Your FREE ASVAB (Armed Services Vocational Aptitude Battery) Practice Test 2026 – 390+ Q&A

Correct answer: An object in motion stays in motion unless a force acts on it

The craft coasts because an object in motion stays in motion unless a force acts on it. This is Newton's first law, the law of inertia: far from any planet nothing pushes or pulls on the craft, so its speed and direction stay the same with the engines off. The idea that "an object in motion stays in motion only while something keeps pushing it" is the old belief that motion needs a steady push, yet the engines are off and the craft keeps going. The idea that "an object in motion stays in motion until it uses up the push given to it" imagines a supply of push stored inside a moving object, which does not exist. The idea that "an object in motion stays in motion until it slows to a stop on its own" is the everyday mistake: objects on Earth slow only because friction and air resistance act on them.

Correct answer: Speed up at a faster rate

The go-kart will speed up at a faster rate. Newton's second law says acceleration equals force divided by mass, so with the same force the smaller mass gains speed faster. "Speed up at a slower rate" describes the heavier truck, not the kart, and "Speed up at a rate that matches the truck" would be true only if the two masses were equal. "Speed up at a rate that slowly drops" is also wrong: a steady force on a fixed mass gives a steady acceleration, so the rate does not fade while the push continues.

Correct answer: Every action force has an equal and opposite reaction force

The swimmer moves forward because every action force has an equal and opposite reaction force, which is Newton's third law. The swimmer pushes the water backward, and the water pushes the swimmer forward just as hard. "Two objects attract each other with a force that depends on their masses" describes gravitation, which explains weight and orbits, not swimming. "An object speeds up in proportion to the net force over its mass" is Newton's second law, which tells how fast a push changes speed but not why pushing backward moves the swimmer forward. "Objects in motion keep their speed and direction unless a force acts on them" is Newton's first law, which explains coasting, not where the forward push comes from.

Correct answer: Light from the sun

Plants get that energy as light from the sun. Chlorophyll absorbs light energy and uses it to join carbon dioxide and water into sugar. Heat from the sun warms the plant, but chlorophyll captures light, not heat, so heat does not power the reaction. Water from the soil is a raw material whose atoms end up in the sugar, but it supplies no energy. The idea of food from the soil is an old mistake: soil supplies minerals that help the plant grow, but plants make their own food, and the soil is not their energy source.

Correct answer: In the leaves

Photosynthesis happens mainly in the leaves, which hold the most chlorophyll and spread out flat to catch sunlight. A green stem can carry out a little photosynthesis, but the work in the stem is mainly support and transport. The work in the roots is to anchor the plant and absorb water and minerals, and the job in the flowers is reproduction.

Correct answer: Carry out photosynthesis to make sugar

In the dark the plant cannot carry out photosynthesis to make sugar, its food, so it burns through its stored sugar and weakens. Photosynthesis needs light energy, and the closet removes it. The plant can still carry out respiration to release energy, which goes on day and night and keeps using up sugar that nothing replaces. Its roots can still carry out osmosis to absorb water, and it can still carry out mitosis to grow taller: plants kept in the dark often grow tall, pale and spindly before they fail.

Correct answer: Group

A vertical column is a group. Elements in the same group have the same number of outer electrons, so they behave alike. A period is a horizontal row, a block is a region of the table named for the sublevel being filled (s, p, d or f), and a series, such as the lanthanide series, is a run of elements along a row.

Correct answer: Na

The symbol for sodium is "Na", from its Latin name natrium, so it does not match the English name. "S" is the tempting first-letter guess, but it stands for sulfur. "Sn" is tin, from the Latin stannum, and "Si" is silicon.

Correct answer: Periods

The horizontal rows are called periods. Moving across a period, the atomic number rises by one from each element to the next, and every element in a row fills the same outer shell. Groups are the vertical columns, blocks are regions of the table named for the sublevel being filled, and orbitals are regions around a nucleus where electrons are likely to be found, not rows of elements.

Correct answer: Metals

Most elements are metals, which fill the left side and center of the periodic table. They tend to be shiny solids that conduct heat and electricity well. Nonmetals sit in the upper right corner, metalloids form a thin staircase between the two regions, and the halogens are a single column, group 17, near the right edge.

Correct answer: Much farther apart and moving more quickly

Gas particles are much farther apart and moving more quickly than liquid particles. They have enough energy to break away from one another, so they travel freely and spread out to fill any container. "Much closer together and moving more slowly" has both points reversed and describes a liquid compared with a gas. "Much farther apart and moving more slowly" gets the spacing right but the speed wrong, and "Much closer together and moving more quickly" gets the speed right but the spacing wrong.

Correct answer: Vaporization

Liquid water turning into steam is vaporization, the change from a liquid to a gas; boiling is vaporization throughout the liquid. Condensation is the reverse, gas turning back into liquid. Sublimation also produces a gas, but it starts from a solid and skips the liquid stage, and melting turns a solid into a liquid.

Correct answer: Freezing

Liquid water becoming ice is freezing, the change from a liquid to a solid. Removing heat slows the particles until they lock into a fixed structure. Melting is the reverse, solid to liquid. Condensation turns a gas into a liquid, and deposition turns a gas directly into a solid, as when frost forms; neither starts from a liquid.

Correct answer: One metal and one nonmetal

An ionic bond most commonly forms between one metal and one nonmetal. The metal gives up electrons to the nonmetal, and the oppositely charged ions attract. Two nonmetals share electrons in covalent bonds, as in water. Two metals are held together by metallic bonding, a sea of shared electrons. One metal and one noble gas rarely react at all, because a noble gas already has a full outer shell.

Correct answer: End up more stable

Atoms bond mainly to end up more stable, usually by filling their outer electron shell. Sharing or transferring electrons lowers their energy, and that lower energy is what makes the bonded atoms more stable. They do not end up more energetic, because bonding releases energy rather than storing it. They do not end up more reactive either: bonded atoms, such as the sodium and chlorine in table salt, are far less reactive than the separate elements. Nor do they end up more massive, because bonding only moves electrons and leaves the mass essentially unchanged.

Correct answer: Vacuole

The vacuole stores water and, when full, presses outward to keep a plant cell firm; in many plant cells it is a large central sac. The cell wall also helps a plant cell keep its shape, but it is a rigid outer layer, not a sac that stores water. The cytoplasm is the jellylike fluid that fills the cell around the organelles, and the nucleus holds the cell's DNA and directs its activities.

Correct answer: A rigid cell wall

A rigid cell wall is the feature found in plant cells but not in typical animal cells. It surrounds the membrane and gives the plant cell extra support and a fixed shape. Animal cells also have a thin cell membrane, which controls what enters and leaves, and many ribosomes, which build proteins, so neither belongs to plants alone. Many lysosomes are, if anything, a feature of animal cells; plant cells use their large vacuole for much of that clean-up work.

Correct answer: Cytoplasm

The jellylike fluid that fills a cell and holds its organelles is the cytoplasm. It fills the space inside the membrane and lets materials move around the cell. Cell sap is the watery fluid stored inside a plant cell's vacuole, not the fluid around the organelles. The nucleus is itself an organelle, the control center that holds the DNA, and the cell membrane is the thin outer boundary that wraps around the cytoplasm rather than filling the cell.

Correct answer: The nervous system

The nervous system uses nerves and the brain to send electrical signals and control the body's responses. The endocrine system also helps control the body, but it works through hormones released into the blood, not through nerves. The immune system defends the body against disease, and the skeletal system supports and protects the body, with the skull and spine shielding the brain and nerves rather than sending signals.

Correct answer: Small intestine

Most nutrient absorption takes place in the small intestine, whose long, folded lining passes digested nutrients into the blood. The large intestine absorbs mainly water and salts from what is left over. The salivary glands start the digestion of starch in the mouth, and the gastric glands in the stomach lining release acid and enzymes; both secrete digestive juices rather than absorbing nutrients.

Correct answer: The muscular system

The muscular system includes the muscles that move the arms and legs; muscles contract and pull on bones to produce movement. The skeletal system supplies the bones the muscles pull on, but it does not include the muscles. The nervous system sends the signals that tell muscles to contract, and the lymphatic system carries lymph and helps fight infection.

Correct answer: Planets circle the Sun and shine with reflected light

What sets the planets apart is that planets circle the Sun and shine with reflected light, while stars make their own light and heat through nuclear fusion. So "planets circle the Sun and shine with their own light" gets the orbit right but describes a star's light, not a planet's. "Planets stay fixed in the sky and shine with reflected light" gets the light right, but planets do not stay fixed: they wander slowly against the background stars from night to night, which is where the word planet, meaning wanderer, comes from. "Planets stay fixed in the sky and shine with their own light" has both points wrong.

Correct answer: Mars

Mars is the Red Planet; iron oxide, a rusty mineral in its soil, gives it a reddish color. Jupiter has a large reddish storm, the Great Red Spot, but the planet itself is banded in tan and white. Venus is covered in bright yellowish-white clouds, and Mercury is a gray, cratered world.

Correct answer: A year

Earth completes one orbit around the Sun in about a year, and that trip is what defines a year. A day is the time Earth takes to spin once on its axis, and a month is roughly the time the Moon takes to go through its phases. A season is only about a quarter of the orbit; the seasons come from the tilt of Earth's axis as it travels around the Sun.

Correct answer: A bigger force to give the same acceleration

The heavier crate requires a bigger force to give the same acceleration. Newton's second law, force equals mass times acceleration, means that more mass needs more force for the same change in motion, so the worker's best effort is not enough. Choosing "a smaller force to give the same acceleration" reverses the law. Both "a smaller force to give a greater acceleration" and "a similar force to give a greater acceleration" are backward too: compared with the lighter crate, a smaller or similar force on the heavier crate gives a smaller acceleration, not a greater one.

Correct answer: Action and reaction forces act in opposite directions

The balloon shows that action and reaction forces act in opposite directions, Newton's third law: the balloon squeezes the air out one way, and the air pushes the balloon the other way. The forces do come in pairs, but "action and reaction forces act in pairs that cancel out" is a common mistake: they act on different objects, one on the air and one on the balloon, so they cannot cancel. Saying that "action and reaction forces act in sequence" or that "action and reaction forces act in unequal amounts" is also wrong, because the two forces arise together at the same instant and are always equal in size.

Correct answer: Liquid

A sample that takes the shape of its container but keeps a fixed volume is a liquid. Its particles stay close together yet can slide past one another, so it flows into the shape of the container without spreading upward. A solid keeps its own shape, and a gas or plasma spreads out to fill the whole container.

Correct answer: Speed up and hit the walls more frequently

Heating makes the gas particles speed up and hit the walls more frequently, and those harder, more frequent collisions are what raise the pressure. The particles do not swell up and push the walls more firmly; a particle's size does not change with temperature. They do not gain more mass and push harder on the walls, because heating adds energy, not matter. Nor do they break into more pieces and hit the walls: the number of particles in the sealed flask stays the same, and only their speed rises.

Correct answer: Ionic bonding

When a metal gives up an electron to a nonmetal, the compound is held together by ionic bonding. The transfer creates a positive ion and a negative ion that attract each other strongly. Covalent bonding would mean the atoms share electrons instead of transferring them. Metallic bonding holds metal atoms to one another, not a metal to a nonmetal, and hydrogen bonding is a weak attraction between molecules, not the bond that holds this compound together.

Correct answer: Mitochondria

Bean-shaped organelles that release energy from sugar are mitochondria, which carry out cellular respiration to power the cell. Chloroplasts do the reverse job in plant cells, capturing light energy to make sugar rather than breaking it down. Lysosomes break down worn-out parts and wastes, not sugar for energy, and ribosomes build proteins.

Correct answer: Excretory system

The organs that filter waste from the blood and make urine, the kidneys, belong to the excretory system. The digestive system also gets rid of waste, but only the undigested food left in the intestines, not waste filtered from the blood. The circulatory system carries waste to the kidneys but does not filter it out, and the respiratory system removes carbon dioxide through the lungs rather than making urine.

Correct answer: 6 protons

An atomic number of 6 means each atom contains 6 protons; the atomic number always equals the number of protons, and it identifies the element as carbon. The number of neutrons can vary between isotopes, so 6 neutrons is not what the atomic number counts. Protons and neutrons together, the nucleons, give the mass number, which is 12 for the most common carbon atom, not 6 nucleons. Carbon's six electrons fill only two shells, not 6 electron shells.

Correct answer: Photosynthesis

Algae release oxygen as a byproduct of photosynthesis: like land plants, they use light energy to turn carbon dioxide and water into sugar and give off oxygen. Respiration runs the other way, using up oxygen to release energy from sugar. Transpiration is the loss of water vapor from a plant's leaves, and chemosynthesis is how some bacteria at deep-sea vents make food from chemical energy instead of light, without giving off oxygen.

Correct answer: Lose energy and come closer together

Dew forms because the vapor particles lose energy and come closer together as they touch the cold grass; the slower particles cling to one another as liquid drops, which is condensation. "Gain energy and spread farther apart" describes evaporation, the reverse change. "Gain energy and come closer together" is wrong because cooling removes energy rather than adding it, and "Lose energy and spread farther apart" is wrong because particles that slow down move closer together, not farther apart.

Correct answer: Gas giants

Jupiter and Saturn are the gas giants, huge planets made mostly of hydrogen and helium with no solid surface to stand on. The ice giants, Uranus and Neptune, are made largely of water, ammonia and methane ices. The terrestrial planets, Mercury, Venus, Earth and Mars, are small and rocky, and dwarf planets such as Pluto are small, icy and rocky worlds.

Correct answer: Covalent bonds

Atoms that share electrons are joined by covalent bonds, so the bonds inside a water molecule are covalent. Ionic bonds form when electrons are transferred from a metal to a nonmetal. Hydrogen bonds are real, but they are weaker attractions between neighboring water molecules, not the bonds inside one molecule. Metallic bonds hold metal atoms together.

