7 = $14 for popcorn. $50 + $14 = $64.
    • DWrong. $78 is 4 × ($12.50 + $7). It buys 4 popcorns instead of 2.

  6. On a map, 1/2 inch stands for 15 miles. Two towns are 4 1/2 inches apart on the map. How many miles apart are the towns?

    1. A30
    2. B33 3/4
    3. C67 1/2
    4. D135
    Show answer and explanation

    Answer: D. If 1/2 inch is 15 miles, 1 inch is 30 miles. 4 1/2 × 30 = 135 miles.

    • AWrong. 30 is the number of miles in 1 inch. It still has to be multiplied by 4 1/2 inches.
    • BWrong. 33 3/4 halves 4 1/2 × 15 instead of doubling it. Each inch is twice 15 miles, not half.
    • CWrong. 67 1/2 is 4 1/2 × 15. It treats each whole inch as 15 miles, but 15 miles is only 1/2 inch.
    • DCorrect. If 1/2 inch is 15 miles, 1 inch is 30 miles. 4 1/2 × 30 = 135 miles.

  7. In a parking lot, the ratio of cars to trucks is 5 to 2. There are 35 vehicles in all. How many are trucks?

    1. A7
    2. B10
    3. C14
    4. D25
    Show answer and explanation

    Answer: B. 5 + 2 = 7 parts, so each part is 35 ÷ 7 = 5 vehicles. Trucks are 2 parts: 2 × 5 = 10.

    • AWrong. 7 divides 35 by 5. The total is split into 5 + 2 = 7 parts, not 5.
    • BCorrect. 5 + 2 = 7 parts, so each part is 35 ÷ 7 = 5 vehicles. Trucks are 2 parts: 2 × 5 = 10.
    • CWrong. 14 takes 2/5 of 35. Trucks are 2 of 7 parts of all vehicles, not 2/5.
    • DWrong. 25 is the number of cars, not trucks.

  8. A driver buys 4 tires that all cost the same and pays a $40 installation charge. The total bill is $520. What is the price of one tire?

    1. A$90
    2. B$120
    3. C$130
    4. D$140
    Show answer and explanation

    Answer: B. Take off the charge first: $520 − $40 = $480 for the tires. Then $480 ÷ 4 = $120 per tire.

    • AWrong. $90 divides $520 by 4 first and then takes the whole $40 charge off one tire.
    • BCorrect. Take off the charge first: $520 − $40 = $480 for the tires. Then $480 ÷ 4 = $120 per tire.
    • CWrong. $130 is $520 ÷ 4. It forgets to take off the $40 installation charge.
    • DWrong. $140 adds the $40 charge ($560 ÷ 4) instead of subtracting it.

  9. A rectangular room has a floor area of 168 square feet. The room is 14 feet long. How many feet of baseboard are needed to go all the way around the room?

    1. A12
    2. B26
    3. C52
    4. D364
    Show answer and explanation

    Answer: C. The width is 168 ÷ 14 = 12 feet. The distance around is 2 × (14 + 12) = 52 feet.

    • AWrong. 12 is the width of the room. It is a step toward the perimeter, not the answer.
    • BWrong. 26 adds one length and one width. A rectangle has two of each.
    • CCorrect. The width is 168 ÷ 14 = 12 feet. The distance around is 2 × (14 + 12) = 52 feet.
    • DWrong. 364 is 2 × (168 + 14). It uses the area as if it were a side length.

  10. A rectangular yard is 40 feet long and 25 feet wide. One 40-foot side runs along a building and needs no fence. Fencing costs $12 per foot. What does the fence cost?

    1. A$780
    2. B$1,080
    3. C$1,260
    4. D$1,560
    Show answer and explanation

    Answer: B. Fence one 40-foot side and both 25-foot sides: 40 + 25 + 25 = 90 feet. 90 × $12 = $1,080.

    • AWrong. $780 fences only 40 + 25 = 65 feet, one long side and one short side.
    • BCorrect. Fence one 40-foot side and both 25-foot sides: 40 + 25 + 25 = 90 feet. 90 × $12 = $1,080.
    • CWrong. $1,260 fences 40 + 40 + 25 = 105 feet. It leaves out a 25-foot side instead of the side along the building.
    • DWrong. $1,560 fences all four sides (130 feet), including the side along the building.

  11. A family borrows $3,600 at 5% simple interest per year and repays the loan in full after 18 months. What is the total amount repaid?

    1. A$270
    2. B$3,780
    3. C$3,870
    4. D$6,840
    Show answer and explanation

    Answer: C. One year of interest is 5% of $3,600 = $180. 18 months is 1 1/2 years, so interest is $270 and the total is $3,600 + $270 = $3,870.

    • AWrong. $270 is the interest alone. The $3,600 borrowed must be repaid too.
    • BWrong. $3,780 charges only 1 year of interest. 18 months is 1 1/2 years.
    • CCorrect. One year of interest is 5% of $3,600 = $180. 18 months is 1 1/2 years, so interest is $270 and the total is $3,600 + $270 = $3,870.
    • DWrong. $6,840 treats 18 months as 18 years of interest.

  12. A store raises the $50 price of a lamp by 20%. Later it puts the lamp on sale at 20% off the new price. What is the sale price?

    1. A$40
    2. B$48
    3. C$50
    4. D$60
    Show answer and explanation

    Answer: B. The new price is $50 + 20% = $60. 20% off $60 is $12, so the sale price is $48.

    • AWrong. $40 takes 20% off the original $50 and skips the increase.
    • BCorrect. The new price is $50 + 20% = $60. 20% off $60 is $12, so the sale price is $48.
    • CWrong. $50 assumes a 20% increase and a 20% decrease cancel. The 20% off is taken from the larger $60.
    • DWrong. $60 is the raised price. The 20% sale discount still has to come off.

  13. The 5 workers on a crew have an average age of 34. One worker retires, and the average age of the other 4 workers is 31. How old is the worker who retired?

    1. A15
    2. B34
    3. C37
    4. D46
    Show answer and explanation

    Answer: D. The ages add to 5 × 34 = 170 before and 4 × 31 = 124 after. The retired worker is 170 − 124 = 46.

    • AWrong. 15 multiplies the new average by 5 (170 − 155). Only 4 workers are left, so their total is 4 × 31 = 124.
    • BWrong. 34 assumes the retired worker was exactly the average age. Then the average would not have changed.
    • CWrong. 37 adds the 3-year drop to 34 only once. The retiree pulled all 4 remaining workers' average down by 3, so the retiree was 4 × 3 = 12 years above 34.
    • DCorrect. The ages add to 5 × 34 = 170 before and 4 × 31 = 124 after. The retired worker is 170 − 124 = 46.

  14. A driver travels 150 miles to a job site at 50 mph and returns by the same route at 75 mph. What is the average speed for the whole round trip?

    1. A60 mph
    2. B62 1/2 mph
    3. C100 mph
    4. D125 mph
    Show answer and explanation

    Answer: A. Going takes 150 ÷ 50 = 3 hours and returning takes 150 ÷ 75 = 2 hours. 300 miles ÷ 5 hours = 60 mph.

    • ACorrect. Going takes 150 ÷ 50 = 3 hours and returning takes 150 ÷ 75 = 2 hours. 300 miles ÷ 5 hours = 60 mph.
    • BWrong. 62 1/2 mph averages the two speeds. More time is spent at the slower speed, so it counts more.
    • CWrong. 100 mph divides 300 miles by only the 3 hours going. The 2 hours back must be added.
    • DWrong. 125 mph adds the two speeds.

  15. A worker earns $16 an hour for up to 40 hours a week and 1 1/2 times that rate for overtime. After a 47-hour week, 20% of the pay is withheld. What is the take-home pay?

    1. A$601.60
    2. B$646.40
    3. C$680.00
    4. D$808.00
    Show answer and explanation

    Answer: B. Regular pay is 40 × $16 = $640. Overtime is 7 hours × $24 = $168. Gross pay is $808, and 80% of $808 is $646.40.

    • AWrong. $601.60 pays all 47 hours at $16 ($752) before withholding. The 7 overtime hours pay $24 each.
    • BCorrect. Regular pay is 40 × $16 = $640. Overtime is 7 hours × $24 = $168. Gross pay is $808, and 80% of $808 is $646.40.
    • CWrong. $680.00 withholds 20% of the $640 regular pay only. The 20% comes out of all $808.
    • DWrong. $808.00 is the pay before taxes. 20% still has to be withheld.

Word Knowledge: 15 questions

Choose the word or phrase closest in meaning to the underlined word. Real test: 15 questions in 9 minutes.

  1. Rapid most nearly means

    1. Aslow
    2. Bloud
    3. Cquick
    4. Dcareful
    Show answer and explanation

    Answer: C. Rapid means moving or happening fast, so quick is the match.

    • AWrong. Slow means taking a long time; it is the opposite of rapid.
    • BWrong. Loud describes a strong sound, not speed.
    • CCorrect. Rapid means fast, and quick means the same thing: a rapid pace is a quick pace.
    • DWrong. Careful means paying close attention to avoid mistakes; it says nothing about speed.

  2. Repair most nearly means

    1. Afix
    2. Bbreak
    3. Cclean
    4. Dreplace
    Show answer and explanation

    Answer: A. To repair something is to fix it so it works again.

    • ACorrect. Repair means to fix something that is broken or damaged.
    • BWrong. To break something is to damage it, the opposite of repair.
    • CWrong. To clean is to remove dirt; a clean item can still be broken.
    • DWrong. To replace is to put a new item in place of the old one, which is what you do instead of repairing it.

  3. Please keep noise to the minimum while the baby naps.
    The underlined word most nearly means

    1. Aquiet hours
    2. Bsteady rate
    3. Cleast amount
    4. Daverage amount
    Show answer and explanation

    Answer: C. A minimum is the smallest amount possible, so keeping noise to a minimum means making as little as you can.

    • AWrong. Quiet hours are set times for keeping noise down. They fit the scene, but minimum refers to an amount, not a time.
    • BWrong. A steady rate is an unchanging pace; it says nothing about how small the amount is.
    • CCorrect. A minimum is the least amount possible.
    • DWrong. An average amount is a typical, middle amount, which is more than the minimum.

  4. The clerk gave a brief answer and kept working.
    The underlined word most nearly means

    1. Arude
    2. Bclear
    3. Cshort
    4. Dlengthy
    Show answer and explanation

    Answer: C. Brief means short, lasting only a little while.

    • AWrong. Rude means impolite. A short answer can seem rude, but brief is about length, not manners.
    • BWrong. Clear means easy to understand; a brief answer may or may not be clear.
    • CCorrect. Brief means short in length or time.
    • DWrong. Lengthy means long, the opposite of brief.

  5. Hazard most nearly means

    1. Adanger
    2. Bsafety
    3. Cwarning
    4. Daccident
    Show answer and explanation

    Answer: A. A hazard is a danger or risk, like ice on a sidewalk.

    • ACorrect. A hazard is a danger: something that could cause harm.
    • BWrong. Safety is freedom from danger, the opposite of a hazard.
    • CWrong. A warning is a notice that danger is near. A sign can warn of a hazard, but the sign is not the hazard.
    • DWrong. An accident is an unplanned event that causes harm. A hazard can lead to an accident, but it is the risk, not the event.

  6. The new bridge will reduce travel time across the river.
    The underlined word most nearly means

    1. Aextend
    2. Blessen
    3. Cmeasure
    4. Dpredict
    Show answer and explanation

    Answer: B. To reduce something is to make it smaller or less, so the bridge will lessen travel time.

    • AWrong. To extend is to make longer, the opposite of reduce here.
    • BCorrect. Reduce means to lessen: to make smaller in amount.
    • CWrong. To measure is to find out how long or large something is, not to change it.
    • DWrong. To predict is to say what will happen in the future.

  7. Firefighters had to evacuate the building before the roof collapsed.
    The underlined word most nearly means

    1. Ainspect
    2. Bcool down
    3. Cclear out
    4. Dbreak into
    Show answer and explanation

    Answer: C. To evacuate a building is to clear everyone out of it for safety.

    • AWrong. To inspect is to look over carefully for problems.
    • BWrong. To cool down is to lower the temperature. Firefighters do cool buildings, but evacuate means to empty them.
    • CCorrect. Evacuate means to clear out: to move everyone out of a place.
    • DWrong. To break into is to force a way inside, which is nearly the opposite of moving people out.

  8. Summit most nearly means

    1. Abase
    2. Bpeak
    3. Ccrowd
    4. Dslope
    Show answer and explanation

    Answer: B. The summit of a mountain is its highest point, or peak.

    • AWrong. The base is the bottom of a mountain, the opposite of the summit.
    • BCorrect. A summit is the peak: the very top of a mountain or hill.
    • CWrong. A crowd is a large group of people.
    • DWrong. A slope is the slanted side of a hill. It is part of the mountain, but not the top.

  9. Deteriorate most nearly means

    1. Adelay
    2. Bdivide
    3. Cworsen
    4. Dimprove
    Show answer and explanation

    Answer: C. To deteriorate is to become worse over time.

    • AWrong. To delay is to put off until later.
    • BWrong. To divide is to split into parts.
    • CCorrect. Deteriorate means to worsen, as when an old road breaks down.
    • DWrong. To improve is to get better, the opposite of deteriorate.

  10. Abandon most nearly means

    1. Akeep
    2. Bdelay
    3. Cchange
    4. Dgive up
    Show answer and explanation

    Answer: D. To abandon something is to give it up completely or leave it behind for good.

    • AWrong. To keep something is to hold on to it, the opposite of abandon.
    • BWrong. To delay is to put off until later; a delayed plan can still go ahead.
    • CWrong. To change is to make different. You might change a plan instead of abandoning it, but a changed plan keeps going.
    • DCorrect. Abandon means to give up completely, as when a crew abandons a sinking ship.

  11. Adversary most nearly means

    1. Aally
    2. Bguest
    3. Creferee
    4. Dopponent
    Show answer and explanation

    Answer: D. An adversary is an opponent or enemy.

    • AWrong. An ally is a friend or partner on your side, the opposite of an adversary.
    • BWrong. A guest is a person visiting or invited somewhere.
    • CWrong. A referee is an official who enforces the rules of a game. A referee oversees opponents but is not one.
    • DCorrect. An adversary is an opponent: someone who competes or fights against you.

  12. Impartial most nearly means

    1. Astrict
    2. Bneutral
    3. Cimpatient
    4. Dprejudiced
    Show answer and explanation

    Answer: B. Impartial means not favoring one side over another, which is what neutral means.

    • AWrong. Strict means demanding that rules be followed. A judge may be strict and still take sides.
    • BCorrect. Impartial means neutral: fair to all sides and favoring none.
    • CWrong. Impatient means unwilling to wait; it only sounds like impartial.
    • DWrong. Prejudiced means favoring or disliking one side unfairly, the opposite of impartial.

  13. Fortitude most nearly means

    1. Afear
    2. Bwealth
    3. Cloyalty
    4. Dcourage
    Show answer and explanation

    Answer: D. Fortitude is courage and strength of mind in facing pain or trouble.

    • AWrong. Fear is the feeling of being afraid, the opposite of fortitude.
    • BWrong. Wealth is a large amount of money or property.
    • CWrong. Loyalty is faithfulness to a person or cause. Like fortitude it is a virtue, but it means being true, not being brave.
    • DCorrect. Fortitude is courage, especially the courage to endure hardship.

  14. The inspector gave the contract a perfunctory review.
    The underlined word most nearly means

    1. Aharshly critical
    2. Bslow and thorough
    3. Chasty and careless
    4. Dofficially approved
    Show answer and explanation

    Answer: C. A perfunctory review is done quickly and with little care, just to get it over with.

    • AWrong. Harshly critical means finding a lot of fault; a perfunctory review barely looks for faults.
    • BWrong. Slow and thorough means careful and complete, the opposite of perfunctory.
    • CCorrect. Perfunctory means done hastily and carelessly, as a routine duty.
    • DWrong. Officially approved means given formal consent. A review can end in approval, but perfunctory describes how the review was done.

  15. The judge showed clemency to the first-time offender.
    The underlined word most nearly means

    1. Amercy
    2. Bfairness
    3. Cseverity
    4. Dcuriosity
    Show answer and explanation

    Answer: A. Clemency is mercy, especially a lighter punishment than could have been given.

    • ACorrect. Clemency means mercy: choosing to be less harsh than one could be.
    • BWrong. Fairness is treating people equally by the rules. A judge should be fair, but clemency means going easier than the rules allow.
    • CWrong. Severity is harshness, the opposite of clemency.
    • DWrong. Curiosity is the wish to know or learn about something.

Paragraph Comprehension: 10 questions

Read each short passage, then answer the question about it. Real test: 10 questions in 27 minutes.

  1. Before climbing a stepladder, open it fully and make sure both spreader bars are locked in place. Set the ladder on firm, level ground. Never stand on the top step or the top cap, because doing so makes the ladder much easier to tip over. Keep your body centered between the side rails, and move the ladder closer instead of leaning out to reach something.

    According to the passage, why should you never stand on the top step of a stepladder?

    1. AThe top step is not made to hold much weight.
    2. BYour hands could not reach the side rails.
    3. CThe ladder is more likely to fall over.
    4. DThe spreader bars could come unlocked.
    Show answer and explanation

    Answer: C. The passage gives one reason for staying off the top step: it makes the ladder much easier to tip over. The key restates that as the ladder being more likely to fall.

    • AWrong. The passage says nothing about how much weight the top step can hold. This is an outside guess, not the reason given.
    • BWrong. The side rails come up only in the advice to keep your body centered. Reaching them is not the reason given for avoiding the top step.
    • CCorrect. The passage says standing on the top step makes the ladder "much easier to tip over," which means it is more likely to fall.
    • DWrong. The spreader bars are mentioned only as something to lock before climbing. The passage does not connect them to the top step.

  2. To replace the bag in your vacuum cleaner, first unplug the machine. Open the front cover by pressing the release button on top. Lift the full bag off its holder and place it in the trash. Slide a new bag onto the holder until it clicks into place. Close the cover, plug the vacuum back in, and run it for a few seconds to test it.

    According to the instructions, what should you do right after opening the front cover?

    1. APress the button.
    2. BInsert a new bag.
    3. CUnplug the vacuum.
    4. DTake out the used bag.
    Show answer and explanation

    Answer: D. The order is unplug, open the cover, remove the full bag, insert a new bag, close and test. Removing the old bag comes right after opening the cover.

    • AWrong. Pressing the release button is how you open the cover, so it happens before, not after, the cover is open.
    • BWrong. A new bag goes in only after the old one has been removed, so this step comes later.
    • CWrong. Unplugging is the first step, done before the cover is opened.
    • DCorrect. The step that follows opening the cover is to lift the full bag off its holder and throw it away, which means taking out the used bag.

  3. Many people think a wagging tail always means a dog is happy. In fact, tail wagging can show many different feelings. A loose, sweeping wag often signals a relaxed, friendly dog, but a stiff, high wag may mean the dog feels tense or is ready to defend itself.

    Which statement best expresses the main idea of the passage?

    1. AA dog's wag can signal more than one mood.
    2. BDogs that feel tense usually stop wagging.
    3. CDogs wag their tails only when they are happy.
    4. DA stiff, high wag shows that a dog is relaxed.
    Show answer and explanation

    Answer: A. The second sentence states the main idea: tail wagging can show many feelings. The examples of loose and stiff wags support it.

    • ACorrect. The passage corrects the idea that wagging always means happiness and explains that different wags show different feelings.
    • BWrong. The passage says tense dogs may wag in a stiff, high way. It never says they stop wagging.
    • CWrong. This is the common belief the passage sets out to correct, not its main idea.
    • DWrong. This twists the passage, which links a stiff, high wag to tension, not to relaxation.

  4. Your new coffee maker is covered by a one-year limited warranty from the date of purchase. During this period, the maker will repair or replace the machine if it fails because of a defect in materials or workmanship. The warranty does not cover damage caused by dropping the machine, by using the wrong voltage, or by failing to remove mineral buildup as described in the cleaning section.

    According to the passage, which problem does the warranty cover?

    1. AA clog from mineral buildup that was never cleaned
    2. BDamage from plugging into the wrong voltage
    3. CA badly made heating part that fails
    4. DA cracked water tank from a fall
    Show answer and explanation

    Answer: C. The warranty covers failures caused by defects in materials or workmanship. A badly made heating part is such a defect; the other three are on the list of exclusions.

    • AWrong. Failing to remove mineral buildup is listed as not covered.
    • BWrong. Using the wrong voltage is listed as not covered.
    • CCorrect. A part that was badly made has a defect in materials or workmanship, which the warranty says it will repair or replace.
    • DWrong. Damage from dropping the machine is listed as not covered.

  5. Honeybees share the location of food through a movement called the waggle dance. A worker bee returning to the hive moves in a figure-eight pattern, shaking its body during the straight middle part of the dance. The angle of that straight run tells other bees which direction to fly compared with the position of the sun. The length of the run conveys how far away the flowers are.

    In the passage, the word conveys most nearly means

    1. Alimits.
    2. Bconceals.
    3. Ccommunicates.
    4. Dmisrepresents.
    Show answer and explanation

    Answer: C. The sentence before uses "tells" for direction; "conveys" plays the same role for distance. To convey information is to communicate it.