Correct answer: $20

The shopper saves $20. To find 25% of $80, multiply 0.25 by 80, which gives 20. $60 is the sale price after the discount (75% of $80), not the amount saved. $25 treats the 25% as 25 dollars. $3.20 comes from dividing 80 by 25 instead of taking 25% of 80.

Correct answer: 90%

The soldier answered 90% correctly: 36 divided by 40 is 0.9, and 0.9 is 90%. 96% takes one point off 100% for each of the 4 missed questions, but on a 40-question quiz each question is worth 2.5 points. 36% simply repeats the number of correct answers as if the quiz had 100 questions. 88% is close, but 36 divided by 40 is exactly 0.9.

Correct answer: $60

The new price is $60. A 20% increase on $50 is 0.20 times 50, or $10, and $50 plus $10 is $60. $10 is only the amount of the increase, not the new price. $70 comes from adding $20, treating the 20% as dollars. $40 comes from subtracting the $10 instead of adding it.

Correct answer: 36

The hall served 36 vegetarian meals, because 0.15 times 240 is 36. 16 comes from dividing 240 by 15 instead of multiplying by 15%. 204 is the number of meals that were not vegetarian, 240 minus 36. 24 is 10% of 240, not 15%.

Correct answer: 36

Last month the dealership sold 36 cars. This month's 45 is 125% of last month's total, so 45 divided by 1.25 gives 36 (check: 25% of 36 is 9, and 36 plus 9 is 45). The answer 60 divides 45 by 0.75, as if this month were 25% below last month; 56 adds 25% to this month's 45 instead of reversing the increase; and 9 is only the size of the increase, not last month's total.

Correct answer: 6 cups

The baker needs 6 cups of sugar. Flour went from 3 to 9 cups, three times as much, so sugar must also triple, from 2 to 6 cups. The 8 cups answer adds the same 6 cups to the sugar instead of scaling it; 13.5 cups turns the ratio upside down, as if there were 3 cups of sugar for every 2 of flour; and 18 cups multiplies the 9 cups of flour by 2 but never divides by 3.

Correct answer: 56

There are 56 enlisted soldiers. The ratio gives 8 enlisted soldiers for every officer, so 7 officers times 8 equals 56. The answer 49 reads 1 to 8 as 1 officer in every group of 8 people, which leaves only 7 enlisted per officer; 15 adds 7 and 8 instead of multiplying; and 9 is just the size of one officer's group (1 plus 8).

Correct answer: 100 miles

The towns are 100 miles apart. Each map inch stands for 25 miles, so 4 inches times 25 miles per inch equals 100 miles. The 29 miles answer adds 4 and 25, 125 miles counts 5 inches instead of 4, and 85 miles multiplies only the 20 in 25 by 4 and then adds the 5; only 4 times the full 25 miles applies the scale to every inch on the map.

Correct answer: 30 gallons

The blend needs 30 gallons of white paint. Red went from 2 parts to 20 gallons, a factor of 10, so white goes from 3 parts to 30 gallons. The 10 gallons answer stops at that scale factor; 21 gallons adds to the white the same 18 gallons that were added to the red instead of multiplying; and 50 gallons is the red and white together (5 parts times 10).

Correct answer: 12 pumps

It takes 12 pumps. Three pumps fill one tank in the given time, so filling four tanks in that same time needs four times as many pumps: 3 times 4 equals 12. The 6 pumps answer adds 3 pumps because the tank count rose by 3 instead of scaling; 4 pumps assumes one pump per tank; and 16 pumps multiplies the 4 tanks by 4, the sum of the ratio's terms (3 plus 1), instead of by 3 pumps per tank.

Correct answer: 165 miles

The truck travels 165 miles. Distance equals speed times time, so 55 miles per hour for 3 hours is 55 times 3, which is 165 miles. The 155 miles answer drops the 1 carried from 5 times 3 in the ones place, 58 miles adds the 3 hours to the speed, and 180 miles rounds the speed up to 60 miles per hour.

Correct answer: 15 miles per hour

The cyclist averages 15 miles per hour. Average speed is distance divided by time, so 60 miles divided by 4 hours equals 15 miles per hour. The 4 miles per hour answer divides the 240 minutes by the 60 miles, which gives minutes per mile rather than a speed; 12 miles per hour divides by 5 hours; and 20 miles per hour divides by 3.

Correct answer: 200 miles

The trains are 200 miles apart. Moving in opposite directions, they separate at 40 plus 60, or 100 miles per hour, and in 2 hours that adds up to 200 miles. The 100 miles answer stops at the combined speed and never multiplies by the 2 hours; 80 miles counts only the slower train's distance; and 40 miles uses the difference in speeds (20 miles per hour), which applies only to trains traveling in the same direction.

Correct answer: 60 miles per hour

The driver must hold 60 miles per hour. Speed equals distance divided by time, so 240 miles divided by 4 hours equals 60 miles per hour. The 6 miles per hour answer drops a zero in the division, 50 miles per hour would take 4.8 hours, and 65 miles per hour about 3.7 hours.

Correct answer: 3 miles

The jogger covers 3 miles. Thirty minutes is half an hour, so 6 miles per hour times 0.5 hour equals 3 miles. The 1.8 miles answer writes 30 minutes as 0.3 hour, 5 miles divides the 30 minutes by the speed of 6, and 0.2 miles divides the speed of 6 by the 30 minutes.

Correct answer: $100

The account earns $100 in interest. Simple interest is principal times rate times time: $1,000 times 0.05 times 2 equals $100. The $50 answer is only one year of interest; $25 divides one year's $50 of interest by the 2 years instead of multiplying; and $150 is three years of interest instead of two.

Correct answer: $80

The loan accrues $80 in one year. Four percent is 0.04, and $2,000 times 0.04 equals $80. The $800 answer writes 4% as 0.4, $500 divides $2,000 by 4 instead of taking 4% of it, and $2,080 is the amount owed after a year, principal plus interest, rather than the interest alone.

Correct answer: $90

The investment earns $90. Simple interest is principal times rate times time: $500 times 0.06 times 3 equals $90. The $590 answer is the balance after 3 years rather than the interest, $95.51 compounds the interest each year ($500 times 1.06 three times is about $595.51, which is $95.51 more than the $500), and $30 is only one year of interest.

Correct answer: 12.0%

The annual rate was 12.0%. The interest was $896 minus $800, or $96, and $96 divided by the $800 principal is 0.12, which is 12.0%. The 10.7% answer divides the $96 by the ending balance of $896 instead of the starting $800; 8.3% turns the division upside down ($800 divided by $96 is about 8.3); and 9.3% makes both slips, dividing the ending balance of $896 by the $96 (about 9.3).

Correct answer: 12 feet

There are 12 feet in 4 yards. One yard equals 3 feet, so 4 times 3 gives 12 feet. The 36 feet answer multiplies by 9, the number of square feet in a square yard; 1 1/3 feet divides 4 by 3 instead of multiplying, converting in the wrong direction; and 7 feet adds 4 and 3 instead of multiplying.

Correct answer: 20 quarts

The tank holds 20 quarts. Each gallon is 4 quarts, so 5 gallons times 4 equals 20 quarts. The 80 quarts answer multiplies by 16, the number of cups in a gallon; 9 quarts adds 5 and 4; and 1.25 quarts divides 5 by 4, converting in the wrong direction.

Correct answer: 250 centimeters

The rope is 250 centimeters long. One meter is 100 centimeters, so 2.5 times 100 equals 250 centimeters. The 205 centimeters answer reads 2.5 meters as 2 meters and 5 centimeters; 25 centimeters multiplies by 10, as if a meter held only 10 centimeters; and 0.025 centimeters divides by 100 instead of multiplying.

Correct answer: 3 hours

The meeting lasts 3 hours. An hour has 60 minutes, so 180 divided by 60 equals 3 hours. The 1.8 hours answer treats an hour as 100 minutes; 18 hours divides by 10 instead of 60; and 2 hours accounts for only 120 of the 180 minutes.

Correct answer: 6 pounds

The crate weighs 6 pounds. A pound is 16 ounces, so 96 divided by 16 equals 6 pounds. The 8 pounds answer divides by 12, as if a pound had 12 ounces the way a foot has 12 inches; 9.6 pounds divides by 10 as if the units were metric; and 0.96 pounds divides by 100, as if a pound held 100 ounces.

Correct answer: 85

The average score is 85. The three scores add to 255, and 255 divided by 3 tests is 85. The 84 answer does not equal 255 divided by 3, 80 is only the lowest of the three scores, and 82.5 averages only the 80 and the 85 and leaves out the 90.

Correct answer: 48 pounds

The four boxes weigh 48 pounds in total. The total is the average times the number of boxes, 12 times 4, which is 48 pounds. The 12 pounds answer repeats the average as if it were the total, 36 pounds multiplies by 3 boxes instead of 4, and 16 pounds adds 4 to 12.

Correct answer: 30 minutes

The average daily trip is 30 minutes. The five times add to 150 minutes, and 150 divided by 5 days equals 30 minutes. The 150 minutes answer stops at the total, 37.5 minutes divides by 4 instead of 5, and 40 minutes takes the middle value of the list as written (30, 35, 40, 25, 20) without first putting the times in order.

Correct answer: One third

The worker can paint one third of the fence. Finishing in 6 hours means one sixth of the fence each hour, so 2 hours covers two sixths, which reduces to one third. The answer one sixth counts only a single hour, one half compares the 2 hours worked with the 4 hours still left instead of with the whole job, and one fourth puts the 2 hours over 2 plus 6 (two eighths) instead of over the 6 hours the whole job takes.

Correct answer: 2 hours

Together the hoses take 2 hours. Each fills one fourth of the pool per hour, so together they fill one half of the pool per hour and finish in 2 hours. The 0.5 hours answer reports that combined rate of one half pool per hour as if it were the time; 4 hours is one hose's time, as if the second hose added nothing; and 8 hours adds the two times instead of combining the rates.

Correct answer: 4 hours

Six workers need 4 hours. The job takes 3 times 8, or 24 worker-hours, and 24 divided by 6 workers is 4 hours. The 16 hours answer doubles the time as if more workers slowed the job down, 8 hours keeps the original time as if the size of the crew made no difference, and 5 hours subtracts the 3 extra workers from the 8 hours instead of scaling the time.

Correct answer: 20%

The discount is 20%. The price dropped by $400 minus $320, which is $80, and $80 divided by the original $400 is 0.20, or 20%. The 80% answer is the share of the price still paid, 125% divides the original $400 by the sale price of $320, and 25% divides the $80 by the sale price of $320 instead of the original $400.

Correct answer: 60 pages

The recruit must read 60 pages a day. Splitting 300 pages evenly over 5 days gives 300 divided by 5, which is 60 pages. The 50 pages answer divides by 6 days instead of 5, 6 pages drops a zero from the quotient, and 75 pages divides by 4, counting the days between the first and the fifth instead of the 5 reading days.

Correct answer: 62.5%

The sandbags on hand are 62.5% of the total needed. Dividing 90 by 144 gives 0.625, which is 62.5%. The 37.5% answer is the share still missing (54 of 144); 0.625% leaves the decimal 0.625 without multiplying by 100; and 0.375% makes both slips, writing the missing share of 0.375 as a percent without multiplying by 100.

Correct answer: 18 gallons

The car needs 18 gallons. It gets 360 divided by 12, or 30 miles per gallon, so 540 miles takes 540 divided by 30, which is 18 gallons. The 30 gallons answer stops at the miles-per-gallon rate, 45 gallons divides 540 by the 12 gallons instead of by the rate, and 8 gallons sets up the proportion upside down (360 divided by 540, times 12).

Correct answer: 5 pounds

The batch contains 5 pounds of salt. A 1 to 9 ratio makes 10 equal parts with 1 part salt, so the salt is one tenth of 50, or 5 pounds. The 45 pounds answer is the water, 5.6 pounds treats the salt as one ninth of the whole batch (50 divided by 9, rounded), and 10 pounds stops at the number of parts in the ratio.

Correct answer: 8

Each squad has 8 soldiers. Dividing 48 soldiers into 6 equal squads gives 48 divided by 6, which is 8. The answer 7 uses 6 times 7, which is only 42 and leaves 6 soldiers over; 9 would need 54 soldiers; and 6 repeats the number of squads.

Correct answer: 1,008

The warehouse receives 1,008 boxes. Seven pallets of 144 boxes is 7 times 144: 7 times 100 is 700, 7 times 40 is 280, and 7 times 4 is 28, which add to 1,008. The 1,050 answer rounds 144 up to 150 to make the multiplication easier but never takes back the 6 extra boxes on each pallet, 1,152 multiplies by 8 pallets instead of 7, and 1,200 makes both slips, using 8 pallets of 150.

Correct answer: 1,350 square feet

The area is 1,350 square feet. A rectangle's area is length times width, so 30 feet times 45 feet equals 1,350 square feet. The 150 square feet answer is the perimeter (2 times 30 plus 2 times 45), 1,200 square feet multiplies 30 by 40 and drops the 5, and 135 square feet loses the zero from 30 (3 times 45).

Correct answer: 40 meters

The garden needs 40 meters of fencing. The perimeter is 2 times 12 plus 2 times 8, or 24 plus 16, which is 40 meters. The 96 meters answer is the area (12 times 8), 32 meters doubles the length but adds the width only once, and 28 meters doubles the width but adds the length only once.

Correct answer: $12

The total is $12. Three cans at $2 cost $6 and two loaves at $3 cost $6, so the bill is $6 plus $6, or $12. The $5 answer adds one price of each item ($2 plus $3), $25 multiplies the item count (3 plus 2) by the price total ($2 plus $3), and $36 multiplies all four numbers together.

Correct answer: $720

The worker earns $720. Weekly pay is the hourly rate times the hours, $18 times 40, which is $720. The $72 answer multiplies by 4 and forgets the zero in 40, $408 multiplies only the 10 of the 18 by 40 and then tacks on the 8, and $58 adds 18 and 40 instead of multiplying.