    • AWrong. The length of the run does not restrict how far bees fly; it tells them the distance.
    • BWrong. This is the opposite. The dance exists to share information, not to hide it.
    • CCorrect. The passage is about bees sharing food locations. Just as the angle "tells" direction, the length of the run conveys, or communicates, distance.
    • DWrong. Nothing suggests the dance gives a false picture of the distance. It reports it accurately enough for other bees to find the food.

  6. Thousands of house fires each year start in clothes dryers, and the leading cause is a buildup of lint. Lint burns easily, and when it collects in the filter or the exhaust duct, it blocks airflow and lets heat build up inside the machine. Cleaning the lint filter before or after every load takes only seconds. The duct that carries hot air outdoors should be cleaned at least once a year.

    Which statement best summarizes the passage?

    1. ARemoving lint helps prevent dryer fires.
    2. BMost house fires start in clothes dryers.
    3. CLint is a material that catches fire easily.
    4. DLint filters should be replaced once a year.
    Show answer and explanation

    Answer: A. The passage links lint to dryer fires and then tells readers how to clear it. Its overall point is that regular lint removal prevents fires.

    • ACorrect. The passage names lint buildup as the main cause of dryer fires and then explains how often to clean the filter and duct.
    • BWrong. The passage says thousands of fires start in dryers, not that most house fires do.
    • CWrong. The passage does say lint burns easily, but that is one supporting detail, not a summary.
    • DWrong. This twists two details. The filter is cleaned every load; it is the duct that should be cleaned yearly, and nothing is said about replacing either.

  7. Most credit cards offer a grace period, the time between the end of a billing cycle and the payment due date. If you pay the full statement balance by the due date, you usually will not be charged interest on purchases from that cycle. If you pay only part of the balance, interest is usually charged on the rest. Cash advances work differently: interest on them often starts the day the cash is withdrawn, with no grace period at all.

    According to the passage, when does interest on a cash advance usually begin?

    1. AOn the payment due date
    2. BWhen the cash is taken out
    3. CWhen the grace period runs out
    4. DAt the close of each billing cycle
    Show answer and explanation

    Answer: B. The last sentence says cash advance interest often starts the day the cash is withdrawn. The other choices describe how the grace period works for purchases.

    • AWrong. The due date marks the end of the grace period for purchases. The passage says cash advances do not get that grace period.
    • BCorrect. The passage says interest on cash advances often starts the day the cash is withdrawn.
    • CWrong. The passage says cash advances have "no grace period at all," so there is no grace period to end.
    • DWrong. The end of the billing cycle starts the grace period for purchases; it is not when cash advance interest begins.

  8. Before the 1880s, most towns in the United States set their clocks by the sun, so noon came when the sun was highest overhead. A traveler heading west found the local time changing slightly at nearly every stop, and railroads struggled to print schedules that made sense. On November 18, 1883, the major railroads adopted standard time zones, and towns within each zone began sharing one time. Congress did not make the zones official until 1918, but many communities followed the railroads' lead right away.

    Which statement best expresses the main idea of the passage?

    1. AMost towns refused to change their clocks until Congress acted.
    2. BTravelers had to reset their watches at nearly every stop.
    3. CCongress created time zones in 1918 to help the railroads.
    4. DRailroads drove the switch to standard time.
    Show answer and explanation

    Answer: D. The passage traces how the railroads' scheduling trouble led them to create time zones, which towns then adopted. That cause and change is the main idea.

    • AWrong. This contradicts the passage, which says many communities followed the railroads right away.
    • BWrong. This is a supporting detail about the old system, not the main point of the passage.
    • CWrong. The railroads created the zones in 1883. Congress only made them official later.
    • DCorrect. The passage explains the scheduling problem sun time caused the railroads, their switch to time zones in 1883, and how towns followed.

  9. Some school districts have moved to a four-day school week, making the remaining days longer to make up the lost hours. Supporters say the schedule saves money on buses and utilities and helps rural districts attract teachers. Critics answer that the savings are often smaller than expected and that working parents may have to pay for child care on the fifth day. Studies of student achievement have found mixed results. Each district considering the change must weigh these trade-offs for itself.

    The author's main purpose in the passage is to

    1. Apresent both sides of a debate.
    2. Bpersuade districts to adopt a four-day week.
    3. Cprove that a four-day week lowers test scores.
    4. Dexplain how rural districts hire new teachers.
    Show answer and explanation

    Answer: A. The author presents benefits, drawbacks, and mixed evidence without taking a side. The purpose is to lay out both sides of the debate.

    • ACorrect. The passage gives the supporters' view, the critics' view, and mixed research, and then leaves the decision to each district.
    • BWrong. The author gives the supporters' reasons but also the critics' and never recommends the change.
    • CWrong. The passage says studies of achievement have found mixed results, so it does not claim this.
    • DWrong. Hiring teachers comes up only as one claimed benefit. The passage does not explain how hiring works.

  10. Starting June 1, the warehouse will change how it handles returned goods. Until now, returns have been checked by whichever associate happened to be free, which led to uneven decisions about whether items could be sold again. Under the new plan, all returns will go to one inspection station staffed by two trained associates on each shift. Items graded A will be restocked the same day, items graded B will go to the outlet store at a discount, and items graded C will be recycled or donated. Managers expect the change to cut the number of damaged products reaching customers.

    It can reasonably be inferred from the memo that under the old system

    1. Aonly trained workers inspected returns.
    2. Breturns sat for weeks before being checked.
    3. Creturned items were never put back on the shelves.
    4. Dsome damaged goods ended up being sold to customers.
    Show answer and explanation

    Answer: D. Managers expect the new process to reduce damaged products reaching customers, and the old checks were uneven. Both point to damaged returns having been resold under the old system.

    • AWrong. This reverses the memo. Returns were checked by whichever associate was free; trained inspectors are part of the new plan.
    • BWrong. The memo never mentions how long returns waited. This is a plausible guess with no support in the passage.
    • CWrong. The memo says decisions about reselling returns were uneven, which means some returns were sold again.
    • DCorrect. Uneven resale decisions, plus the hope that the change will cut the damaged products reaching customers, imply some damaged items were being resold.

Mathematics Knowledge: 15 questions

High school math: number properties, algebra, geometry. No calculator. Real test: 15 questions in 31 minutes.

  1. If x/4 = 7, then x =

    1. A7/4
    2. B3
    3. C11
    4. D28
    Show answer and explanation

    Answer: D. Multiply both sides by 4: x = 7 × 4 = 28.

    • AWrong. 7/4 divides 7 by 4, but undoing a division by 4 means multiplying by 4.
    • BWrong. 3 subtracts 4 from 7; the 4 divides x, so it is undone by multiplying.
    • CWrong. 11 adds 4 to 7 instead of multiplying by 4.
    • DCorrect. Multiply both sides by 4: x = 7 × 4 = 28.

  2. What is the perimeter of a rectangle 8 feet long and 3 feet wide?

    1. A11 ft
    2. B19 ft
    3. C22 ft
    4. D24 ft
    Show answer and explanation

    Answer: C. Perimeter = 2 × (length + width) = 2 × (8 + 3) = 22 ft.

    • AWrong. 11 ft adds one length and one width; a rectangle has two of each.
    • BWrong. 19 ft adds both lengths but only one width (8 + 8 + 3).
    • CCorrect. 2 × (8 + 3) = 22 ft.
    • DWrong. 24 is the area (8 × 3 square feet), not the distance around.

  3. One letter is chosen at random from the 11 letters of the word MISSISSIPPI. What is the probability that it is an S?

    1. A1/11
    2. B1/4
    3. C4/11
    4. D4/7
    Show answer and explanation

    Answer: C. The word has 4 S’s among its 11 letters, so the probability is 4/11.

    • AWrong. 1/11 counts only one S; there are four.
    • BWrong. 1/4 counts the 4 different letters (M, I, S, P) instead of all 11 letters.
    • CCorrect. 4 S’s out of 11 letters gives 4/11.
    • DWrong. 4/7 compares S’s to the other letters (4 to 7) instead of to all 11.

  4. 2/3 + 3/4 =

    1. A5/12
    2. B1/2
    3. C5/7
    4. D17/12
    Show answer and explanation

    Answer: D. The LCD is 12: 2/3 = 8/12 and 3/4 = 9/12, so the sum is 17/12 (or 1 5/12).

    • AWrong. 5/12 uses the common denominator 12 but adds the old numerators 2 + 3 without rewriting them.
    • BWrong. 1/2 multiplies the fractions (6/12) instead of adding them.
    • CWrong. 5/7 adds the numerators and the denominators straight across.
    • DCorrect. 8/12 + 9/12 = 17/12.

  5. Which expression means “7 less than 3 times a number n”?

    1. A3n − 7
    2. B7 − 3n
    3. C7n − 3
    4. D3(n − 7)
    Show answer and explanation

    Answer: A. “3 times a number n” is 3n, and “7 less than” that means subtract 7 from it: 3n − 7.

    • ACorrect. “7 less than 3n” means start with 3n and take away 7: 3n − 7.
    • BWrong. 7 − 3n reverses the order; “7 less than” subtracts 7 from the other quantity.
    • CWrong. 7n − 3 swaps the two numbers: n is multiplied by 3, not 7.
    • DWrong. 3(n − 7) subtracts 7 from n before multiplying; the phrase subtracts 7 from 3n.

  6. Which of the following is a prime number?

    1. A39
    2. B49
    3. C51
    4. D53
    Show answer and explanation

    Answer: D. 53 has no factors other than 1 and itself. The others are composite: 39 = 3 × 13, 49 = 7 × 7, 51 = 3 × 17.

    • AWrong. 39 = 3 × 13, so it is not prime.
    • BWrong. 49 = 7 × 7, so it is not prime.
    • CWrong. 51 = 3 × 17 (its digits add to 6, a multiple of 3), so it is not prime.
    • DCorrect. 53 is not divisible by 2, 3, 5 or 7 (the primes up to √53), so it is prime.

  7. Which of the following is equal to 0.00052?

    1. A5.2 × 10⁻⁵
    2. B5.2 × 10⁻⁴
    3. C5.2 × 10⁻³
    4. D5.2 × 10⁴
    Show answer and explanation

    Answer: B. The decimal point moves 4 places to the right to get 5.2, so 0.00052 = 5.2 × 10⁻⁴.

    • AWrong. 10⁻⁵ counts all five digits after the decimal point; the point moves only 4 places.
    • BCorrect. Moving the decimal point 4 places right gives 5.2, so the exponent is −4.
    • CWrong. 10⁻³ counts only the three zeros; the point must move past the 5 as well.
    • DWrong. 10⁴ has the right count but a positive exponent, which makes a large number.

  8. 2/9 ÷ 2/3 =

    1. A4/27
    2. B1/3
    3. C3
    4. D27/4
    Show answer and explanation

    Answer: B. Multiply by the reciprocal of the divisor: 2/9 × 3/2 = 6/18 = 1/3.

    • AWrong. 4/27 multiplies the fractions without flipping the second one.
    • BCorrect. 2/9 × 3/2 = 6/18 = 1/3.
    • CWrong. 3 flips the first fraction instead of the second: 9/2 × 2/3.
    • DWrong. 27/4 flips both fractions: 9/2 × 3/2.

  9. What are the solutions of x² − 5x − 14 = 0?

    1. Ax = 2 or x = 7
    2. Bx = −2 or x = 7
    3. Cx = −7 or x = 2
    4. Dx = −1 or x = 14
    Show answer and explanation

    Answer: B. Factor: x² − 5x − 14 = (x + 2)(x − 7), so x = −2 or x = 7.

    • AWrong. Ignores the signs: (x − 2)(x − 7) = x² − 9x + 14.
    • BCorrect. (x + 2)(x − 7) = x² − 5x − 14, so x = −2 or x = 7.
    • CWrong. Swaps the signs: (x + 7)(x − 2) = x² + 5x − 14, which has +5x.
    • DWrong. Uses the factor pair 1 and 14: (x + 1)(x − 14) = x² − 13x − 14, so the middle term is wrong.

  10. In the figure, lines m and n are parallel. If ∠1 measures 70°, what is the measure of ∠2?

    mn12
    1. A20°
    2. B70°
    3. C110°
    4. D290°
    Show answer and explanation

    Answer: C. ∠1 and ∠2 are on the same side of the transversal, between the parallel lines, so they add to 180°: 180° − 70° = 110°.

    • AWrong. 20° subtracts 70° from 90°; these angles are supplementary, not complementary.
    • BWrong. 70° assumes the angles are equal; same-side interior angles add to 180° instead.
    • CCorrect. Same-side interior angles add to 180°, so ∠2 = 180° − 70° = 110°.
    • DWrong. 290° subtracts 70° from 360°, the total around a point.

  11. (2³)² ÷ 2⁴ =

    1. A2
    2. B4
    3. C8
    4. D32
    Show answer and explanation

    Answer: B. (2³)² = 2⁶ = 64 and 2⁴ = 16, so 64 ÷ 16 = 4. (Or 2⁶⁻⁴ = 2² = 4.)

    • AWrong. 2 adds the exponents in (2³)² (making 2⁵) instead of multiplying them.
    • BCorrect. (2³)² = 2⁶; 2⁶ ÷ 2⁴ = 2² = 4.
    • CWrong. 8 reads 2⁴ as 2 × 4 = 8, so 64 ÷ 8 = 8.
    • DWrong. 32 squares the exponent (2⁹) instead of multiplying 3 × 2.

  12. If 3ˣ⁺¹ = 81, what is the value of x?

    1. A3
    2. B4
    3. C26
    4. D27
    Show answer and explanation

    Answer: A. 81 = 3⁴, so x + 1 = 4 and x = 3.

    • ACorrect. 81 = 3⁴, so x + 1 = 4 and x = 3.
    • BWrong. 4 is the value of x + 1; 1 still has to be subtracted.
    • CWrong. 26 divides 81 by 3 and subtracts 1, treating the exponent as a multiplier.
    • DWrong. 27 divides 81 by 3, treating the exponent as a multiplier.

  13. Solve for x: −3x + 7 ≤ 22

    1. Ax ≥ −5
    2. Bx ≤ −5
    3. Cx ≤ 5
    4. Dx ≥ 5
    Show answer and explanation

    Answer: A. Subtract 7: −3x ≤ 15. Dividing by −3 flips the sign: x ≥ −5.

    • ACorrect. Subtract 7 (−3x ≤ 15), then divide by −3 and flip the sign: x ≥ −5.
    • BWrong. x ≤ −5 divides by −3 but forgets to flip the inequality sign.
    • CWrong. x ≤ 5 drops the negative on −3x and solves 3x ≤ 15.
    • DWrong. x ≥ 5 flips the sign but loses the negative: 15 ÷ (−3) is −5, not 5.

  14. What is the distance between the points (−2, 3) and (4, −5)?

    1. A2√17
    2. B10
    3. C14
    4. D100
    Show answer and explanation

    Answer: B. The horizontal change is 4 − (−2) = 6 and the vertical change is −5 − 3 = −8, so d = √(6² + 8²) = √100 = 10.

    • AWrong. 2√17 uses 4 − 2 = 2 for the horizontal change; subtracting −2 gives 6. √(2² + 8²) = √68 = 2√17.
    • BCorrect. d = √(6² + 8²) = √100 = 10.
    • CWrong. 14 adds the changes (6 + 8) instead of using the Pythagorean theorem.
    • DWrong. 100 is d²; the square root was never taken.

  15. A circle is drawn inside a square with side length 8 so that it touches all four sides, as shown. What is the area of the region inside the square but outside the circle?

    8
    1. A64 − 8π
    2. B32 − 16π
    3. C64 − 64π
    4. D64 − 16π
    Show answer and explanation

    Answer: D. The square’s area is 8² = 64. The circle’s diameter is 8, so r = 4 and its area is π × 4² = 16π. The region is 64 − 16π.

    • AWrong. 64 − 8π subtracts the circle’s circumference (2π × 4) instead of its area.
    • BWrong. 32 − 16π starts from the square’s perimeter (4 × 8 = 32) instead of its area.
    • CWrong. 64 − 64π uses 8 as the radius; 8 is the diameter.
    • DCorrect. Square 8² = 64 minus circle π × 4² = 16π gives 64 − 16π.

Electronics Information: 15 questions

Electricity, circuits, and electronic components. Real test: 15 questions in 10 minutes.

  1. Electric current is measured in which unit?

    1. AVolts
    2. BOhms
    3. CWatts
    4. DAmperes
    Show answer and explanation

    Answer: D. Current, the rate at which electric charge flows, is measured in amperes (amps).

    • AWrong. Volts measure voltage, the electrical pressure that pushes current, not the current itself.
    • BWrong. Ohms measure resistance, the opposition a material gives to current.
    • CWrong. Watts measure power, the rate energy is used (volts × amperes).
    • DCorrect. Current is the flow of electric charge, and its unit is the ampere, or amp.

  2. Which of these materials is the best conductor of electricity?

    1. ARubber
    2. BGlass
    3. CDry wood
    4. DCopper
    Show answer and explanation

    Answer: D. Copper is a metal with many free electrons, so current flows through it easily. Rubber, glass, and dry wood are insulators.

    • AWrong. Rubber is an insulator; it is used to cover wires because current does not flow through it.
    • BWrong. Glass is an insulator; it was long used for the insulators that hold power lines.
    • CWrong. Dry wood has very high resistance and acts as an insulator.
    • DCorrect. Copper is a metal with many free electrons, which is why it is used for household wiring.

  3. What component does the schematic symbol shown represent?

    1. ACapacitor
    2. BInductor
    3. CDiode
    4. DResistor
    Show answer and explanation

    Answer: D. A zigzag line is the standard US symbol for a resistor.

    • AWrong. A capacitor is drawn as two parallel plates with a gap between them.
    • BWrong. An inductor is drawn as a row of loops or humps, like a coil.
    • CWrong. A diode is drawn as a triangle pointing at a straight bar.
    • DCorrect. A zigzag line between two leads is the standard US resistor symbol.

  4. The letters LED stand for:

    1. ALow-energy detector
    2. BLinear electric driver
    3. CLight-emitting diode
    4. DLight-energy divider
    Show answer and explanation

    Answer: C. An LED is a light-emitting diode, a diode that gives off light when current flows through it in the forward direction.

    • AWrong. An LED gives off light rather than detecting it; light is detected by parts such as photodiodes.
    • BWrong. "Linear electric driver" is not a standard component name.
    • CCorrect. LED stands for light-emitting diode, a diode that glows when forward current flows.
    • DWrong. "Light-energy divider" is not a real component; the D stands for diode.

  5. Which component does the schematic symbol shown stand for?

    1. ATransistor
    2. BCapacitor
    3. CFuse
    4. DDiode
    Show answer and explanation

    Answer: D. A triangle pointing at a straight bar is a diode. Conventional current flows in the direction the triangle points.

    • AWrong. A transistor symbol has three leads (base, collector, emitter), usually inside a circle.
    • BWrong. A capacitor is drawn as two parallel plates with a gap.
    • CWrong. A fuse is drawn as an S-shaped line or a small rectangle.
    • DCorrect. A triangle pointing at a bar is a diode; current flows in the direction of the triangle.

  6. Unlike a fuse, a circuit breaker that has tripped:

    1. ACan be reset and used again
    2. BMust be thrown away and replaced
    3. CKeeps letting current flow
    4. DRaises the voltage of the circuit
    Show answer and explanation

    Answer: A. A breaker opens its contacts on overload and can be switched back on once the problem is fixed. A blown fuse must be replaced.

    • ACorrect. A breaker's contacts open on overload and can be reset by flipping the handle back on.
    • BWrong. Having to be replaced is true of a blown fuse, not a breaker.
    • CWrong. A tripped breaker is open, so current stops; that is its purpose.
    • DWrong. A breaker only opens or closes the circuit; it does not change the voltage.

  7. What is a relay?

    1. AA resistor whose value changes with light
    2. BA capacitor that releases charge on a timer
    3. CA diode that gives off light when it conducts
    4. DA switch that is opened or closed by an electromagnet
    Show answer and explanation

    Answer: D. A relay uses a small current through a coil to make a magnetic field that moves switch contacts, letting a small circuit control a larger one.

    • AWrong. A resistor that changes with light is a photoresistor, or photocell.
    • BWrong. A capacitor discharging on a timer describes a timing circuit, not a relay.
    • CWrong. A diode that gives off light is an LED.
    • DCorrect. A relay's coil becomes an electromagnet that pulls switch contacts open or closed.

  8. A hair dryer has a resistance of 12 Ω and runs on 120 V. How much power does it use?

    1. A10 W
    2. B144 W
    3. C1,200 W
    4. D1,440 W
    Show answer and explanation

    Answer: C. P = V² ÷ R = (120 × 120) ÷ 12 = 1,200 W. Also, I = 120 ÷ 12 = 10 A and 120 V × 10 A = 1,200 W.

    • AWrong. 10 is the current in amperes (120 ÷ 12), not the power.
    • BWrong. 144 W squares the resistance (12 × 12) instead of the voltage.
    • CCorrect. P = V² ÷ R = 14,400 ÷ 12 = 1,200 W.
    • DWrong. 1,440 W multiplies volts by ohms (120 × 12), which is not a power formula.

  9. Which change makes an electromagnet stronger?

    1. AReducing the current through the coil
    2. BReplacing the iron core with a plastic core
    3. CReversing the direction of the current
    4. DAdding more turns of wire to the coil
    Show answer and explanation

    Answer: D. An electromagnet's strength grows with the number of turns and the current. Each added turn adds to the magnetic field.