Correct answer: Five eighths

Five eighths of the pizza remains. Eating 3 of 8 equal slices leaves 5 slices, or five eighths. The answer three eighths is the part eaten, three fifths compares the slices eaten with the slices left instead of with the whole pizza, and five elevenths adds the 3 eaten slices to the 8 in the denominator.

Correct answer: 16

The board makes 16 pieces. Dividing 12 feet by three fourths of a foot is 12 times 4/3, which is 16. The 9 answer multiplies 12 by three fourths instead of dividing, 144 converts the 12 feet to inches and stops there without dividing by the 9 inches in each piece, and 4 divides 12 by the 3 of three fourths but never multiplies by the 4.

Correct answer: $6

The shopper gets $6 in change. Change is the amount paid minus the cost, $20 minus $14, which is $6. The $16 answer borrows for the ones place but never reduces the tens, $14 subtracts the smaller digit from the larger in each column (4 minus 0, then 2 minus 1), and $34 adds the two amounts.

Correct answer: 7

There are 7 groups, because 28 students divided into groups of 4 is 28 / 4 = 7. Answering 4 mistakes the size of each group for the number of groups, 8 groups of 4 would need 32 students, and 6 groups of 4 would hold only 24 students.

Correct answer: 480 cubic feet

The volume is 480 cubic feet, because volume is length times width times height: 10 x 6 x 8 = 480. Multiplying only the length and width gives the floor area, so 60 cubic feet is wrong; adding the three dimensions (10 + 6 + 8) gives 24 cubic feet; and 376 cubic feet is the surface area, 2 x (60 + 80 + 48) = 376 square feet, not the space inside the room.

Correct answer: $32

Each person pays $32, because the $96 bill split three ways is 96 / 3 = 32. Splitting the bill between only two people gives $48, and $30 and $36 are near 32 but do not make three equal shares of $96 (3 x 30 = 90, 3 x 36 = 108).

Correct answer: 20

The recruit does 20 push-ups in the fourth minute: starting from 8 in the first minute and adding 4 for each of the next three minutes gives 8 + 4 + 4 + 4 = 20. Multiplying the starting 8 by the 4 minutes gives 32, adding 4 for all four minutes (8 + 4 x 4) gives 24, and 56 is the total for all four minutes rather than the count in the fourth.

Correct answer: 12 gallons

The driver adds 12 gallons. A tank one fourth full already holds 16 / 4 = 4 gallons, so 16 - 4 = 12 gallons fill the remaining three fourths. The answer 4 gallons is the fuel already in the tank, 3 gallons takes three fourths of those 4 gallons instead of three fourths of the whole tank, and 16 gallons is the whole tank, ignoring the 4 gallons already in it.

Correct answer: 1,500

The factory makes 1,500 widgets a week: 250 per day times 6 operating days is 250 x 6 = 1,500. Counting a five-day work week gives 250 x 5 = 1,250, 1,200 misreads 250 as 200 (200 x 6), and 1,750 counts a full 7-day week (250 x 7).

Correct answer: Plentiful

Abundant most nearly means plentiful: there is a large supply, more than enough of something. 'Scarce' is the opposite, describing too little; 'redundant' means repetitive or no longer needed, which is not the same as plentiful; and 'abandoned' only looks like abundant and means left behind or deserted.

Correct answer: Empty

Vacant most nearly means empty, with no one occupying the space. 'Vague' looks similar but means unclear; 'quiet' describes a lack of noise, which an occupied room can also have; and 'taken' describes a seat or room already in use, the opposite of vacant.

Correct answer: Hide

Conceal most nearly means hide, to keep something out of sight. 'Reveal' is the opposite, to show; 'seal' means to close something up tightly, and a sealed jar can still sit in plain view; and 'cancel' only resembles conceal in sound and means to call something off.

Correct answer: Unfriendly

Hostile most nearly means unfriendly, showing open dislike or opposition. 'Hospitable' looks similar but means welcoming to guests, nearly the opposite; 'defensive' describes protecting yourself from criticism or attack rather than turning against others; and 'impatient' means unwilling to wait.

Correct answer: Industrious

Diligent most nearly means industrious, putting steady, careful effort into work. 'Intelligent' sounds similar but describes mental ability, not effort; 'negligent' means careless about duties, nearly the opposite; and 'indulgent' means giving in easily to wishes or pleasures.

Correct answer: Weariness

Fatigue most nearly means weariness, the worn-out feeling that follows hard work or lack of rest. 'Dizziness' is a spinning, unsteady feeling; 'laziness' is an unwillingness to work, not the result of working hard; and 'soreness' is pain in the muscles, which can come with fatigue but is not the same thing.

Correct answer: Stubborn

Obstinate most nearly means stubborn, refusing to change an opinion or course of action. 'Obscure' looks similar but means unclear or little known; 'obedient' means willing to follow orders, nearly the opposite; and 'hesitant' means slow to act out of doubt, which is uncertainty rather than firm refusal.

Correct answer: Essential

Vital most nearly means essential, something that cannot be done without. 'Desirable' means worth wanting, but a desirable thing may still be done without; 'optional' is the opposite, left to choice; and 'visible' only begins like vital and means able to be seen.

Correct answer: Shrink

The best antonym for expand is shrink, to become smaller. 'Extend' and 'unfold' both describe spreading out or growing longer, so they are close to expand in meaning; 'expend' looks similar but means to spend or use up.

Correct answer: Descend

The best antonym for ascend is descend, to move downward. 'Elevate' means to raise, which is close to ascend in meaning; 'advance' means to move forward, not down; and 'dissent' sounds like descend but means to disagree.

Correct answer: Stingy

The best antonym for generous is stingy, unwilling to give or spend. 'Lavish' means giving or spending freely, which is close to generous; 'kindly' describes a warm, good-natured person, also close to generous; and 'gentle' only begins like generous and means mild or soft.

Correct answer: Permanent

The best antonym for temporary is permanent, lasting indefinitely. 'Momentary' means lasting only a moment, which is close to temporary; 'temporal' looks similar but means related to time or to worldly matters; and 'temperate' also begins like temporary but means mild or moderate, as in a temperate climate.

Correct answer: Fearless

The best synonym for brave is fearless, ready to face danger. 'Reckless' means acting without thought for danger, which is carelessness rather than courage; 'cautious' means careful to avoid risk, nearly the opposite; and 'boastful' means bragging, which can sound bold without being brave.

Correct answer: Quick

The best synonym for rapid is quick, moving or happening at high speed. 'Rabid' and 'vapid' only look like rapid: rabid means infected with rabies or fanatical, and vapid means dull and lifeless; 'steep' describes a sharp slope, so a steep rise is a sharp one, not necessarily a fast one.

Correct answer: Gigantic

The best synonym for enormous is gigantic, extremely large in size. 'Numerous' means great in number, not in size; 'generous' means giving freely; and 'infamous' means well known for something bad, a sense that belongs to the related noun enormity rather than to enormous.

Correct answer: Tired

The best synonym for weary is tired, worn out from effort or lack of rest. 'Wary' looks almost the same but means watchful and cautious; 'teary' means close to crying; and 'dizzy' means unsteady, with the feeling that things are spinning, which is not the same as being worn out.

Correct answer: Beforehand

The prefix pre- means beforehand, so a preview is a look at something before it is shown in full. 'Afterward' is the meaning of post-, as in postwar; 'throughout' is the meaning of per-, as in pervade; and 'underneath' is the meaning of sub-, as in subway.

Correct answer: Badly

The prefix mis- means badly or wrongly, so to misjudge is to judge badly. 'Overly' is the meaning of over-, as in overcook; 'partly' is the meaning of semi-, as in semiconscious; and 'again' is the meaning of re-, as in rebuild.

Correct answer: Free of

The suffix -less means without, or free of, so harmless means free of harm. 'Full of' is the meaning of -ful, the opposite; 'less of' reads the suffix as the word less, but harmless means no harm at all, not a smaller amount; and 'fond of' is the meaning of -phile, as in bibliophile.

Correct answer: The doer of an action

The suffix -er names the doer of an action, so a teacher is a person who teaches. 'The object of an action', the one who receives it, is the meaning of -ee, as in employee; 'the result of an action' is the meaning of -ment, as in payment; and 'the site of an action' is the meaning of -ory or -ery, as in factory or bakery.

Correct answer: Not fair

Adding un- makes unfair, which means not fair, because un- turns a word into its negative. 'Partly fair' is what semi- would add, as in semiconscious; 'overly fair' is what over- would add, as in overconfident; and 'fair before' is the meaning pre- would add, as in prepaid.

Correct answer: Full of

The suffix -ful means full of, so hopeful means full of hope. 'Free of' is the meaning of -less, the opposite; 'fond of' is the meaning of -phile, as in bibliophile; and 'act of' is the meaning of -tion or -ment, as in creation or movement.

Correct answer: Again

The prefix re- means again, so to rebuild is to build again. 'After' is the meaning of post-, as in postwar; 'under' is the meaning of sub-, as in submarine; and 'apart' is a meaning of dis-, as in disassemble.

Correct answer: Able to be

The suffix -able means capable of being acted on, so readable means capable of being read. 'Having no' is the meaning of -less, as in harmless; 'quality of being' is the meaning of -ness or -ity, as in kindness or clarity; and 'full of' is the meaning of -ful, as in hopeful.

Correct answer: Carry

The root port means carry, so to transport is to carry something from one place to another. 'Cross' belongs to the prefix trans-, meaning across, not to port; 'throw' comes from the root ject, as in eject; and 'pull' comes from the root tract, as in tractor.

Correct answer: Look

The root spect means look, so to inspect is to look at something closely. 'Hear' is another sense word, but it is the meaning of the root aud, as in audience; 'wait' comes from the everyday sense of expect, not from the root itself; and 'hold' is the meaning of the root tain, as in retain.

Correct answer: Water

The root aqua means water, so an aquarium is a tank of water for fish and plants. 'Fish' are what an aquarium usually holds, but the root for fish is pisc, not aqua; 'blue' comes from aqua's later use as a color name, not from the root's meaning; and 'earth' is the meaning of terra or geo.

Correct answer: Speak

The root dict means say or speak, so to dictate is to speak words for someone else to record. 'Write' is what the listener does and comes from the root scrib, as in scribble; 'teach' relates to the root doc, as in doctrine; and 'read' relates to the root leg, as in legible.

Correct answer: Unable to be seen

Invisible most nearly means unable to be seen, because in- means not and vis means see. 'Able to be seen' is the meaning of visible, the word without its prefix; 'seen from inside' reads in- as inside, a sense it has in words such as inhale but not here; and 'seen from far off' is the idea of tele-, as in telescope.

Correct answer: Life

The root bio means life, so biology is the study of living things. 'Study' is the meaning of the ending -ology, not of bio; 'book' is the meaning of the look-alike root biblio, as in bibliography; and 'plant' is the meaning of the root phyto, as in phytoplankton.

Correct answer: Hand

The root manu means hand, so a manual task is done by hand. 'Make' comes from the second half of manufacture, the root fact, not from manu; 'work' describes manual labor in general but is not what the root means; and 'many' only looks like manu and is the meaning of multi, as in multiply.

Correct answer: Bitterly cold

In this sentence frigid most nearly means bitterly cold, because the soldiers shivered and put on heavy coats. 'Stiffly formal' is another real sense of frigid, used for a cold manner, but nothing in the sentence describes anyone's behavior; 'overly crowded' and 'dimly lit' describe space and light, and neither would make the soldiers shiver.

Correct answer: Reserved

In this sentence reticent most nearly means reserved, inclined to keep quiet, because Marcus is contrasted with his talkative brother and rarely spoke. 'Resentful' only looks like reticent and means bitter about being treated unfairly; 'distracted' and 'uninformed' could explain one silent meeting, but neither is the opposite of talkative, which the word unlike calls for.

Correct answer: Strenuous

In this sentence arduous most nearly means strenuous, demanding great effort, which is why the hikers needed several rest breaks. 'Lengthy' fits the sentence loosely, but a long trail is not necessarily a hard one; 'hazardous' means dangerous, which rest breaks would not address; and 'ardent' looks similar but means passionate.

Correct answer: Refilled

In this sentence replenished most nearly means refilled: the heavy rain brought the dry reservoirs back up to full, and then past full until they overflowed. Drained is the opposite of what the rain did; polluted means made dirty, and nothing in the sentence says the water was spoiled; and repaired means fixing damage, which the sentence never describes.

Correct answer: Sensible

Prudent most nearly means sensible: a prudent person uses good judgment and thinks ahead before acting, like a prudent saver who plans for emergencies. Reckless is the opposite; hesitant describes someone slow to act out of doubt, not someone acting wisely; and modest describes someone humble about their abilities, a different quality.

Correct answer: Shy

Timid most nearly means shy: a timid person lacks confidence and is easily frightened. Bold is the opposite; sly, which looks similar, describes someone sneaky or cunning; and weak describes a lack of strength rather than a lack of courage.

Correct answer: Peak

Summit most nearly means peak, the highest point of a mountain or hill. The bottom is the lowest part of the mountain, a ridge is a long, narrow line of high ground rather than its single top point, and a slope is the inclined side that climbers go up to reach the summit.

Correct answer: Scanty

Meager most nearly means scanty, describing an amount too small to be enough, as in a meager meal. Ample is the opposite; shabby describes something worn out or in poor condition rather than small in amount; and eager, which looks similar, means keen or enthusiastic.

Correct answer: Peaceful

The best synonym is peaceful, since serene describes a calm, untroubled state, like a serene lake at dawn. Serious and sincere look and sound similar but mean solemn and honest; cheerful describes a happy, upbeat mood, which a serene person may or may not have, so it is not the same quality.

Correct answer: Solid

The best synonym is solid, because sturdy describes something strongly built that holds up under force, like a sturdy table. Fragile is the opposite; stubborn describes an unwilling attitude, not physical strength; and heavy refers to weight, since a light object can still be sturdy.