    • AWrong. Less current makes a weaker magnetic field.
    • BWrong. Iron concentrates the magnetic field; plastic does not, so the magnet gets weaker.
    • CWrong. Reversing the current swaps the north and south poles but leaves the strength the same.
    • DCorrect. Each extra turn adds to the magnetic field, so more turns make a stronger electromagnet.

  10. The transformer shown has 100 primary turns and 500 secondary turns. With 24 volts AC on the primary, what is the secondary voltage?

    24 VACPrimary100 turnsSecondary500 turnsOutput
    1. A4.8 V
    2. B24 V
    3. C120 V
    4. D12,000 V
    Show answer and explanation

    Answer: C. Voltage scales with the turns ratio: 24 × (500 ÷ 100) = 120 V.

    • AWrong. 4.8 V uses the turns ratio upside down (24 × 100 ÷ 500); more secondary turns step the voltage up, not down.
    • BWrong. 24 V assumes no change, which is true only when both coils have the same number of turns.
    • CCorrect. The secondary has 5 times as many turns, so 24 V × 5 = 120 V.
    • DWrong. 12,000 V multiplies 24 by 500 without dividing by the 100 primary turns.

  11. Which change increases the resistance of a copper wire?

    1. AUsing a thicker wire of the same length
    2. BUsing a shorter piece of the same wire
    3. CCooling the wire to a lower temperature
    4. DUsing a longer piece of the same wire
    Show answer and explanation

    Answer: D. A wire's resistance rises with its length and falls as it gets thicker. Cooling a metal wire lowers its resistance.

    • AWrong. A thicker wire gives current more room, so its resistance goes down.
    • BWrong. A shorter wire has less resistance, since resistance is proportional to length.
    • CWrong. Cooling a metal lowers its resistance; heating it raises resistance.
    • DCorrect. Resistance is proportional to length, so a longer piece of the same wire has more resistance.

  12. A GFCI (ground-fault circuit interrupter) outlet trips when it senses:

    1. AA difference between the current in the hot and neutral wires
    2. BThe line voltage rising above 120 volts
    3. CTotal current above the breaker's rating
    4. DThe outlet box getting too warm
    Show answer and explanation

    Answer: A. A GFCI compares hot and neutral current. If some current leaks to ground, such as through a person, the two no longer match and it trips.

    • ACorrect. A GFCI compares hot and neutral current; a mismatch means current is leaking to ground, possibly through a person.
    • BWrong. Over-voltage is handled by surge protectors, not by a GFCI.
    • CWrong. Overcurrent is the job of the fuse or circuit breaker; a GFCI can trip at a few thousandths of an amp.
    • DWrong. A GFCI does not sense temperature; it measures current imbalance.

  13. A resistor is marked with color bands brown, black, red (followed by a gold tolerance band). What is its resistance?

    1. A10 Ω
    2. B100 Ω
    3. C1,000 Ω
    4. D10,000 Ω
    Show answer and explanation

    Answer: C. Brown = 1, black = 0, and the red multiplier = × 100. 10 × 100 = 1,000 Ω.

    • AWrong. 10 Ω reads the first two bands but ignores the red multiplier band.
    • BWrong. 100 Ω applies a × 10 multiplier, which is brown's value, not red's.
    • CCorrect. Brown (1), black (0), red (× 100): 10 × 100 = 1,000 Ω.
    • DWrong. 10,000 Ω adds three zeros, which is the orange multiplier, not red.

  14. In the circuit shown, what is the equivalent resistance of R1, R2, and R3?

    +12 VR1 = 4 ΩR2 = 6 ΩR3 = 12 Ω
    1. A0.5 Ω
    2. B2 Ω
    3. C4 Ω
    4. D22 Ω
    Show answer and explanation

    Answer: B. 1/R = 1/4 + 1/6 + 1/12 = 3/12 + 2/12 + 1/12 = 6/12, so R = 2 Ω.

    • AWrong. 0.5 is 6/12, the value of 1/R; it must be inverted to get R.
    • BCorrect. 1/R = 1/4 + 1/6 + 1/12 = 6/12, so R = 12/6 = 2 Ω.
    • CWrong. 4 Ω is R1 alone; parallel resistors combine to less than the smallest one.
    • DWrong. 22 Ω adds the resistors, which is the rule for series, not parallel.

  15. Why is a fuse or circuit breaker placed in the hot wire rather than the neutral wire?

    1. AThe hot wire carries more current than the neutral
    2. BOpening the hot wire disconnects the device from the voltage
    3. CA device in the neutral would not trip on an overload
    4. DThe neutral wire is not part of the complete circuit
    Show answer and explanation

    Answer: B. The same current flows in the hot and neutral wires, so either spot would stop an overload. But opening only the neutral leaves the device connected to 120 V; opening the hot wire removes the voltage.

    • AWrong. In a simple circuit the same current flows in the hot and neutral wires.
    • BCorrect. With the hot wire opened, the device is cut off from 120 V, so it cannot shock anyone who touches it.
    • CWrong. The same overload current flows in the neutral, so a device there would trip; the problem is that the load would stay live.
    • DWrong. The neutral is the return path that completes the circuit back to the source.

Auto Information: 10 questions

How cars work: engine, fuel, electrical, brakes, drivetrain. Real test: 10 questions in 7 minutes.

  1. Which part circulates coolant through the engine and radiator?

    1. AFuel pump
    2. BWater pump
    3. COil pump
    4. DThermostat
    Show answer and explanation

    Answer: B. The water pump, usually driven by a belt, pushes coolant through the engine and radiator. The thermostat only controls when coolant flows to the radiator.

    • AWrong. The fuel pump moves gasoline from the tank to the engine; it does not handle coolant.
    • BCorrect. The belt-driven water pump pushes coolant through the engine block, cylinder head, and radiator.
    • CWrong. The oil pump circulates engine oil to the bearings and other moving parts, not coolant.
    • DWrong. The thermostat is a valve that decides when coolant may flow to the radiator; it does not pump anything.

  2. What is the main purpose of engine oil?

    1. ATo raise the engine's compression pressure
    2. BTo cool the exhaust gases before they exit
    3. CTo clean the fuel before it is burned
    4. DTo reduce friction and wear between moving parts
    Show answer and explanation

    Answer: D. Oil forms a film between moving metal parts so they do not grind against each other. It also helps carry away heat and dirt.

    • AWrong. Compression pressure comes from the piston squeezing the mixture; oil only helps the rings seal.
    • BWrong. Exhaust gases leave through the exhaust system and are not cooled by engine oil.
    • CWrong. Fuel is cleaned by the fuel filter; engine oil does not mix with the fuel in a four-stroke engine.
    • DCorrect. Oil forms a thin film between moving metal parts so they slide instead of grinding, which cuts friction and wear.

  3. What is the correct order of the four strokes in a four-stroke engine?

    1. AIntake, compression, power, exhaust
    2. BIntake, power, compression, exhaust
    3. CCompression, intake, power, exhaust
    4. DIntake, compression, exhaust, power
    Show answer and explanation

    Answer: A. The piston draws in the mixture (intake), squeezes it (compression), is driven down by combustion (power), and pushes out burned gases (exhaust).

    • ACorrect. Intake draws in the air-fuel mixture, compression squeezes it, power is the push from combustion, and exhaust clears the burned gas.
    • BWrong. Power cannot come before compression; the mixture has to be squeezed before it is ignited.
    • CWrong. Compression cannot come first; the cylinder has nothing to squeeze until the intake stroke fills it.
    • DWrong. Exhaust before power would push the mixture out before it burns; exhaust is the last stroke of the cycle.

  4. The oil pressure warning light comes on while you are driving. What should you do?

    1. AKeep driving and change the oil at the next service
    2. BAdd coolant to the radiator right away
    3. CPull over safely and shut off the engine
    4. DTurn on the heater to cool the engine
    Show answer and explanation

    Answer: C. The light means oil is not reaching the engine at a safe pressure. Running without oil pressure can ruin the bearings within minutes, so stop, shut the engine off, and check the oil.

    • AWrong. Waiting for the next service risks serious damage; the light warns of low pressure right now, not a routine oil change.
    • BWrong. Coolant belongs to the cooling system; the oil pressure light is about the lubrication system.
    • CCorrect. Without oil pressure, bearings and other moving parts can be ruined quickly, so stop in a safe place, shut off the engine, and check the oil.
    • DWrong. Running the heater can help an overheating engine, but it does nothing for low oil pressure.

  5. Blue-gray smoke from the exhaust usually means the engine is:

    1. ABurning oil
    2. BBurning coolant
    3. CRunning too rich
    4. DRunning too lean
    Show answer and explanation

    Answer: A. Blue-gray smoke comes from oil getting into the combustion chamber, often past worn rings or valve seals. Coolant makes white smoke and a rich mixture makes black smoke.

    • ACorrect. Blue-gray smoke is oil burning in the cylinders, usually after it slips past worn piston rings or valve seals.
    • BWrong. Burning coolant makes thick white smoke with a sweet smell.
    • CWrong. A rich mixture leaves unburned fuel that comes out as black smoke.
    • DWrong. A lean mixture has extra air; it can cause misfires and overheating but not blue smoke.

  6. The tool shown is used to measure

    .004.008.012.016.020
    1. AEngine oil pressure
    2. BTire tread depth
    3. CBattery state of charge
    4. DSmall gaps between parts
    Show answer and explanation

    Answer: D. This is a feeler gauge: a set of thin steel blades, each marked with its thickness in inches. The blade that just slides into a gap tells how wide the gap is, as when checking valve clearance.

    • AWrong. Oil pressure is read with a pressure gauge connected to an oil passage in the engine.
    • BWrong. Tread depth is measured with a tread-depth gauge that has a sliding probe.
    • CWrong. Battery charge is checked with a voltmeter or a battery hydrometer.
    • DCorrect. Each blade has an exact thickness (.004 in, .008 in, and so on), so the blade that just fits a gap measures it.

  7. A front-wheel-drive car makes a rhythmic clicking noise only when turning sharply while moving. What is the most likely cause?

    1. ALow power-steering fluid
    2. BWorn brake pads
    3. CIncorrect wheel alignment
    4. DA worn outer CV joint
    Show answer and explanation

    Answer: D. Worn outer constant-velocity joints click when they operate at sharp angles. Low power-steering fluid usually causes a whine, not a click.

    • AWrong. Low power-steering fluid usually makes a whining or groaning noise when turning, not a rhythmic click.
    • BWrong. Worn brake pads squeal or grind when braking, not only when turning.
    • CWrong. Bad alignment causes pulling and uneven tire wear, not a clicking noise.
    • DCorrect. Outer CV joints bend to their sharpest angles in tight turns, so a worn one clicks rhythmically then.

  8. A front tire is wearing much faster on its inner edge than anywhere else. What is the most likely cause?

    1. AIncorrect wheel alignment
    2. BOverinflation
    3. CUnderinflation
    4. DUnbalanced wheels
    Show answer and explanation

    Answer: A. Wear on one edge points to alignment (camber or toe). Overinflation wears the center, underinflation wears both edges, and imbalance causes vibration and cupping.

    • ACorrect. Wear on just one edge points to an alignment problem, usually camber or toe that is out of spec.
    • BWrong. Overinflation makes the tread bulge in the middle, which wears the center of the tire.
    • CWrong. Underinflation wears both outer edges, not just the inner one.
    • DWrong. Unbalanced wheels cause vibration and patchy (cupped) wear, not steady wear along one edge.

  9. Which part uses a small current from the ignition switch to send heavy battery current to the starter motor?

    1. AStarter solenoid
    2. BVoltage regulator
    3. CIgnition coil
    4. DAlternator diode
    Show answer and explanation

    Answer: A. The starter solenoid is a heavy-duty relay. A small current energizes its coil, which closes contacts that carry the large starter current and also engages the starter gear.

    • ACorrect. The starter solenoid is a heavy-duty switch: a small current from the ignition switch closes contacts that carry the large starter current.
    • BWrong. The voltage regulator controls the alternator’s output to keep system voltage steady.
    • CWrong. The ignition coil steps voltage up to fire the spark plugs; it has nothing to do with the starter.
    • DWrong. Alternator diodes change the alternator’s AC output to DC for charging; they do not switch starter current.

  10. After braking hard down a long, steep hill, a driver finds the brakes are much less effective. What is the most likely cause?

    1. AThe brake lines filled with air on the way down
    2. BThe tires lost pressure from the heat
    3. CThe brakes have overheated, causing brake fade
    4. DThe master cylinder ran out of brake fluid
    Show answer and explanation

    Answer: C. Long, steady braking overheats the pads, rotors, or fluid, reducing friction (brake fade). Using a lower gear lets the engine help slow the car.

    • AWrong. Air gets into brake lines through a leak or when the system is opened for repair, not from heavy braking.
    • BWrong. Heat makes tire pressure rise slightly; it does not make the tires lose pressure and cut braking.
    • CCorrect. Long, steady braking overheats the pads, rotors, or fluid until friction drops off, which is called brake fade.
    • DWrong. An empty master cylinder comes from a leak and makes the pedal sink to the floor; it is not caused by braking on a hill.

Shop Information: 10 questions

Tools, fasteners, measuring, and shop practices. Real test: 10 questions in 6 minutes.

  1. Which tool checks whether a shelf is perfectly horizontal?

    1. APlumb bob
    2. BTape measure
    3. CTry square
    4. DLevel
    Show answer and explanation

    Answer: D. A level has a bubble vial that centers when the surface is horizontal. A plumb bob checks vertical, not horizontal.

    • AWrong. A plumb bob hangs on a string to find true vertical, not horizontal.
    • BWrong. A tape measure gives lengths, not whether a surface is level.
    • CWrong. A try square checks that two surfaces meet at 90°.
    • DCorrect. A level’s bubble centers between the lines when the surface is horizontal.

  2. Which power tool is best for cutting a curved shape in thin plywood?

    1. ACircular saw
    2. BMiter saw
    3. CTable saw
    4. DJigsaw
    Show answer and explanation

    Answer: D. A jigsaw's narrow, up-and-down blade can follow curves. Circular, miter, and table saws are designed for straight cuts.

    • AWrong. A circular saw has a large, round blade that can only cut straight lines.
    • BWrong. A miter saw makes straight crosscuts at set angles.
    • CWrong. A table saw rips and crosscuts in straight lines.
    • DCorrect. A jigsaw’s narrow blade moves up and down and can be steered along a curved line.

  3. In a nail size such as 16d, what does the "d" stand for?

    1. ADiameter
    2. BDepth
    3. CDrive
    4. DPenny
    Show answer and explanation

    Answer: D. The "d" comes from the old abbreviation for the English penny. A higher penny number means a longer nail; a 16d nail is 3½ inches long.

    • AWrong. The d does not stand for diameter; a nail’s thickness is given separately.
    • BWrong. The penny number tells the nail’s length, not how deep to drive it.
    • CWrong. Drive is not a sizing term; nails are sized by penny number.
    • DCorrect. The d is the old abbreviation for penny; a higher penny number means a longer nail, and a 16d nail is 3½ in long.

  4. The tool shown is used to

    1. ACut curves in thin boards
    2. BShave and smooth the surface of a board
    3. CDrill holes at an exact angle
    4. DScrape old paint off a wall
    Show answer and explanation

    Answer: B. This is a hand plane: a flat sole, a front knob, a rear handle, and a blade set at an angle. It shaves thin layers of wood to flatten and smooth a board.

    • AWrong. Curves are cut with a coping saw or a jigsaw; a plane’s flat sole can only make flat surfaces.
    • BCorrect. The angled blade sticks out a hair below the flat sole and shaves thin curls of wood as the plane is pushed.
    • CWrong. Holes are drilled with a drill and bit; a plane has no turning cutter.
    • DWrong. Paint is removed with a paint scraper or putty knife; a plane is made for shaving wood.

  5. Which screwdriver bit fits the screw head shown?

    1. AHex (Allen)
    2. BPhillips
    3. CSquare
    4. DTorx
    Show answer and explanation

    Answer: D. The recess is a six-pointed star with rounded lobes. That shape takes a Torx bit.

    • AWrong. A hex (Allen) key fits a six-sided recess with straight, flat sides, not rounded lobes.
    • BWrong. A Phillips bit fits a cross-shaped (+) recess.
    • CWrong. A square (Robertson) bit fits a recess with four straight sides.
    • DCorrect. The six rounded lobes of the star-shaped recess match a Torx bit.

  6. The bolt shown is a

    Side viewUnderside of head
    1. AAnchor bolt
    2. BCarriage bolt
    3. CLag bolt
    4. DMachine bolt
    Show answer and explanation

    Answer: B. A smooth, rounded head with a square neck under it identifies a carriage bolt. The square neck bites into the wood so the bolt does not spin while the nut is tightened.

    • AWrong. An anchor bolt is set into concrete, often with a bent L-shaped end, to hold framing down.
    • BCorrect. The domed head and square neck mark a carriage bolt, which is tightened from the nut end only.
    • CWrong. A lag bolt (lag screw) has a hex head and a pointed, coarse wood-screw thread, and uses no nut.
    • DWrong. A machine bolt has a hex or square head that is turned with a wrench, with no dome or square neck.

  7. Which single tool can measure the outside diameter of a pipe, its inside diameter, and the depth of a hole?

    1. AOutside micrometer
    2. BVernier or dial caliper
    3. CTry square
    4. DFeeler gauge
    Show answer and explanation

    Answer: B. A caliper has outside jaws, inside jaws, and a depth rod. A standard outside micrometer measures only outside dimensions.

    • AWrong. An outside micrometer measures only outside sizes; it cannot measure an inside diameter or a depth.
    • BCorrect. A caliper has outside jaws, inside jaws, and a depth rod, so one tool does all three measurements.
    • CWrong. A try square checks right angles; it does not measure diameters.
    • DWrong. A feeler gauge measures small gaps between parts.

  8. In metalworking, "tapping" a hole means:

    1. ACutting internal threads in it
    2. BCutting external threads on a rod
    3. CEnlarging it to an exact size with a reamer
    4. DMarking its center with a punch
    Show answer and explanation

    Answer: A. A tap cuts threads inside a drilled hole so a bolt or screw can thread into it. A die cuts external threads on a rod.

    • ACorrect. A tap cuts threads inside a drilled hole so a bolt or screw can thread into it.
    • BWrong. External threads on a rod are cut with a die.
    • CWrong. Enlarging a hole to an exact size with a smooth finish is reaming.
    • DWrong. Marking the center of a hole is done with a center punch.

  9. A bolt is labeled 3/8-16 × 2. What does the 16 tell you?

    1. AThe length of the bolt in sixteenths
    2. BThe width of the bolt head
    3. CThe strength grade of the steel
    4. DThe number of threads per inch
    Show answer and explanation

    Answer: D. In inch bolt sizes, 3/8 is the diameter, 16 is threads per inch, and 2 is the length in inches.

    • AWrong. The length is the last number, 2 (inches), not the 16.
    • BWrong. Head size is not part of this callout; a 3/8 in bolt head usually takes a 9/16 in wrench.
    • CWrong. Strength grade is shown by marks on the bolt head, not by the size numbers.
    • DCorrect. In 3/8-16 × 2, 3/8 in is the diameter, 16 is the number of threads per inch, and 2 in is the length.

  10. To check a corner for square, a carpenter marks a point 9 ft from the corner along one side and 12 ft along the other. If the corner is exactly 90°, how far apart should the two marks be?

    1. A3 ft
    2. B10.5 ft
    3. C15 ft
    4. D21 ft
    Show answer and explanation

    Answer: C. This is the 3-4-5 rule multiplied by 3: √(9² + 12²) = √225 = 15 ft. 21 ft is the sum of the two sides, and 3 ft is their difference.

    • AWrong. 3 ft is the difference between the two sides (12 − 9).
    • BWrong. 10.5 ft is the average of the two sides, not the diagonal.
    • CCorrect. The marks form a right triangle, so the distance is √(9² + 12²) = √225 = 15 ft, the 3-4-5 rule times 3.
    • DWrong. 21 ft is the sum of the two sides; the diagonal of a right triangle is shorter than that.

Mechanical Comprehension: 15 questions

Levers, pulleys, gears, fluids, and forces, often with a diagram. Real test: 15 questions in 22 minutes.

  1. The tank is filled with water. At which point is the water pressure greatest?

    ABCDwater surface
    1. AA
    2. BB
    3. CC
    4. DD
    Show answer and explanation

    Answer: D. Water pressure depends on depth below the surface, not on sideways position. Point D is the deepest, so the pressure there is greatest.

    • AWrong. A is near the surface, so there is little water above it pressing down.
    • BWrong. B is off to one side, but sideways position does not matter; B is shallower than D.
    • CWrong. C is deeper than A and B but still shallower than D.
    • DCorrect. Pressure depends only on depth below the surface, and D is the deepest point.

  2. A worker pushes a crate 10 ft across a floor with a steady force of 30 lb. How much work does the worker do?

    1. A3 ft·lb
    2. B40 ft·lb
    3. C300 ft·lb
    4. D3,000 ft·lb
    Show answer and explanation

    Answer: C. Work = force × distance = 30 lb × 10 ft = 300 ft·lb.

    • AWrong. 3 ft·lb divides the force by the distance; work is force times distance.
    • BWrong. 40 ft·lb adds the force and the distance instead of multiplying them.
    • CCorrect. Work = force × distance = 30 × 10 = 300 ft·lb.
    • DWrong. 3,000 ft·lb has an extra zero, as if the crate moved 100 ft.