Correct answer: Loss

The best antonym is loss, because a loss means being beaten while a victory means winning. Triumph means nearly the same as victory, a battle is the contest itself that ends in either a win or a loss, and effort is the work put in, not the outcome.

Correct answer: Modern

The best antonym is modern, because modern means belonging to the present day while ancient means belonging to the distant past. Antique and primitive both describe old things, so they sit close to ancient rather than opposite it, and classic describes something of lasting quality, whether old or new.

Correct answer: Below

The prefix sub- means below, so a submarine is a vessel that travels below the surface of the sea. Above is the meaning of super-, as in superstructure; across is the meaning of trans-, as in transatlantic; and without is the meaning of non-, as in nonstop.

Correct answer: A person who practices something

The suffix -ist indicates a person who practices something, so an artist is someone who makes art and a cyclist is someone who rides. A person who receives something is the meaning of -ee, as in payee; a place where goods are produced is the meaning of -ery, as in bakery; and a place where supplies are stored is the meaning of -ary, as in granary.

Correct answer: Between

The prefix inter- means between, so an interstate highway runs between states. Within is the meaning of the look-alike prefix intra-, as in intramural; before is the meaning of pre-, as in preview; and through is the meaning of dia-, as in diameter.

Correct answer: The act or result of doing something

The suffix -tion indicates the act or result of doing something, so creation is the act of creating or the thing created. A person or thing that does something is the meaning of -er or -or, as in creator; a person or party that receives something is the meaning of -ee, as in payee; and the study or science of something is the meaning of -ology, as in biology.

Correct answer: Hear

The root audi means hear, so something audible can be heard, as in audio and audience. Watch comes from the roots vis and spect, as in vision and spectator; speak comes from dict and loqu, and touch comes from tact, as in tactile.

Correct answer: Earth

The root geo means earth, so geography is the study of the earth and its features. Life comes from the root bio, light comes from photo, and star comes from astro, as in biology, photograph, and astronomy.

Correct answer: Unconvinced

In this sentence skeptical most nearly means unconvinced, because the detective doubted nearly everything the witness said and was not persuaded by it. Indifferent would mean the detective did not care what she said, impatient would mean the detective wanted her to hurry up, and unfriendly describes a cold manner toward her rather than doubt about her words.

Correct answer: Honeybees matter because they pollinate crops that people eat

The main idea is that honeybees matter because they pollinate crops that people eat: the passage says that without pollination many fruits, vegetables, and nuts could not grow. 'Honeybees matter because they make honey that people enjoy' reverses the opening point that bees do far more than make honey. 'Honeybees carry pollen that sticks to them as they gather nectar' is a detail about how pollination happens, not the main idea. 'Honeybees feed a whole community with honey that they make' misreads the last sentence, where the hive feeds a community through the crops it pollinates, not through honey.

Correct answer: Lighthouses warn distant ships to avoid hazards at sea

The main point is that lighthouses warn distant ships to avoid hazards at sea: the paragraph describes the light that lets ships far from shore see the signal and steer clear of hidden rocks. 'Lighthouses are older than most ships' picks up only the phrase for centuries; the paragraph is about what lighthouses do, not how old they are. 'Ships sail at night to stay clear of the hidden rocks' is never stated; it is the light that sweeps at night, and nothing says ships choose to sail then. 'Hidden rocks make the waters near shore deadly for ships' overstates background that explains why lighthouses are needed; it is not what the paragraph is about.

Correct answer: Why Recycling Makes Sense

The best title is 'Why Recycling Makes Sense', because every sentence gives a benefit of recycling: less trash in landfills, saved raw materials, and lower energy use. 'How Recycling Plants Work' is never discussed; the passage says nothing about how recycled goods are processed. 'Why Recycling Fills Up Landfills' reverses the first sentence, which says recycling reduces the trash sent to landfills. 'How Cities Enforce Recycling Rules' is too narrow, since the rule that residents separate their recyclables appears only in the last sentence, as a result of the benefits.

Correct answer: Desert animals avoid the heat and come out at night

The passage is mainly about how desert animals avoid the heat and come out at night: they stay hidden in burrows while the sun blazes and emerge to hunt when darkness brings cooler air. 'Foxes are the most common hunters found in the desert' is never stated; foxes are just one animal in a list. 'The desert sun is hot enough to harm most living things' stretches the background about daytime heat into a claim the passage does not make. 'Desert animals stay in the cool shade and sleep at night' reverses the passage, since night is when they come out to hunt.

Correct answer: Anxious about arriving late

Maria most likely feels anxious about arriving late: she frowns, taps her foot, and keeps checking the time while the bus runs ten minutes behind and her interview starts in half an hour. 'Relieved about arriving early' misreads the detail that she reached the stop early; the late bus has since wiped out that head start. 'Calm about the slow bus' is the opposite of her frowning and foot tapping. 'Confused about the bus route' has no support, since nothing suggests she is unsure where the bus goes.

Correct answer: The family enjoyed their evening together without power

You can infer that the family enjoyed their evening together without power, since the children called it one of the best nights they could remember after an evening of stories and card games by candlelight. 'The family would prefer living without power from now on' stretches one good night into a lasting choice the passage never suggests. 'The family was frightened by the storm and the darkness' and 'The family was upset that the storm ruined their plans' both run against the happy ending, and no plans are ever mentioned.

Correct answer: He was hardworking and committed to his job

The passage suggests he was hardworking and committed to his job: he arrived early every day, asked questions, took careful notes, stayed late, and earned public praise from the manager. 'He was anxious and slow to learn his duties' misreads his questions and notes as worry and struggle rather than effort. 'He was hoping to ask his boss for a raise' is never suggested; the passage never mentions pay. 'He was too slow to finish his work for the day' misreads his staying late, which the praise shows was dedication, not falling behind.

Correct answer: A storm is on its way

A storm is on its way: the sky turns deep gray, the wind whips through the trees, the air grows heavy, and people hurry inside to close their windows. 'Night is on its way' would explain a darkening sky but not the whipping wind or the rush to shut windows. 'An earthquake is on its way' picks up on the quiet birds but ignores the gray sky and wind. 'A heat wave is on its way' fits the heavy, still air but not the dark sky and strong wind.

Correct answer: To inform readers about the importance of drinking water

The author most likely wrote this passage to inform readers about the importance of drinking water: it states that water is essential, lists the jobs water does in the body, and describes what happens when people drink too little. 'To warn readers that a lack of drinking water is deadly' overstates the passage, which mentions only feeling tired, dizzy, or unable to concentrate. 'To show readers how drinking water carries nutrients to cells' takes one detail from a list as the whole purpose. 'To help readers compare drinking water with other drinks' does not fit, because no other drink is mentioned.

Correct answer: To urge readers to take care around a pool

The author's main purpose is to urge readers to take care around a pool: the passage opens with a warning never to run, then tells readers to walk, watch their step, and follow the lifeguard. 'To teach readers how to become a pool lifeguard' misreads the mention of the lifeguard, whose instructions readers are told to follow. 'To tell readers about an injury at a pool' misreads the warning that a fall can cause injury; no actual injury is described. 'To explain to readers why a wet pool deck is slippery' takes the supporting reason as the purpose, when the passage uses it to persuade readers to walk.

Correct answer: A mood of tension and suspense

The author is trying to create a mood of tension and suspense: the bridge groans, the river churns far below, a plank wobbles, and Sarah grips the rope with her heart pounding. 'A mood of comfort and safety' is the opposite of these danger signals. 'A sense of loneliness and sadness' misreads Sarah crossing alone; the details point to fear of falling, not grief. 'A sense of fun and playfulness' does not fit a scene in which she does not dare look down.

Correct answer: To spark interest and introduce the main topic

The author begins this way to spark interest and introduce the main topic: the vivid picture of a future morning draws readers in, and the next sentence announces that the article will explore the technologies behind it. 'To show cars and kitchens like these are the norm today' misreads the word imagine and the phrase may soon, which show these things do not exist yet. 'To describe what the author cooks and eats' takes the imagined kitchen literally; the kitchen in the passage cooks for you. 'To warn about costs and the dangers of technology' reverses the tone, since the article calls these technologies exciting.

Correct answer: To recount a personal experience and the lesson learned

The author's purpose is to recount a personal experience and the lesson learned: the passage tells in the first person how volunteering changed the author and ends with the lesson that small acts of kindness matter. 'To persuade readers to adopt and care for homeless pets' assumes a call to action the passage never makes. 'To explain how to feed and walk the animals at a shelter' takes the list of weekend tasks as instructions, which the passage does not give. 'To argue that homeless pets need more food and care' is never stated; the author describes helping the animals but makes no appeal on their behalf.

Correct answer: Build and repair muscle

According to the passage, proteins help the body build and repair muscle, stated directly in the list of food groups. 'Supply and store energy' borrows the role the passage gives to grains, which supply energy. 'Provide vitamins and fiber' borrows the role of fruits and vegetables, which provide vitamins, and the passage never mentions fiber. 'Digest and absorb foods' is never mentioned in the passage.

Correct answer: Sunday

According to the passage, the library is closed all day on Sunday, stated plainly in the last sentence. Saturday is the tempting choice because the library closes early that day, but it is still open until five in the afternoon. Tuesday and Thursday fall in the Monday through Friday stretch, when the library is open from nine in the morning until eight in the evening.

Correct answer: Warmth from the sun

According to the passage, warmth from the sun causes water to evaporate: heat from the sun lifts water from oceans and lakes into the air. 'Cooling of the air' gets the process backward, since cooling is what turns the vapor into clouds after it has evaporated. 'Rain from the clouds' is how water falls back to earth at the end of the cycle. 'Movement of the air' is never mentioned in the passage.

Correct answer: Fit the back panel into the grooves

According to the directions, the step that comes immediately after attaching the bottom shelf is to fit the back panel into the grooves, which the passage introduces with the word then. 'Screw the bottom shelf into the side panels' is the step itself, not the one after it. 'Lay the side panels flat on the floor' is the first step, and 'Tighten the screws on the shelf' belongs to the final step, which comes after the back panel is in place.

Correct answer: They eat harmful insects

According to the passage, spiders are helpful because they eat harmful insects, including pests that damage crops and spread disease. 'They rarely bite people' is true according to the passage, but it explains why spiders are harmless, not why they are helpful. 'They pollinate garden crops' confuses spiders with insects such as bees and is never stated. 'They fear most humans' reverses the passage, which says some people fear spiders.

Correct answer: Even small amounts of exercise can improve health

The main idea is that even small amounts of exercise can improve health: the passage builds to the point that even ten-minute walks several times a day add up to real benefits. 'Exercise strengthens the heart and can help sleep' repeats benefits listed in the first sentence, which are supporting details. 'Most busy adults can rarely find the time to exercise' overstates the passage, which says only that many adults say they are too busy. 'Walking can work better than other exercise' is never claimed; walking is offered as an easy example, not compared with anything.

Correct answer: Proud and delighted

James feels proud and delighted about his report card: a wide grin spreads across his face when he sees his high grades, and he rushes to show his parents. 'Nervous and frightened' describes how he felt only before opening it, when his hands trembled. 'Disappointed and upset' does not fit a row of high grades, and 'Calm and uninterested' does not fit someone who rushes to the kitchen calling for his parents.

Correct answer: To persuade readers to purchase a truck

The author's main purpose is to persuade readers to purchase a truck, shown by sales phrases such as once-in-a-lifetime chance and unbeatable power and the push to visit a dealer today. 'To show readers how a truck engine works' mistakes a sales claim about power for an explanation of engines. 'To give readers the latest truck prices' treats the ad as a news report, when the low prices are offered as a reason to buy and no prices are listed. 'To warn readers that truck prices are about to rise' misreads the urgency, which says the trucks will sell out, not that prices will go up.

Correct answer: It shut down and was left empty long ago

You can conclude that the factory shut down and was left empty long ago: its windows are broken, it is chained shut, weeds grow through the lot, and its sign is faded and rusted. 'It still employs a small crew of workers' ignores the chained gates, which show no one works there now. 'It closed last week when workers went on strike' does not fit the weeds and rust, which take a long time to develop, and no strike is mentioned. 'It was sold and will reopen next month' has no support in the passage.

Correct answer: Frozen lakes

According to the passage, the ice originally came from frozen lakes, where companies cut large blocks in winter. 'Insulated storehouses' is where the ice was kept after it was cut, and 'ice delivery wagons' carried it to homes during the year, so neither is where it came from. 'Local ice factories' are never mentioned; the passage says the blocks were cut from lakes, not made.

Correct answer: 81

The value is 81, because 3 to the fourth power means four factors of 3: 3 x 3 x 3 x 3 = 9 x 9 = 81. The value 18 adds the two squares, 9 + 9, instead of multiplying them. The value 12 multiplies the base by the exponent (3 x 4) instead of multiplying four factors of 3. The value 64 swaps the base and the exponent, giving 4 x 4 x 4.

Correct answer: 6x

Combining like terms works only on the coefficients: 5 + 3 - 2 = 6, and the x stays to the first power, so the result is 6x. 10x adds all three coefficients and ignores the minus sign on 2x. 6x^3 gets the coefficient right but multiplies the x's together as if the terms were a product, which raises the power. 10x^3 makes both of those slips at once.

Correct answer: 12

sqrt(144) asks for the number that, multiplied by itself, gives 144. Since 12 times 12 = 144, the answer is 12. 72 halves 144, treating a square root as division by 2. 13 is a misremembered square: 13 times 13 = 169, not 144. 14 is another misremembered square: 14 times 14 = 196, not 144.

Correct answer: 8

Subtracting 7 from both sides isolates x: x = 15 - 7 = 8, and the check 8 + 7 = 15 confirms it. 22 adds 7 to 15 instead of subtracting it. -8 subtracts in the wrong order, working out 7 - 15. -22 makes both mistakes, adding the 7 and also flipping the sign.