  3. The pinion gear turns clockwise, as shown. Which way does the rack move?

    pinionrack
    1. ATo the left
    2. BTo the right
    3. CUp and down
    4. DIt does not move
    Show answer and explanation

    Answer: A. On a gear turning clockwise, the teeth at the bottom move to the left. Those teeth are meshed with the rack, so they carry it to the left.

    • ACorrect. On a pinion turning clockwise, the bottom teeth move to the left, and they carry the rack with them.
    • BWrong. The top of the pinion moves right, but the rack meshes with the bottom teeth, which move left.
    • CWrong. The pinion slides the rack along its length; nothing in the setup lifts it up and down.
    • DWrong. The pinion is meshed with the rack, so turning the pinion must move the rack.

  4. Wheel A drives wheel B with a crossed belt. Wheel A turns clockwise. How does wheel B turn?

    AB
    1. AClockwise, faster than A
    2. BClockwise, slower than A
    3. CCounterclockwise, slower than A
    4. DCounterclockwise, faster than A
    Show answer and explanation

    Answer: D. A crossed belt makes the driven wheel turn the opposite way, so B turns counterclockwise. B is smaller than A, so it must turn faster to keep up with the belt.

    • AWrong. An open belt would keep the same direction, but this belt is crossed, which reverses the direction.
    • BWrong. Both parts are wrong: the crossed belt reverses the direction, and the smaller wheel turns faster, not slower.
    • CWrong. The direction is right, but a smaller wheel must turn more times to keep up with the same belt, so B is faster.
    • DCorrect. The crossed belt reverses the direction, and B is smaller than A, so B turns counterclockwise and faster.

  5. Force F pushes down on the left end of the bar to lift the load on the right end. At which fulcrum point would the smallest force F lift the load?

    FloadABCDpossible fulcrum points
    1. AA
    2. BB
    3. CC
    4. DD
    Show answer and explanation

    Answer: D. The closer the fulcrum is to the load, the longer the effort arm is compared with the load arm, so less force is needed. Point D is closest to the load.

    • AWrong. A is farthest from the load, giving the shortest effort arm and the longest load arm, so it needs the most force.
    • BWrong. At B the load arm is still longer than the effort arm, so more force is needed than at C or D.
    • CWrong. C is closer to the load than A or B, but D is closer still.
    • DCorrect. With the fulcrum at D, closest to the load, the effort arm is longest compared with the load arm, so F is smallest.

  6. Each frame shown is made of straight bars joined at the corners by single pins that let the bars pivot. Which frame will best keep its shape when pushed sideways at the top?

    ABCD
    1. AA
    2. BB
    3. CC
    4. DD
    Show answer and explanation

    Answer: A. Only frame A is divided into triangles by its diagonal brace. A triangle cannot change shape unless one of its bars changes length, while the other frames can fold over at their pins.

    • ACorrect. The diagonal brace splits frame A into two triangles, and a pinned triangle cannot change shape.
    • BWrong. A square pinned at every corner can lean over into a diamond; nothing braces it.
    • CWrong. A pentagon pinned at its corners can fold; more sides make a frame less rigid, not more.
    • DWrong. A rectangle is just a wider square: without a diagonal it can still lean over at its pins.

  7. A 50-lb crate rests on a level floor. The coefficient of sliding friction between the crate and the floor is 0.3. What horizontal force keeps the crate sliding at a steady speed?

    1. A1.5 lb
    2. B15 lb
    3. C35 lb
    4. D50 lb
    Show answer and explanation

    Answer: B. Friction force = coefficient × weight = 0.3 × 50 = 15 lb. At steady speed the push just equals friction.

    • AWrong. 1.5 lb misplaces the decimal point: 0.3 × 50 is 15, not 1.5.
    • BCorrect. Sliding friction = 0.3 × 50 = 15 lb, and at steady speed the push equals the friction.
    • CWrong. 35 lb subtracts friction from the weight; the push only has to match friction, 15 lb.
    • DWrong. 50 lb is the crate’s weight; a sideways push only has to overcome friction, which is less than the weight.

  8. A 100-lb load hangs from a rope wound on an axle of radius 3 in. The axle is fixed to a wheel of radius 12 in, and force F pulls on a rope wound on the wheel. Ignoring friction, what force F holds the load?

    12 in3 inF100 lb
    1. A25 lb
    2. B33 lb
    3. C100 lb
    4. D400 lb
    Show answer and explanation

    Answer: A. For a wheel and axle, F × wheel radius = load × axle radius: F × 12 = 100 × 3, so F = 25 lb.

    • ACorrect. F × 12 = 100 × 3, so F = 25 lb.
    • BWrong. 33 lb divides the load by the 3-in axle radius alone; the force depends on the ratio 12 ÷ 3 = 4.
    • CWrong. 100 lb ignores the wheel; its larger radius lets a smaller force hold the load.
    • DWrong. 400 lb applies the ratio backwards (100 × 12 ÷ 3), as if F pulled on the axle.

  9. A wooden block floats in fresh water. Salt water is denser than fresh water. When the same block is placed in salt water, it will

    fresh watersalt water?
    1. Afloat higher in the water.
    2. Bfloat lower in the water.
    3. Cfloat at the same level.
    4. Dsink to the bottom.
    Show answer and explanation

    Answer: A. A floating block displaces its own weight of liquid. Salt water weighs more per cubic foot, so a smaller volume of it matches the block’s weight, and the block rides higher.

    • ACorrect. Salt water is denser, so a smaller volume of it matches the block’s weight; the block rides higher.
    • BWrong. Denser water gives more lift for each cubic foot under the surface, so the block needs less depth, not more.
    • CWrong. The block’s weight is the same, but the water is denser, so less of the block has to be under water.
    • DWrong. A block that floats in fresh water gets even more support from denser salt water, so it cannot sink.

  10. A 4,000-lb truck moving at 15 ft/s runs into a parked 2,000-lb car, and the two lock together. How fast do they move just after the collision?

    1. A5 ft/s
    2. B7.5 ft/s
    3. C10 ft/s
    4. D15 ft/s
    Show answer and explanation

    Answer: C. Momentum is conserved: 4,000 × 15 = 60,000 before, and (4,000 + 2,000) × v = 60,000 after, so v = 10 ft/s.

    • AWrong. 5 ft/s uses the car’s share of the total weight (15 × 2,000 ÷ 6,000); the moving truck is 4,000 of the 6,000 lb.
    • BWrong. 7.5 ft/s halves the speed, which would be right only if the truck and car weighed the same.
    • CCorrect. 4,000 × 15 = 60,000, and 60,000 ÷ 6,000 = 10 ft/s.
    • DWrong. 15 ft/s assumes the truck keeps its speed, but its momentum is now shared with the car.

  11. Gears A, B, and C each mesh with the other two. What happens when someone tries to turn gear A clockwise?

    ABC
    1. AThe gears jam and cannot turn
    2. BGear C turns clockwise
    3. CGear C turns counterclockwise
    4. DGears B and C turn counterclockwise
    Show answer and explanation

    Answer: A. If A turns clockwise, B and C must both turn counterclockwise. But B and C also mesh with each other, and two meshed gears must turn in opposite directions, so the gears lock.

    • ACorrect. A clockwise forces B and C both counterclockwise, yet B and C mesh and must turn opposite ways. The contradiction locks the gears.
    • BWrong. C meshes with A, so it could never turn the same way as A.
    • CWrong. That is what A alone would do to C, but B, also meshed with C, would force C to turn the other way.
    • DWrong. A would push both B and C counterclockwise, but B and C mesh with each other and cannot turn the same way.

  12. The strip is brass bonded to steel. Brass expands more than steel when heated. When the strip is heated, what happens to its free end?

    brasssteelclamp
    1. AIt bends down, toward the steel.
    2. BIt bends up, toward the brass.
    3. CIt stays straight and gets longer.
    4. DIt stays straight and gets shorter.
    Show answer and explanation

    Answer: A. The brass on top grows longer than the steel beneath it. The longer layer ends up on the outside of the curve, so the strip bends toward the steel, which is down.

    • ACorrect. Brass grows more than steel, so the brass side becomes the outside of the curve and the strip bends down toward the steel.
    • BWrong. Bending up would put the steel on the outside of the curve, but the brass, which grows more, must be on the outside.
    • CWrong. The two metals grow by different amounts, and since they are bonded together, the strip must curve rather than stay straight.
    • DWrong. Heating makes both metals expand, not shrink.

  13. In the pulley system shown, the rope is tied to the lower block, and its free end is pulled straight up with force F. Ignoring friction and the weight of the pulleys, what force F holds the 210-lb load?

    210 lbF
    1. A52.5 lb
    2. B70 lb
    3. C105 lb
    4. D210 lb
    Show answer and explanation

    Answer: B. Three strands pull up on the lower block: the tied strand and both sides of the lower pulley, including the free end pulled upward. The mechanical advantage is 3, so F = 210 ÷ 3 = 70 lb.

    • AWrong. 52.5 lb divides by 4, but only three strands pull up on the lower block.
    • BCorrect. The tied strand and both sides of the lower pulley (including the free end) pull up: 210 ÷ 3 = 70 lb.
    • CWrong. 105 lb divides by 2, missing that the upward free end also pulls on the lower block.
    • DWrong. 210 lb gives no advantage at all, but the lower block hangs from three strands.

  14. A 10-ft beam is bolted to support A at its left end and rests on support B, 8 ft from A. A 400-lb load rests on the right end of the beam. Ignoring the beam’s weight, how much force does support B carry?

    boltAB400 lb8 ft2 ft
    1. A100 lb
    2. B320 lb
    3. C400 lb
    4. D500 lb
    Show answer and explanation

    Answer: D. Taking turning effects about A: B × 8 = 400 × 10, so B = 500 lb. B carries more than the load because bolt A must pull down with 100 lb to keep the beam from tipping.

    • AWrong. 100 lb is the downward pull the bolt at A must supply, not the force on B.
    • BWrong. 320 lb applies the ratio backwards (400 × 8 ÷ 10).
    • CWrong. 400 lb assumes B carries just the load, but the load sits past B, so B carries more.
    • DCorrect. About A: B × 8 = 400 × 10, so B = 500 lb, with bolt A pulling down 100 lb.

  15. The forearm holds a 10-lb weight 14 in from the elbow. The biceps muscle pulls straight up 2 in from the elbow. Ignoring the forearm’s weight, what force F must the muscle exert to hold the weight still?

    F10 lbelbow2 in14 in
    1. A1.43 lb
    2. B5 lb
    3. C20 lb
    4. D70 lb
    Show answer and explanation

    Answer: D. The elbow is the fulcrum of this third-class lever: F × 2 = 10 × 14 = 140, so F = 70 lb. The muscle is close to the pivot, so it must pull much harder than the weight.