Correct answer: x squared plus 5x plus 6

Multiplying every term of the first factor by every term of the second gives x squared plus 2x plus 3x plus 6, and combining 2x and 3x leaves x squared plus 5x plus 6. 'x squared plus 6' multiplies only the first terms and the last terms and drops the two middle products. 'x squared plus 6x plus 6' uses the product 3 times 2 for the middle coefficient instead of the sum 3 plus 2. 'x squared plus x plus 6' subtracts 2x from 3x instead of adding them.

Correct answer: 42

Seven factorial equals 7 times 6 times 5 factorial, so dividing by 5 factorial leaves 7 times 6, which is 42. 35 multiplies 7 by 5, as if the 5 were a factor left over after cancelling. 13 adds 7 and 6 instead of multiplying them. 7 cancels the 6 along with 5 factorial, which would be the answer to 7 factorial divided by 6 factorial.

Correct answer: 180 degrees

The three interior angles of every triangle add up to 180 degrees. 360 degrees is the angle sum of a quadrilateral, which has four sides. 540 degrees is the angle sum of a pentagon, found from (5 - 2) times 180. 60 degrees is the size of each single angle in an equilateral triangle, not the total of all three.

Correct answer: 18

Exponents come before multiplication: 3 squared is 9, and 2 times 9 = 18. 36 doubles the 3 first and then squares 6, which is the value of (2x)^2 rather than 2x^2. 11 adds 2 to 9 instead of multiplying. 6 multiplies 2 by 3 and ignores the exponent altogether.

Correct answer: 12

In prime factors, 24 = 2^3 times 3 and 36 = 2^2 times 3^2. The factors they share are 2^2 and 3, and 4 times 3 = 12, so the greatest common factor is 12. 6 uses each shared prime only once; it divides both numbers but is not the greatest such factor. 72 is the least common multiple, the smallest number that both 24 and 36 divide into. 3 keeps the shared 3 but leaves out the shared 2^2.

Correct answer: 3/4

The greatest common factor of 18 and 24 is 6, and dividing both by 6 gives 3/4. 4/3 flips the fraction, putting the denominator on top. 2/3 divides 18 by 9 but 24 by 8, using a different divisor on the top and the bottom. 3/2 makes both of those slips: it flips the fraction to 24 over 18 and then divides 24 by 8 but 18 by 9.

Correct answer: 10 pi

Circumference is 2 times pi times the radius, so 2 times pi times 5 = 10 pi. 25 pi is pi times 5 squared, the area of the circle rather than the distance around it. 50 pi mixes the two formulas, 2 times pi times the radius squared. 7 pi adds 2 and 5 instead of multiplying them.

Correct answer: -15

Adding two negative numbers gives a negative result whose size is the sum of the two sizes: 6 + 9 = 15, so the sum is -15. 15 adds the sizes correctly but drops the negative signs. -54 multiplies 6 by 9 instead of adding them. 54 is the product of the two numbers, since a negative times a negative is positive, but the question asks for a sum.

Correct answer: 7

4x means 4 times x, so dividing both sides by 4 gives x = 28 / 4 = 7, and 4 times 7 = 28 checks. 24 subtracts 4 from 28, treating 4x as 4 + x. 32 adds 4 to 28 instead of dividing. 112 multiplies 28 by 4 instead of dividing by it.

Correct answer: 30

The area of a triangle is one half times base times height, so 1/2 times 10 times 6 = 30. 60 multiplies base by height but forgets the one half. 16 adds the base and the height, 10 + 6, instead of multiplying. 32 is 2 times (10 + 6), the perimeter formula for a rectangle.

Correct answer: One eighth

A negative exponent means take the reciprocal: 2 to the negative third power is 1 over 2 cubed, which is 1/8, so the value is 'One eighth'. 'Negative eight' treats the negative exponent as a minus sign in front of 2 cubed. 'Eight' drops the negative from the exponent and gives plain 2 cubed. 'Negative one eighth' takes the reciprocal correctly but then wrongly makes the result negative.

Correct answer: (x + 3)(x - 3)

x^2 - 9 is a difference of squares, x^2 - 3^2, so it factors as (x + 3)(x - 3); multiplying back gives x^2 - 3x + 3x - 9 = x^2 - 9. (x - 3)(x - 3) uses the same sign twice and multiplies out to x^2 - 6x + 9. (x + 9)(x - 9) uses 9 instead of its square root and gives x^2 - 81. (x - 9)(x - 9) makes both slips and gives x^2 - 18x + 81.

Correct answer: 14

Order of operations does multiplication before addition: 2 times 5 = 10, then 4 + 10 = 14. 30 works left to right, adding 4 + 2 first and then multiplying by 5. 10 does the multiplication 2 times 5 but stops there and never adds the 4. 13 multiplies 4 by 2 and then adds 5, pairing the wrong numbers.

Correct answer: 28

A square has four equal sides, so its perimeter is 4 times 7 = 28. 49 is 7 squared, the area of the square. 14 doubles the side, counting only two of the four sides. 11 adds 4 to 7 instead of multiplying.

Correct answer: x > 8

Adding 5 to both sides gives x > 3 + 5, so the solution is x > 8; adding the same number to both sides does not change the direction of an inequality. x < 8 reverses the inequality, which only happens when both sides are multiplied or divided by a negative number. x ≥ 8 wrongly includes 8, but 8 - 5 = 3, and 3 is not greater than 3. x ≤ 8 reverses the direction and also includes the boundary.

Correct answer: 3

In slope-intercept form, y = mx + b, the slope m is the coefficient of x, so the slope here is 3. 2 is b, the y-intercept, where the line crosses the y-axis. -2/3 is the x-intercept, found by setting y = 0 and solving 3x + 2 = 0. 2/3 divides the intercept 2 by the coefficient 3, which gives neither the slope nor an intercept.

Correct answer: 11

sqrt(49) = 7 and sqrt(16) = 4, so the sum is 7 + 4 = 11. 65 adds 49 and 16 and never takes the square roots. 28 multiplies the two roots, 7 times 4, instead of adding them. 3 subtracts the roots, 7 - 4, instead of adding them.

Correct answer: 17

A prime number has exactly two factors, 1 and itself. Every whole number between 13 and 17 has other factors, while 17 does not, so 17 is the next prime. 14 is the very next number, but it equals 2 times 7. 19 is prime, but 17 comes before it. 11 is prime, but it comes before 13, not after it.

Correct answer: 3x + 12

The distributive property multiplies 3 by each term inside the parentheses: 3 times x plus 3 times 4 gives 3x + 12. 3x + 4 multiplies only the x and leaves the 4 untouched. x^3 + 12 writes 3 times x as x^3, which actually means x times x times x. x^3 + 4 makes both of those mistakes.

Correct answer: 1/2

0.5 is five tenths, 5/10, and dividing the top and bottom by 5 gives 1/2. 1/5 reads 'point five' as one fifth. 1/20 treats 0.5 as five hundredths, 5/100. 5/9 is the fraction for the repeating decimal 0.555 and so on, not for 0.5.

Correct answer: 64

The volume of a cube is the edge length cubed: 4 times 4 times 4 = 64. 16 squares the edge, which gives the area of one face. 12 multiplies the edge by the exponent, 4 times 3, instead of cubing it. 81 swaps the base and the exponent and works out 3 to the fourth power.

Correct answer: 27

Multiplying both sides by 3 undoes the division: x = 9 times 3 = 27, and 27 divided by 3 = 9 checks. 3 divides 9 by 3 instead of multiplying. 1/3 solves 3 divided by x = 9 instead, working out 3 / 9. 12 adds 3 to 9 instead of multiplying by 3.

Correct answer: 39

Square first, then subtract: 8 squared = 64 and 5 squared = 25, and 64 - 25 = 39. 9 subtracts first and then squares, (8 - 5) squared. 89 adds the squares, 64 + 25, instead of subtracting them. 6 doubles each number instead of squaring it, 16 - 10.

Correct answer: Five thirds

A reciprocal swaps the numerator and the denominator, so the reciprocal of three fifths is 'Five thirds'; as a check, 3/5 times 5/3 = 1. 'Negative three fifths' is the opposite of three fifths, not its reciprocal. 'Negative five thirds' is the negative reciprocal, the one used for perpendicular slopes. 'Two fifths' is the amount that must be added to three fifths to make 1.

Correct answer: 60 degrees

The three angles of an equilateral triangle are equal and total 180 degrees, so each one is 180 / 3 = 60 degrees. 180 degrees is the total of all three angles, not the size of one. 120 degrees is each exterior angle of an equilateral triangle. 90 degrees is a right angle, which an equilateral triangle does not have.

Correct answer: x^5

When powers of the same base are multiplied, the exponents are added: x^2 times x^3 = x^(2 + 3) = x^5. x^6 multiplies the exponents, which is the rule for raising a power to a power. 2x^5 adds the exponents correctly but also adds the unwritten coefficients 1 and 1, which multiplying does not do. 2x^6 makes both of those slips at once.

Correct answer: 12

Absolute value is the distance from zero on the number line, so the absolute value of negative 12 is 12. -12 keeps the negative sign, but a distance cannot be negative. 1/12 is the reciprocal, which absolute value does not involve. -1/12 is the reciprocal of negative 12, which confuses absolute value with taking a reciprocal.

Correct answer: 18

The diameter runs all the way across the circle through the center, so it is twice the radius: 2 times 9 = 18. 9 is the radius itself, mistaken for the diameter. 11 adds 2 to the radius instead of multiplying. 4.5 halves the radius instead of doubling it.

Correct answer: 4

Undo the steps in reverse order: subtract 3 from both sides to get 2x = 8, then divide both sides by 2 to get x = 4. 8 subtracts the 3 but never divides by 2. 7 adds 3 instead of subtracting it, getting 2x = 14 and then x = 7. 14 adds the 3 and also skips the division.

Correct answer: 1000

10 to the third power means 10 times 10 times 10, which is 1000: a 1 followed by three zeros. 30 multiplies 10 by 3 instead of using 3 as an exponent. 13 adds 10 and 3. 59049 swaps the base and the exponent and works out 3 to the tenth power.

Correct answer: 12

The multiples of 4 are 4, 8, 12, 16 and the multiples of 6 are 6, 12, 18; the first number on both lists is 12. 6 takes the larger number, which works only when the smaller number divides it, and 6 is not a multiple of 4. 2 is the greatest common factor of 4 and 6, not a multiple. 10 adds 4 and 6, and 10 is not a multiple of 4 or 6.

Correct answer: 16

The parentheses mean the whole number negative 4 is squared: negative 4 times negative 4 = 16, because a negative times a negative is positive. -16 keeps the negative sign, which would only be right for -4^2 written without parentheses. 8 doubles 4 instead of squaring it. -8 doubles and also keeps the negative sign.

Correct answer: 5

By the Pythagorean theorem, the hypotenuse squared = 3 squared + 4 squared = 9 + 16 = 25, and sqrt(25) = 5. 6 is the area of the triangle, one half times 3 times 4, not the length of a side. 7 adds the legs directly, 3 + 4, without squaring them. 12 multiplies the legs, 3 times 4, instead of squaring and adding them.

Correct answer: 3x

Divide the coefficients and subtract the exponents: 6 / 2 = 3 and x^2 / x = x, so the result is 3x. 4x subtracts the coefficients, 6 - 2, instead of dividing them. 3x^3 adds the exponents, which is the rule for multiplying powers, not dividing them. 4x^3 makes both of those mistakes.

Correct answer: 5/6

Convert to a common denominator first: 2/3 = 4/6, and 4/6 + 1/6 = 5/6. 3/9 adds the numerators and the denominators straight across, 2 + 1 over 3 + 6. 5/12 converts correctly but then adds the denominators as well, 6 + 6. 1/9 multiplies the fractions, 2/3 times 1/6 = 2/18, instead of adding them.

Correct answer: 7

A coefficient is the number that multiplies the variable, so in 7y the coefficient is 7. The letter y is the variable itself, not its coefficient. 7y is the whole term rather than its numerical part. 1 is the exponent on y, which is not written because y means y^1.

Correct answer: 7

Add 7 to both sides to get 3x = 21, then divide both sides by 3 to get x = 7; as a check, 3 times 7 - 7 = 14. 21 adds the 7 but never divides by 3. 18 treats 3x as 3 + x, so 3 + x - 7 = 14 gives x = 18. 4 makes two slips: it subtracts 7 from 14 instead of adding it, and it also treats 3x as 3 + x, so 3 + x = 7 gives x = 4.

Correct answer: 16

Two to the fourth power means four 2s multiplied together: 2 times 2 times 2 times 2 equals 16. The answer 8 multiplies the base by the exponent (2 times 4), 6 adds them (2 plus 4), and 32 multiplies in one 2 too many, which is 2 to the fifth power.

Correct answer: 9

The square root of 81 is 9, because 9 times 9 equals 81. The answer 27 takes the factor pair 3 times 27 instead of the equal pair 9 times 9, 40.5 halves 81 instead of taking its root, and 8 falls short, because 8 times 8 is only 64.

Correct answer: 25 pi

The area of a circle is pi times the radius squared; 5 squared is 25, so the area is 25 pi. The answer 10 pi is the circumference (2 times pi times the radius), 20 pi works that circumference formula with the diameter of 10 in place of the radius, and 5 pi multiplies pi by the radius without squaring it.

Correct answer: 3x + 12

Distributing the 4 gives 8x + 12, and subtracting 5x leaves 3x + 12. The answer 3x + 3 multiplies only the 2x by 4 and leaves the 3 unchanged; -3x + 12 subtracts in the wrong order, taking 8x away from 5x; and -3x + 3 makes both of those slips.

Correct answer: 36

Multiplying both sides of x/4 = 9 by 4 isolates x, so x equals 9 times 4, which is 36. The answer 2.25 divides 9 by 4 instead of multiplying, 0.44 divides 4 by 9 (about 0.44), and 5 subtracts 4 from 9 as if the equation said x plus 4 equals 9.

Correct answer: 6

Because 6 factorial equals 6 times 5 factorial, dividing by 5 factorial cancels everything except the 6. The answer 1 cancels the 6 as well, 144 divides 720 by 5 instead of by 5 factorial (120), and 720 works out 6 factorial but never divides by 5 factorial.

Correct answer: 180

The three interior angles of every triangle add up to 180 degrees. The value 60 is the size of each angle in an equilateral triangle, 360 is the sum of the interior angles of a quadrilateral (or of a triangle's exterior angles), and 540 is the interior-angle sum of a pentagon.

Correct answer: Current

In V = IR the letter I stands for current, measured in amperes; V is voltage and R is resistance. Inductance is written with the letter L and measured in henries, impedance is written Z, and power is written P and measured in watts.

Correct answer: 3 amperes

Ohm's law solved for current is I = V/R, so 12 volts divided by 4 ohms gives 3 amperes. The answer 48 amperes multiplies voltage by resistance; 36 amperes uses the power formula (voltage squared divided by resistance), which gives watts rather than amperes; and 8 amperes subtracts the resistance from the voltage instead of dividing.

Correct answer: 12 volts

Ohm's law gives V = IR, so 2 amperes times 6 ohms equals 12 volts. The answer 3 volts divides resistance by current, 0.33 volts divides current by resistance, and 24 volts uses the power formula (current squared times resistance), which gives watts rather than volts.

Correct answer: 30 ohms

Ohm's law solved for resistance is R = V/I, so 120 volts divided by 4 amperes gives 30 ohms. The answer 480 ohms multiplies voltage by current, which is the power in watts; 3600 ohms squares the voltage and divides by the current, borrowing the power formula R = V^2/P with the current in place of the power; and 116 ohms simply subtracts the current from the voltage.

Correct answer: Ohm

Resistance, the opposition to current flow, is measured in ohms. The ampere is the unit of current, the volt is the unit of voltage (electrical pressure), and the farad is the unit of capacitance.

Correct answer: Amperes

Electric current, the rate at which charge flows, is measured in amperes. Coulombs measure a quantity of charge rather than its rate of flow (one ampere is one coulomb per second), volts measure voltage, and ohms measure resistance.

Correct answer: Volt

Voltage, the electrical pressure that drives current, is measured in volts; one volt is one joule of energy for each coulomb of charge. The ohm measures resistance, the joule measures the energy itself rather than energy per unit of charge, and the watt measures power, the rate at which energy is used.

Correct answer: Voltage

Voltage is the electrical pressure, or potential difference, that pushes electrons through a conductor. Current is the flow of electrons that voltage produces, resistance is the opposition to that flow, and power is the rate at which electrical energy is used, measured in watts.

Correct answer: Each resistor carries the same current

A series circuit has only one path, so each resistor carries the same current. The idea that the first resistor gets the most current treats current as if it were used up along the way, while 'each resistor carries a third of the current' and 'the smallest resistor gets the most current' both describe how current divides among parallel branches, not a series loop.

Correct answer: 15 ohms

Resistances in series simply add, so 5 ohms plus 10 ohms equals 15 ohms. The answer 3.33 ohms uses the parallel formula (product over sum, 50 divided by 15), 7.5 ohms averages the two resistances, and 2 ohms divides 10 by 5 instead of adding.

Correct answer: 5 ohms

Two equal resistors in parallel combine to half the value of one, so two 10-ohm resistors give 5 ohms (product over sum: 100 divided by 20). The answer 20 ohms adds them as if they were in series, 0.2 ohms adds the reciprocals (1/10 + 1/10) but never inverts the result, and 0.05 ohms makes both mistakes, adding the resistances as if in series and then inverting that sum (1/20).

Correct answer: Each branch has the same voltage

Every branch of a parallel circuit connects across the same two points of the source, so each branch has the same voltage, the full voltage of the source. Saying each branch has part of the total voltage describes a series circuit; each branch farther from the source has lower voltage treats voltage as used up along the wires; and each branch has the voltage set by its resistance confuses voltage with branch current, which is what depends on resistance.

Correct answer: The failed bulb breaks the single current path

A series string gives current only one route, so the failed bulb breaks the single current path and every bulb goes dark. A short would let current bypass the dead bulb and keep the others lit, so 'the failed bulb shorts out the rest of the string' is wrong; 'the failed bulb raises the resistance of the others' is wrong because their filaments are unchanged; and 'the failed bulb blows the fuse inside the plug' is wrong because an open filament draws no extra current.

Correct answer: Copper

Copper conducts electricity better than any other metal listed here, which is why it is the standard choice for wiring. Aluminum conducts only about 60 percent as well as copper, and nickel and iron conduct far less well still.

Correct answer: It insulates the wire to prevent electric shock

Rubber resists the flow of electricity: it insulates the wire to prevent electric shock and keeps current inside the conductor. Saying it shields the wire to block magnetic interference is wrong because that takes a metal braid or foil; it grounds the wire to drain off stray current is wrong because rubber does not conduct; and it cools the wire to lower its resistance is wrong because rubber holds heat in rather than carrying it away.

Correct answer: It strongly opposes the flow of current

An insulator's electrons are tightly bound, so it strongly opposes the flow of current. If it readily permits the flow of current, the material is a conductor; if it limits the flow of current to one direction, the part is a diode; and if it turns the flow of current into light, the part is a light-emitting diode.

Correct answer: Silver

Silver is a metal with abundant free electrons, the best electrical conductor of all, so it lets electricity flow freely. Silicon is a semiconductor that conducts poorly unless it is specially treated, and porcelain and glass are insulators used to block current.

Correct answer: To act as a one-way valve for current

The job of a diode is to act as a one-way valve for current: it lets current flow in one direction and blocks it in the reverse direction. A capacitor is the part used to store charge in an electric field, a transistor is used to make a weak signal much stronger, and a transformer is used to step alternating voltage up or down.

Correct answer: Amplify or switch an electrical signal

A transistor's main jobs are to amplify or switch an electrical signal, using a small input current to control a much larger one. A capacitor is the part used to store or release an electric charge, a resistor is used to limit or divide the current in a circuit, and a transformer is used to raise or lower an alternating voltage.

Correct answer: Light-emitting diode

A light-emitting diode (an LED) gives off light when current flows through it in the forward direction. A Zener diode holds a steady voltage when it is reverse-biased, a Schottky barrier diode switches quickly with a low voltage drop, and a photodiode detects light rather than producing it; none of these three is built to give off light.

Correct answer: A diode

A diode converts AC to DC because it lets current pass in one direction and blocks the reversing half of each AC cycle, a process called rectification. A transformer changes the size of an AC voltage but leaves it alternating, a capacitor smooths the output after rectification but cannot rectify on its own, and a resistor simply limits current.

Correct answer: To store electric charge

A capacitor's main purpose is to store electric charge on two plates separated by an insulator and release it when the circuit needs it. A resistor is the part used to limit the flow of current, a transistor is used to amplify a weak current, and a transformer is used to step up a supply voltage.

Correct answer: Farads

Capacitance is measured in farads, named for Michael Faraday; a one-farad capacitor stores one coulomb of charge for each volt applied. Henries measure inductance, coulombs measure a quantity of charge rather than the ability to store it, and ohms measure resistance.

Correct answer: In the electric field of its plates

A capacitor stores energy in the electric field of its plates, which builds up as opposite charges collect on them. Energy held in the magnetic field of its wire coil describes an inductor, energy held in a chemical reaction within its cells describes a battery, and energy held in a steady current within its leads is wrong because no steady current crosses the insulating gap between the plates.

Correct answer: The current doubles too

Ohm's law says current equals voltage divided by resistance, so with the resistance fixed, doubling the voltage means the current doubles too. Saying the current is halved reverses the relationship, the current is unchanged ignores the voltage in the formula, and the current quadruples confuses current with power, which rises fourfold when the voltage across a fixed resistor doubles.

Correct answer: Opposition a material offers to current flow

Resistance is the opposition a material offers to current flow, and it is measured in ohms. The pressure that pushes current through a conductor is voltage, the rate at which charge passes a point is current, and the ability to store charge on two plates is capacitance.

Correct answer: Parallel, so each part has its own path

The best choice is parallel, so each part has its own path: if one branch fails open, current still flows through the others and the rest of the circuit keeps working. The options 'series, so each part shares one path' and 'single loop, so each part has the same current' both describe one path that a single failure breaks for every part, and 'series, so each part gets the full voltage' is also false, because series parts divide the source voltage among them.

Correct answer: 18 ohms

Resistances in series add, so three 6-ohm resistors give 6 + 6 + 6 = 18 ohms. The answer 2 ohms uses the parallel rule for equal resistors (6 divided by 3), 0.5 ohms adds the reciprocals (three times 1/6) and stops before inverting, and 216 ohms multiplies the three resistances together.

Correct answer: Thicker wires have less electrical resistance

A wire's resistance falls as its cross-section grows, so thicker wires have less electrical resistance and waste less energy as heat over long distances. The idea that thicker wires let the current travel faster is wrong, because at the same current the electrons in a thicker wire actually drift more slowly; the claim that thicker wires keep current from leaking to ground describes the job of the insulators on the towers; and the claim that thicker wires step up the voltage on the line describes the job of transformers.

Correct answer: 1 ampere

The original resistance is 24 volts divided by 2 amperes, or 12 ohms; doubled, it becomes 24 ohms, and 24 volts divided by 24 ohms gives 1 ampere. The answer 4 amperes assumes current rises with resistance when it actually falls, 24 amperes stops at the new resistance value and reports it as the current, and 12 amperes reports the original resistance instead of working out a current at all.

Correct answer: Resistance

In V = IR the letter R stands for resistance, measured in ohms; V is voltage and I is current. Resistivity is a property of a material, written with the Greek letter rho; reactance is the opposition from capacitors and inductors, written X; and conductance is the reciprocal of resistance, written G and measured in siemens.

Correct answer: Dry wood

Dry wood is a good insulator because it has almost no free electrons or dissolved ions to carry current. Graphite is a form of carbon that conducts electricity well, salt water conducts through its dissolved ions, and aluminum is a metal widely used in power lines.

Correct answer: The much larger current through its other leads

In a switching transistor, a small current into one terminal controls the much larger current through its other leads, turning that larger current on or off. It does not set 'the voltage of the power source', which the supply itself fixes, or 'the direction of current in its power supply', which stays the same whether the transistor is on or off; and 'the color of the light given off at its junction' describes an LED, not a switching transistor.

Correct answer: Capacitor

A capacitor is the right part: it stores electric charge between its plates and can dump that charge almost instantly, which is what fires the bright burst of a camera flash. A 'resistor' only limits current and turns energy into heat, a 'diode' only lets current pass in one direction, and a 'transistor' switches or amplifies current but does not hold a store of energy.

Correct answer: It increases

'It increases' is correct: in series the current must pass through every resistor on the single path, so each added resistor adds its value to the total. 'It drops' and 'it is halved' describe adding resistors in parallel, where extra paths lower the total, and 'it is unchanged' ignores the added resistance altogether.

Correct answer: Watts

Watts are the unit of electrical power, the rate at which energy is used or delivered. 'Joules' measure the energy itself rather than the rate of using it, 'amperes' measure the flow of current, and 'ohms' measure resistance.

Correct answer: 600 watts

Power equals voltage times current, so 120 volts x 5 amperes = 600 watts. '24 watts' comes from dividing 120 by 5, which actually gives the resistance in ohms; '2880 watts' comes from squaring 120 and dividing by 5 as if 5 were the resistance; and '3000 watts' comes from squaring 5 and multiplying by 120 as if 120 were the resistance.

Correct answer: Alternating current

Ordinary US wall outlets supply alternating current, which reverses direction many times each second. 'Direct current' is what batteries supply, 'pulsating direct current' is what a rectifier produces from AC inside some chargers, and 'three-phase current' feeds factories and large buildings rather than ordinary home outlets.

Correct answer: Hertz

Frequency, the number of complete cycles an alternating current makes each second, is measured in hertz. 'Henries' sounds similar but measures inductance, 'seconds' measure the period of one cycle rather than how many cycles occur, and 'ohms' measure resistance.

Correct answer: Direct current

A battery supplies direct current, which flows steadily in one direction. 'Alternating current' reverses direction over and over, 'pulsating current' rises and falls in surges rather than flowing steadily, and 'induced current' is produced by a changing magnetic field, not by a battery's chemical reaction.

Correct answer: To cut off current that exceeds safe limits

A fuse exists 'to cut off current that exceeds safe limits': its thin metal strip melts during an overload and opens the circuit, protecting the wiring. 'To step up voltage that runs too low' is the job of a transformer, 'to smooth voltage that swings too much' is the job of a filter capacitor, and 'to block current that attempts to flow backward' is the job of a diode.

Correct answer: Reset for reuse after it trips

A circuit breaker can 'reset for reuse after it trips': once the fault is cleared it is simply switched back on and used again, while a blown fuse has melted and must be replaced. 'Cut the current after it overloads' is something a fuse does as well, so it is not the difference; 'limit current after it surges' describes a current limiter, and 'reduce the voltage after it spikes' describes a surge suppressor; a breaker does neither.

Correct answer: To carry fault current to the earth safely

The ground wire exists 'to carry fault current to the earth safely': if a hot wire touches a metal case, the ground gives that current a low-resistance path away from people. 'To return normal current to the service panel' is the job of the neutral wire, 'to feed current from the panel to outlets' is the job of the hot wire, and 'to shut off the current safely during an overload' is the job of a fuse or circuit breaker.

Correct answer: Increase or decrease the voltage

A transformer is used to 'increase or decrease the voltage' of an alternating current, using two coils with different numbers of turns. 'Store or release the electric charge' is what a capacitor does, 'start or stop the current flow' is what a switch does, and 'rectify or smooth the current' is what the diodes and filter capacitors of a power supply do.

Correct answer: Reduce the output voltage

A step-down transformer is built to 'reduce the output voltage' below the input voltage: its output coil has fewer turns than its input coil. 'Raise the output voltage' describes a step-up transformer, 'hold the output voltage constant' is the job of a voltage regulator, and 'rectify the output voltage' is the job of a rectifier, which turns alternating current into direct current; a transformer changes the voltage level but does neither of those.