    • AWrong. 1.43 lb applies the arm ratio backwards (10 × 2 ÷ 14); the muscle is on the short arm, so it must pull harder, not softer.
    • BWrong. 5 lb divides the weight by the muscle’s 2-in distance and ignores the weight’s 14-in arm.
    • CWrong. 20 lb multiplies the weight by the muscle’s 2-in distance instead of balancing the turning effects.
    • DCorrect. The elbow is the fulcrum: F × 2 = 10 × 14 = 140, so F = 70 lb.

Assembling Objects: 15 questions

Pick the figure that shows how the parts fit or connect. Real test: 15 questions in 18 minutes.

  1. Which figure best shows how the objects in the first box will look when point A is connected to point B?

    ABAB
    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: A. Point A is at the edge of the circle and point B is at the middle of a side of the triangle. Only one choice joins exactly those two points — the shapes may be turned, which does not change where the line attaches.

    • ACorrect. The line joins the edge of the circle (A) to the middle of a side of the triangle (B), exactly as marked. The shapes are only turned, which doesn't change where the line attaches.
    • BWrong. The line meets the triangle at the center, but B is at the middle of a side.
    • CWrong. The line leaves the circle at the center, but A is at the edge; and the line meets the triangle at the center, but B is at the middle of a side.
    • DWrong. The line leaves the circle at the center, but A is at the edge.

  2. Which figure best shows how the objects in the first box will look when point A is connected to point B?

    ABAB
    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: C. Point A is at the middle of a side of the triangle and point B is at a corner of the triangle. Only one choice joins exactly those two points — the shapes may be turned, which does not change where the line attaches.

    • AWrong. The line leaves the triangle at a corner, but A is at the middle of a side.
    • BWrong. The line leaves the triangle at a corner, but A is at the middle of a side; and the line meets the triangle at the middle of a side, but B is at a corner.
    • CCorrect. The line joins the middle of a side of the triangle (A) to a corner of the triangle (B), exactly as marked. The shapes are only turned, which doesn't change where the line attaches.
    • DWrong. The line meets the triangle at the middle of a side, but B is at a corner.

  3. Which figure best shows how the pieces in the first box will fit together?

    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: D. The loose pieces are two trapezoids that make a rectangle. Only one choice is cut into exactly those pieces at the same size; the others need a piece that is not in the box.

    • AWrong. This rectangle is cut into four rectangles, but the box holds two trapezoids.
    • BWrong. This rectangle is cut into a square and two right triangles, but the box holds two trapezoids.
    • CWrong. This rectangle is cut into three right triangles, but the box holds two trapezoids.
    • DCorrect. This rectangle is cut into two trapezoids: exactly the pieces in the box, at the same size.

  4. Which figure best shows how the pieces in the first box will fit together?

    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: C. The loose pieces are a right triangle and a trapezoid that make a rectangle. Only one choice is cut into exactly those pieces at the same size; the others need a piece that is not in the box.

    • AWrong. This rectangle is cut into four rectangles, but the box holds a right triangle and a trapezoid.
    • BWrong. This rectangle is cut into three right triangles, but the box holds a right triangle and a trapezoid.
    • CCorrect. This rectangle is cut into a right triangle and a trapezoid: exactly the pieces in the box, at the same size.
    • DWrong. This rectangle is cut into a square and two right triangles, but the box holds a right triangle and a trapezoid.

  5. Which figure best shows how the objects in the first box will look when point A is connected to point B?

    ABAB
    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: D. Point A is at the center of the circle and point B is at a corner of the triangle. Only one choice joins exactly those two points — the shapes may be turned, which does not change where the line attaches.

    • AWrong. The line leaves the circle at the edge, but A is at the center.
    • BWrong. The line meets the triangle at the middle of a side, but B is at a corner.
    • CWrong. The line meets the triangle at the center, but B is at a corner.
    • DCorrect. The line joins the center of the circle (A) to a corner of the triangle (B), exactly as marked. The shapes are only turned, which doesn't change where the line attaches.

  6. Which figure best shows how the objects in the first box will look when point A is connected to point B?

    ABAB
    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: D. Point A is at the edge of the circle and point B is at the center of the circle. Only one choice joins exactly those two points — the shapes may be turned, which does not change where the line attaches.

    • AWrong. The line leaves the circle at the center, but A is at the edge.
    • BWrong. The line leaves the circle at the center, but A is at the edge; and the line meets the circle at the edge, but B is at the center.
    • CWrong. The line meets the circle at the edge, but B is at the center.
    • DCorrect. The line joins the edge of the circle (A) to the center of the circle (B), exactly as marked. The shapes are only turned, which doesn't change where the line attaches.

  7. Which figure best shows how the pieces in the first box will fit together?

    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: B. The loose pieces are a square and two right triangles that make a rectangle. Only one choice is cut into exactly those pieces at the same size; the others need a piece that is not in the box.

    • AWrong. This rectangle is cut into three right triangles, but the box holds a square and two right triangles.
    • BCorrect. This rectangle is cut into a square and two right triangles: exactly the pieces in the box, at the same size.
    • CWrong. This rectangle is cut into a right triangle and a trapezoid, but the box holds a square and two right triangles.
    • DWrong. This rectangle is cut into four rectangles, but the box holds a square and two right triangles.

  8. Which figure best shows how the objects in the first box will look when point A is connected to point B?

    ABAB
    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: C. Point A is at a corner of the hexagon and point B is at the middle of a side of the pentagon. Only one choice joins exactly those two points — the shapes may be turned, which does not change where the line attaches.

    • AWrong. The line leaves the hexagon at the middle of a side, but A is at a corner; and the line meets the pentagon at a corner, but B is at the middle of a side.
    • BWrong. The line leaves the hexagon at the middle of a side, but A is at a corner.
    • CCorrect. The line joins a corner of the hexagon (A) to the middle of a side of the pentagon (B), exactly as marked. The shapes are only turned, which doesn't change where the line attaches.
    • DWrong. The line leaves the hexagon at the center, but A is at a corner.

  9. Which figure best shows how the pieces in the first box will fit together?

    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: A. The loose pieces are two right triangles that make a triangle. Only one choice is cut into exactly those pieces at the same size; the others need a piece that is not in the box.

    • ACorrect. This triangle is cut into two right triangles: exactly the pieces in the box, at the same size.
    • BWrong. This triangle is cut into an equilateral triangle and a trapezoid, but the box holds two right triangles.
    • CWrong. This triangle is cut into three triangles, but the box holds two right triangles.
    • DWrong. This triangle is cut into four equilateral triangles, but the box holds two right triangles.

  10. Which figure best shows how the objects in the first box will look when point A is connected to point B?

    ABAB
    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: B. Point A is at the widest corner of the kite and point B is at the middle of a side of the pentagon. Only one choice joins exactly those two points — the shapes may be turned, which does not change where the line attaches.

    • AWrong. The line leaves the kite at the center, but A is at the widest corner.
    • BCorrect. The line joins the widest corner of the kite (A) to the middle of a side of the pentagon (B), exactly as marked. The shapes are only turned, which doesn't change where the line attaches.
    • CWrong. The line meets the pentagon at a corner, but B is at the middle of a side.
    • DWrong. The line meets the pentagon at the center, but B is at the middle of a side.

  11. Which figure best shows how the pieces in the first box will fit together?

    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: C. The loose pieces are four rectangles that make a rectangle. Only one choice is cut into exactly those pieces at the same size; the others need a piece that is not in the box.

    • AWrong. This rectangle is cut into a square and two right triangles, but the box holds four rectangles.
    • BWrong. This rectangle is cut into three right triangles, but the box holds four rectangles.
    • CCorrect. This rectangle is cut into four rectangles: exactly the pieces in the box, at the same size.
    • DWrong. This rectangle is cut into a right triangle and a trapezoid, but the box holds four rectangles.

  12. Which figure best shows how the pieces in the first box will fit together?

    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: B. The loose pieces are two triangles and a rectangle that make a hexagon. Only one choice is cut into exactly those pieces at the same size; the others need a piece that is not in the box.

    • AWrong. This hexagon is cut into three diamonds, but the box holds two triangles and a rectangle.
    • BCorrect. This hexagon is cut into two triangles and a rectangle: exactly the pieces in the box, at the same size.
    • CWrong. This hexagon is cut into a triangle and a five-sided piece, but the box holds two triangles and a rectangle.
    • DWrong. This hexagon is cut into two trapezoids, but the box holds two triangles and a rectangle.

  13. Which figure best shows how the objects in the first box will look when point A is connected to point B?

    ABAB
    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: A. Point A is at the 51° corner of the right triangle and point B is at the center of the circle. Only one choice joins exactly those two points — the shapes may be turned, which does not change where the line attaches.

    • ACorrect. The line joins the 51° corner of the right triangle (A) to the center of the circle (B), exactly as marked. The shapes are only turned, which doesn't change where the line attaches.
    • BWrong. The line leaves the right triangle at the sharpest corner, but A is at the 51° corner.
    • CWrong. The line leaves the right triangle at the middle of the longest side, but A is at the 51° corner.
    • DWrong. The line meets the circle at the edge, but B is at the center.

  14. Which figure best shows how the objects in the first box will look when point A is connected to point B?

    ABAB
    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: C. Point A is at the middle of the shortest side of the rectangle and point B is at the middle of the longest side of the right triangle. Only one choice joins exactly those two points — the shapes may be turned, which does not change where the line attaches.

    • AWrong. The line leaves the rectangle at a corner, but A is at the middle of the shortest side.
    • BWrong. The line meets the right triangle at the square corner, but B is at the middle of the longest side.
    • CCorrect. The line joins the middle of the shortest side of the rectangle (A) to the middle of the longest side of the right triangle (B), exactly as marked. The shapes are only turned, which doesn't change where the line attaches.
    • DWrong. The line meets the right triangle at the 51° corner, but B is at the middle of the longest side.

  15. Which figure best shows how the pieces in the first box will fit together?

    1. A
    2. B
    3. C
    4. D
    Show answer and explanation

    Answer: D. The loose pieces are an equilateral triangle and a trapezoid that make a triangle. Only one choice is cut into exactly those pieces at the same size; the others need a piece that is not in the box.

    • AWrong. This triangle is cut into two right triangles, but the box holds an equilateral triangle and a trapezoid.
    • BWrong. This triangle is cut into three triangles, but the box holds an equilateral triangle and a trapezoid.
    • CWrong. This triangle is cut into four equilateral triangles, but the box holds an equilateral triangle and a trapezoid.
    • DCorrect. This triangle is cut into an equilateral triangle and a trapezoid: exactly the pieces in the box, at the same size.
The ASVAB Practice Exams team

Built and maintained by the ASVAB Practice Exams team. Every question is original, written to a subtest blueprint drawn from the official samples and DoD technical reports, and checked by a second reviewer who answers it without the key. About this site →