Correct answer: A magnetic field around a coil

An inductor stores energy as 'a magnetic field around a coil', built up while current flows through the coil. 'An electric field between plates' is a capacitor's way of storing energy, 'chemical energy inside a battery' is a battery's way, and 'heat energy dissipated in a resistor' is lost rather than stored.

Correct answer: A magnetic field

A coil carrying current produces 'a magnetic field' and acts as an electromagnet, the principle behind motors, relays and transformers. 'A static charge' builds up from friction between insulators, not from current in a wire; 'a chemical reaction' is what drives a battery, not what a coil produces; and 'a sound wave' needs something vibrating, such as a speaker cone pushed by a coil's magnetic field, so the coil itself produces only the field.

Correct answer: The current surges to a very high level

In a short circuit, 'the current surges to a very high level': with almost no resistance in the path, Ohm's law gives a huge current that can overheat wires, which is why fuses and breakers exist. 'The current sinks to a very low level' gets the effect backward, 'the load draws far more power than usual' is wrong because the short bypasses the load, and 'the load resistance climbs sharply' is wrong because the short lowers the resistance of the circuit rather than raising the load's.

Correct answer: It drops, since there is more room for current flow

'It drops, since there is more room for current flow' is correct: a thicker wire has a larger cross-sectional area, so it has lower resistance than a thinner wire of the same material and length. 'It rises, since there is more metal to cross' has the effect backward, 'it holds steady, since length is the deciding factor' ignores that area matters too, and 'it holds steady, since the material is the same' ignores that thickness changes resistance even when the material does not change.

Correct answer: 3.0 volts

Batteries connected in series add their voltages, so 1.5 volts + 1.5 volts = 3.0 volts at the bulb. '1.5 volts' is the total for two batteries wired in parallel, not in series; '2.25 volts' comes from multiplying 1.5 by 1.5 instead of adding; and '0.75 volts' comes from splitting 1.5 volts between the two batteries instead of adding.

Correct answer: Intake, compression, power, then exhaust

The order is 'intake, compression, power, then exhaust': the piston draws in the air-fuel mixture, squeezes it, is driven down when it burns, and then pushes the burned gases out. 'Intake, power, compression, then exhaust' fires the mixture before it has been compressed, while 'intake, exhaust, compression, then power' and 'intake, exhaust, power, then compression' push the fresh mixture out before it has been burned.

Correct answer: The power stroke

The mixture is ignited at the start of 'the power stroke', and the expanding gases force the piston down; it is the only stroke that delivers work to the crankshaft. During 'the intake stroke' the mixture is only being drawn in, during 'the compression stroke' it is squeezed but not yet burning, and during 'the exhaust stroke' the burned gases are pushed out.

Correct answer: Fresh air-fuel mixture

On the intake stroke the descending piston creates low pressure that pulls 'fresh air-fuel mixture' in through the open intake valve. 'Spent exhaust gases' are pushed out on the exhaust stroke, 'raw liquid gasoline' would not burn without being mixed with air, and 'pressurized engine oil' is pumped to the bearings by the oil pump rather than drawn into the cylinder.

Correct answer: It forces the burned gases out

On the exhaust stroke the piston rises with the exhaust valve open, so 'it forces the burned gases out' and clears the cylinder for a fresh charge. 'It admits the fresh fuel mixture' describes the intake stroke, 'it compresses the fuel charge' describes the compression stroke, and 'it drives the piston downward' describes the power stroke, when the burning mixture forces the piston down.

Correct answer: Exhaust stroke

After the power stroke drives the piston down, the piston rises on the 'exhaust stroke' to push out the burned gases. The 'intake stroke' comes after the exhaust stroke, the 'compression stroke' comes after the intake stroke, and a second 'power stroke' cannot follow until a fresh charge has been drawn in and compressed.

Correct answer: To turn the chemical energy of fuel into motion

An internal combustion engine exists 'to turn the chemical energy of fuel into motion': burning fuel pushes the pistons, and the crankshaft turns that push into rotation. 'To turn waste heat from the engine into cabin warmth' is the job of the heater core, 'to turn the rotation of the engine into electricity' is the job of the alternator, and 'to turn the harmful exhaust into cleaner gases' is the job of the catalytic converter.

Correct answer: Crankshaft

The 'crankshaft' turns the pistons' up-and-down motion into rotation; the connecting rods push on its offset throws the way legs push bicycle pedals. The 'camshaft' is driven by the crankshaft and opens the valves, the 'flywheel' is bolted to the crankshaft to smooth its rotation, and the 'transmission' only changes the gear ratio of rotation the crankshaft has already produced.

Correct answer: Diesel fuel

A diesel engine runs on 'diesel fuel', which it injects into air that compression has made hot enough to ignite it without a spark. 'Diesel exhaust fluid' is a urea solution sprayed into the exhaust to cut emissions and is never burned as fuel, while 'liquefied petroleum gas' and 'compressed natural gas' are gaseous fuels normally burned in spark-ignition engines.

Correct answer: Ignition system

The 'ignition system' produces the spark that fires the air-fuel mixture, so no spark at the cylinders points straight to it. A fault in the 'fuel system' leaves the engine without fuel but does not stop the spark, the 'lubrication system' supplies oil to moving parts, and the 'cooling system' carries away heat; neither of those last two makes the spark.

Correct answer: To ignite the air-fuel mixture with a spark

A spark plug exists 'to ignite the air-fuel mixture with a spark' that jumps the gap at its tip at the right moment. 'To route the spark to each plug with a rotor' is the job of the distributor, 'to spray gasoline into the combustion chamber with a nozzle' is the job of a direct fuel injector, and 'to warm the combustion chamber with a heating element' is the job of a glow plug on a diesel engine.

Correct answer: Ignition coil

The 'ignition coil' is a step-up transformer that turns the battery's roughly 12 volts into the thousands of volts needed to jump the spark plug gap. The 'ignition switch' only switches the circuits on when the driver turns it, the 'starter solenoid' is a heavy relay that sends battery current to the starter, and the 'starter motor' cranks the engine; none of them raises the voltage.

Correct answer: To keep the engine from overheating

The cooling system exists 'to keep the engine from overheating': coolant absorbs combustion heat and carries it to the radiator. 'To keep the engine parts from wearing out' is the job of the lubrication system, 'to keep the engine exhaust from polluting' is the job of the emission controls such as the catalytic converter, and 'to keep the engine from stalling at idle' is the job of the idle air control and fuel system.

Correct answer: Radiator

The 'radiator' passes hot coolant through thin tubes and fins so the air flowing through it carries the heat away. The 'water pump' circulates the coolant, the 'thermostat' controls when coolant flows to the radiator, and the 'fan belt' drives the fan or pump from the crankshaft; none of them gives off the coolant's heat to the air.

Correct answer: To regulate coolant flow and engine temperature

The thermostat is there 'to regulate coolant flow and engine temperature': it stays shut while the engine warms up, then opens to send coolant to the radiator and keep the engine at operating temperature. 'To push coolant through the radiator and engine block' is the water pump's job, 'to seal the radiator and hold coolant pressure' is the radiator cap's job, and 'to sense coolant temperature and signal a gauge' is the temperature sender's job.

Correct answer: Cooling system

A gauge in the red and steam from under the hood mean the 'cooling system' is not removing heat, often because of low coolant, a stuck thermostat or a failed water pump; the steam is boiling coolant. The 'ignition system' makes the spark, the 'charging system' keeps the battery charged, and the 'fuel system' delivers fuel, and none of them holds the coolant that is boiling off.

Correct answer: To slow or stop the vehicle

The brake system exists 'to slow or stop the vehicle', using friction to turn its motion into heat. 'To turn or steer the vehicle' is the job of the steering system, 'to start or accelerate the vehicle' is the job of the engine, starter and throttle, and 'to cushion or level the vehicle' is the job of the suspension.

Correct answer: Brake caliper

The 'brake caliper' straddles the rotor, and hydraulic pressure pushes its pistons so the pads clamp the spinning rotor. The 'master cylinder' creates that hydraulic pressure at the pedal but does not touch the pads, a 'wheel cylinder' pushes the shoes outward in a drum brake rather than squeezing pads on a disc, and a 'brake drum' is the spinning part that shoes press against in a drum brake, not a part that squeezes pads.

Correct answer: Pressurized fluid from the master cylinder

In a hydraulic system the force travels as 'pressurized fluid from the master cylinder': the pedal pushes brake fluid through the lines, and because a liquid barely compresses, that pressure reaches every wheel. 'Compressed air from the onboard storage tank' is how the air brakes on heavy trucks work, 'a steel cable linked from the pedal to each wheel' is how purely mechanical brakes work, and 'electric current from the vehicle battery' is how the electric brakes on some trailers work, not a hydraulic system.

Correct answer: The hydraulic brake lines

A leak in 'the hydraulic brake lines' lets brake fluid escape, so pressure cannot build: the pedal sinks toward the floor and stopping takes much longer. A leak in 'the brake booster hose' loses vacuum assist and makes the pedal hard rather than sinking, 'the exhaust manifold gasket' seals the exhaust gas leaving the cylinders, and 'the intake manifold' carries air to the cylinders; a leak in either of those last two lets exhaust gas out or draws outside air in, but loses no brake fluid, so it cannot make the pedal sink.

Correct answer: To cut harmful pollutants in the exhaust

A catalytic converter exists 'to cut harmful pollutants in the exhaust': its catalysts change carbon monoxide, unburned hydrocarbons and nitrogen oxides into less harmful gases. 'To quiet the loud noise of the exhaust' is the muffler's job, 'to measure the oxygen left in the exhaust' is the oxygen sensor's job, and 'to collect the exhaust from each cylinder' is the exhaust manifold's job.

Correct answer: Between the engine and the tailpipe

The catalytic converter sits in the exhaust system 'between the engine and the tailpipe', usually ahead of the muffler, where the exhaust is still hot enough for the catalysts to work. 'Between the gas tank and the engine' is the fuel line, where a fuel filter sits; 'between the air filter and the engine' is the intake, where the throttle body sits; and 'between the engine and the transmission' is where the clutch or torque converter sits.

Correct answer: The catalysts need heat to drive chemical reactions

'The catalysts need heat to drive chemical reactions': a converter does little until it reaches its light-off temperature, which is why most emissions come out in the first minutes after a cold start. 'The soot needs heat to burn off the filter' describes a diesel particulate filter, not a catalytic converter; 'the warm metal swells to let more exhaust through' is not how a converter works, since expansion is not what cleans the gas; and 'the warm exhaust slows down to let the filter trap more' treats the converter as a filter, when it changes the gases chemically instead of trapping them.

Correct answer: Because the strokes take half a crankshaft turn apiece

'Because the strokes take half a crankshaft turn apiece' explains it: the full cycle needs two crankshaft turns, and only one of its four strokes is a power stroke. 'Because a single stroke uses one full crankshaft revolution' would spread the cycle over four turns, 'because the camshaft spins at twice the engine speed' is backward since the camshaft turns at half crankshaft speed, and 'because the camshaft needs two turns to open a valve' is wrong because the camshaft opens each valve once on every one of its turns.

Correct answer: A bolt

A bolt is the fastener described: it has a smooth shank below the head and a threaded end, and it is paired with a nut to clamp parts together. A nail is driven in and held by friction with no thread to take a nut, a dowel is a plain peg held by glue or a tight fit, and a screw threads into the material itself instead of taking a nut.

Correct answer: To spread the clamping load and protect the surface

A washer is used to spread the clamping load and protect the surface, so the bolt head or nut does not dig into or crush the workpiece. A tap, not a washer, is the tool used to cut new threads into the material. Oil or anti-seize compound is what is used to lubricate the threads and reduce the friction, and a washer is far too thin to raise the nut so the wrench has more room to turn.

Correct answer: A rivet

A rivet is the permanent fastener described: it is pushed through aligned holes and its tail is mushroomed, so it can only be removed by drilling or cutting it out. A screw can simply be backed out with a screwdriver, a cotter pin has legs that are bent over but can be straightened and pulled back out, and a spring pin is a split steel tube held by its own tension that can be driven out with a punch.

Correct answer: Lock nut

A lock nut is the answer: its nylon insert or distorted thread grips the bolt and resists loosening under vibration. A castle nut is slotted so a cotter pin can hold it, with no nylon or deformed metal; a jam nut is a thin nut tightened against a second nut; and a square nut is simply a four-sided nut with no locking feature.

Correct answer: Flat head

A flat head, also called a countersunk head, is the answer: its cone-shaped underside seats in a beveled hole so the top finishes flush with or below the surface. An oval head is countersunk underneath but leaves a rounded dome standing above the surface, while a round head and a truss head both sit fully on top of the material.

Correct answer: Phillips

A Phillips screw is the answer because its head has a cross-shaped recess that matches a plus-shaped driver tip. A slotted screw has a single straight groove; a hex socket screw has a six-sided recess turned by an Allen wrench; and a Robertson screw has a square recess.

Correct answer: Self-tapping screw

A self-tapping screw is the answer: its hard, sharp threads form their own mating threads as it is driven, so no pre-tapped hole is needed. A self-locking screw has a nylon patch or deformed thread to resist loosening, but it still needs a threaded hole, and a hex-head cap screw and a socket cap screw are machine fasteners that go into a tapped hole or a nut.

Correct answer: Set screw

A set screw is the answer: it is usually headless and threaded along its whole length, and its tip is tightened against a shaft to keep a pulley or gear hub from slipping. A thumb screw has a large knurled head for turning by hand, a dowel screw is a double-ended screw that joins two pieces of wood end to end, and a wood screw has a head and holds pieces of wood together rather than locking a hub to a shaft.

Correct answer: A caliper

A caliper is the right tool: its outside jaws, inside jaws and depth rod measure all three dimensions of a small part accurately. A micrometer in its standard form measures only outside dimensions, a bore gauge measures only inside diameters, and a ruler cannot read inside, outside and depth sizes with real precision.

Correct answer: A square

A square is the best choice because its two arms are fixed at exactly 90 degrees, so it shows at once whether two boards meet at a true right angle. A level checks whether a surface is horizontal or vertical, a plumb bob hangs straight down to mark a vertical line, and a tape rule measures length, not angles.

Correct answer: A level

A level is the answer: the bubble in its liquid-filled vial centers between the marks when the surface is truly horizontal, or truly vertical on the plumb vial. A plumb line uses a hanging weight and shows only vertical, a chalk line snaps a straight mark, and a compass has a liquid-filled capsule but its needle points to magnetic north rather than showing level.

Correct answer: Micrometer

A micrometer is the answer: its finely threaded spindle reads a thickness such as a wire's diameter to a thousandth of an inch or finer, making it the most accurate of these tools. A dial caliper reads to about a thousandth but is less precise than a micrometer, a feeler gauge measures the width of a gap rather than the size of a part, and a yardstick reads only to fractions of an inch.

Correct answer: A hacksaw

A hacksaw is the answer: its fine-toothed blade is held under tension in a rigid frame and is made for cutting metal. A jigsaw is a handheld power saw whose blade is not held in a frame, while a coping saw and a scroll saw tension a thin blade but are built mainly for cutting curves in wood.

Correct answer: Crosscut saw

A crosscut saw is the answer: its knife-like teeth are filed to sever wood fibers cleanly across the grain. A rip saw has chisel-like teeth for cutting along the grain, a coping saw cuts curves with a thin blade held in a frame, and a dovetail saw is a small, stiff-backed joinery saw whose fine teeth are usually filed for rip cuts along the grain.

Correct answer: A coping saw

A coping saw is the answer: its very thin, replaceable blade is stretched in a deep U-shaped frame, so it can turn tight curves in thin wood. A keyhole saw has a narrow blade with no frame and cuts rough openings, a bow saw has a coarse blade in a frame for cutting logs and branches, and a pruning saw has a curved blade for trimming limbs.

Correct answer: File

A file is the answer: its flat or half-round face is covered with rows of hardened teeth that remove small amounts of metal or wood to smooth and shape it. A plane shaves wood with a single blade, a reamer enlarges and finishes a drilled hole, and a chisel cuts with one sharp beveled edge.

Correct answer: A chisel

A chisel is the answer: its single beveled cutting edge is struck with a mallet to pare, carve or chip away wood and other material. A plane has a beveled blade but is pushed along the surface rather than struck, a scraper smooths a surface with a burred edge, and a hatchet is swung by its handle to chop rather than driven with a mallet.

Correct answer: Claw hammer

A claw hammer is the answer: its flat face drives nails and its curved, split claw grips nail heads to pull them out. A club hammer has two flat faces for striking chisels, a ball-peen hammer has a rounded peen for shaping metal, and a dead-blow hammer has a shot-filled head that stops rebound; none of these three has a claw.

Correct answer: Ball-peen hammer

A ball-peen hammer is the answer: it has a flat face for striking punches and chisels and a rounded peen for shaping metal and setting rivets. A brick hammer has a chisel-shaped end for splitting brick, a tack hammer is a small, light hammer for upholstery tacks, and a soft-face hammer has plastic or rubber faces for blows that will not mark the work.

Correct answer: A mallet

A mallet is the correct choice because its wooden or rubber head gives a softer blow that will not split a chisel handle or dent a finished surface. A sledgehammer, a club hammer and a tack hammer all have hard steel faces that would mar the work.

Correct answer: A sledgehammer

A sledgehammer is the best choice because its long handle and heavy head, swung with both hands, deliver far more striking force than any of the others. A riveting hammer is a light one-handed hammer for setting rivets, a drilling hammer is a short-handled hammer of a few pounds for striking chisels, and a wood mallet gives soft blows that would barely move a stake.

Correct answer: Torque wrench

A torque wrench is the answer because it measures or limits the twisting force applied, so the bolt can be tightened to an exact specification. An impact wrench hammers fasteners tight with no precise control of the final torque, a socket wrench turns a bolt quickly but gives no reading of how tight it is, and a pipe wrench grips round pipe with toothed jaws that would chew a bolt head.

Correct answer: Pop rivets set with a hand riveter

Pop rivets set with a hand riveter are the right choice because a pop, or blind, rivet is inserted and pulled tight entirely from the front, permanently clamping thin sheets when the back cannot be reached. Solid rivets peened with a hammer need a bucking bar held against the hidden back side to form the second head; sheet-metal screws driven with a drill can be backed out again, so the joint is not permanent; and machine screws tightened with a driver need a nut or a tapped hole on the far side.

Correct answer: A piston

A piston, such as the one in an internal combustion engine, is not a classic simple machine; it is one part of a complex engine. The six classic simple machines are the lever, the wheel and axle, the pulley, the inclined plane, the wedge and the screw, so a pulley, a wedge and a lever are all simple machines.

Correct answer: Inclined plane

An inclined plane is the simple machine at work: the ramp lets the barrel be raised by pushing it along a longer, gentler slope instead of lifting it straight up. A lever pivots on a fulcrum, a movable pulley runs a rope over a grooved wheel, and a wheel and axle is a wheel turning a shaft; the barrel rolls, but the machine doing the lifting here is the ramp.

Correct answer: A wedge

A wedge is the simple machine at work in both: two sloping faces meet at a thin edge, so a forward or downward push becomes a sideways force that splits or cuts. A lever turns about a fixed pivot, a screw is an inclined plane wrapped around a shaft, and a wheel and axle is a wheel turning a shaft; none of them splits material by being driven into it.

Correct answer: How much the machine multiplies the effort force

Mechanical advantage describes how much the machine multiplies the effort force: it is the output force divided by the input force, so a value of 4 means the load force is four times the effort. Efficiency, not mechanical advantage, tells how much of the input work the machine puts to use; power tells how much work the machine does each second; and the idea of how much more work the machine puts out than it takes in is a misconception, because a machine cannot create energy.

Correct answer: 4

The mechanical advantage is 4: divide the load (output force) by the effort (input force), so 200 pounds divided by 50 pounds equals 4. Dividing the other way, 50 by 200, gives 0.25; dividing the force saved, 150 pounds, by the 200-pound load gives 0.75; and dividing that same 150 pounds by the 50-pound effort gives 3, which counts only the force added beyond the effort instead of the whole load.

Correct answer: The effort must move through a longer distance

The effort must move through a longer distance: a machine cannot create energy, so when it lowers the force needed, that smaller force has to be applied over a longer distance to do the same work. 'The load must travel through a longer distance' is backwards, since with a mechanical advantage above 1 the load moves less than the effort. 'The machine must supply extra energy itself' breaks conservation of energy, because an ideal machine puts out exactly the work put into it, and 'the machine must make the load lighter overall' is false, because the load weighs the same; only the force needed to move it changes.

Correct answer: Between the effort and the load

In a first-class lever the fulcrum is between the effort and the load, as on a seesaw or a pry bar, so pushing down on one side lifts the load on the other. A fulcrum at the outer end, with the load in between, makes a second-class lever; a fulcrum at the outer end, with the effort in between, makes a third-class lever; and a fulcrum at the point where the load sits gives the load no lever arm, so the bar would not lift it at all.

Correct answer: Second-class

A wheelbarrow is a second-class lever: the wheel is the fulcrum at one end, the effort is applied at the handles at the other end, and the load sits between them, so the effort arm is always longer than the load arm. A first-class lever has the fulcrum in the middle, and a third-class lever has the effort in the middle. Although the wheel turns on an axle, the lifting is done by the frame pivoting on the wheel, so it is a lever and not a wheel and axle.

Correct answer: The effort acts between the fulcrum and the load

In a third-class lever the effort acts between the fulcrum and the load, as when the biceps pulls on the forearm between the elbow and the hand; the load end moves farther and faster than the effort, but more effort is needed than the load weighs. 'The fulcrum is between the load and the effort' describes a first-class lever; 'the load is between the fulcrum and the effort' describes a second-class lever; and 'the load and the effort travel the same distance' is false here, because the load end moves farther than the effort.

Correct answer: 6 feet

The 40-pound child must sit 6 feet from the fulcrum. The seesaw balances when weight times distance is equal on both sides: 60 pounds times 4 feet is 240, and 240 divided by 40 pounds is 6 feet, so the lighter child sits farther out. Stopping at the weight ratio, 60 divided by 40, gives 1.5 feet; turning the ratio upside down, 4 times 40 divided by 60, gives about 2.7 feet; and assuming both children sit at the same distance gives 4 feet, which would leave the heavier side down.

Correct answer: Its long effort arm multiplies the force supplied

Its long effort arm multiplies the force supplied: the worker pushes far from the fulcrum while the rock sits close to it, so a small push becomes a large lifting force, which is a large mechanical advantage. 'Its long heavy shaft adds extra weight to the push' is wrong because the bar's own weight is tiny next to the force it produces; 'its long arm moves the rock farther than the hands' is backwards, since the rock end moves a much shorter distance; and 'its long handle creates extra energy for the user' is impossible, because a lever trades distance for force without creating energy.

Correct answer: It changes the direction of the force applied

A single fixed pulley is used mainly because it changes the direction of the force applied: pulling down on one side of the rope raises the flag on the other side, and the pull needed still equals the flag's weight because the mechanical advantage is 1. 'It cuts the amount of force needed in half' describes a single movable pulley, not a fixed one. 'It doubles the distance the hands must travel' and 'it doubles how fast the flag climbs the pole' are both wrong, because with a fixed pulley the hands and the flag move the same distance at the same speed.

Correct answer: 2

The ideal mechanical advantage of a single movable pulley is 2: the two rope segments holding up the pulley share the load, so the worker pulls with about half the force but must pull the rope twice as far. A value of 1 belongs to a single fixed pulley, which only changes the direction of the pull; 0.5 comes from dividing the effort by the load instead of the load by the effort; and 1.5 is the kind of lower, actual value friction leaves in a real pulley, not the ideal value the question asks for.

Correct answer: 4

The mechanical advantage is 4: in a block and tackle the ideal mechanical advantage equals the number of rope segments supporting the movable block, so four segments give 4, and the effort is one-fourth of the load but must move four times as far. Counting the free end the worker pulls as a fifth supporting segment gives 5; treating the block and tackle like a single fixed pulley, which only changes the direction of the pull, gives 1; and doubling the four segments gives 8.

Correct answer: 100 pounds

About 100 pounds of effort is needed: with a mechanical advantage of 3, the effort equals the load divided by 3, and 300 divided by 3 is 100, though the rope must be pulled three times as far as the load rises. Dividing by 4, as if the mechanical advantage were one more than stated, gives 75 pounds; multiplying the load by 3 instead of dividing gives 900 pounds; and halving the load, as a single movable pulley would, gives 150 pounds.

Correct answer: 8 feet

The worker must pull the rope 8 feet: the effort distance equals the load distance times the mechanical advantage, so 2 feet times 4 is 8 feet. Dividing instead, 2 by 4, gives 0.5 feet, which would mean the pulleys saved both force and distance; assuming the rope moves only as far as the load gives 2 feet; and adding 2 and 4 gives 6 feet. The force saved is always paid back as extra distance the effort travels.

Correct answer: 3 to 1

The gear ratio is 3 to 1: divide the driven gear's 30 teeth by the driver gear's 10 teeth, so the driver turns three times for each turn of the driven gear, which turns more slowly but with more torque. Writing it the other way, 1 to 3, inverts the ratio; subtracting the teeth, 30 minus 10, gives 20 to 1; and adding them gives 40 to 1. Neither a sum nor a difference of tooth counts is a ratio.

Correct answer: It turns at a lower speed with greater torque

It turns at a lower speed with greater torque. The 36-tooth driven gear has three times as many teeth as the 12-tooth driver, so it makes one turn for every three turns of the driver, and a gear pair that cuts speed by a ratio multiplies torque by the same ratio. 'It turns at a higher speed with less torque' describes the reverse setup, a large gear driving a small one. 'It turns at a higher speed with greater torque' and 'it turns at a lower speed with less torque' are both impossible for a gear pair, because speed and torque always trade against each other: one goes up only when the other goes down.

Correct answer: Opposite directions, whatever their sizes

The answer is opposite directions, whatever their sizes. Where the teeth interlock, both gear rims move the same way at the contact point, so one gear must spin clockwise while the other spins counterclockwise; an idler gear is needed to make two gears turn the same way. 'Same direction, whatever their sizes' is the classic mistake of picturing the gears like wheels on one axle. 'Opposite directions only when sizes differ' and 'same direction only when sizes match' both wrongly tie direction to gear size: two equal gears in direct mesh still turn opposite ways, and size changes only speed and torque.

Correct answer: 200 revolutions per minute

The driven gear turns at 200 revolutions per minute. A gear with half as many teeth must make two turns for every turn of the driver, so its speed is 100 x 2 = 200. The answer 50 revolutions per minute comes from inverting the ratio and halving the speed instead of doubling it. The answer 150 revolutions per minute comes from adding half of 100 to 100, as if half the teeth meant half again as fast. The answer 100 revolutions per minute assumes meshed gears turn at the same speed, ignoring the tooth ratio.

Correct answer: So that the driven gear turns the same way as the driver

An idler gear is used so that the driven gear turns the same way as the driver. Each external mesh reverses direction, so with one gear in between the direction is reversed twice and ends up matching the driver's. 'So that the driven gear turns at the same speed as the driver' is wrong because the speeds still depend on the driver's and driven gear's tooth counts; they match only if those two gears happen to be the same size. 'So that the driven gear turns faster than the driver' and 'so that the driven gear turns with more torque than the driver' both credit the idler with changing the gear ratio, but the idler's own tooth count cancels out of the ratio.

Correct answer: Nearly incompressible

Liquids are nearly incompressible, so a push on a confined liquid is passed almost fully to the other end instead of being used up squeezing the fluid. 'Highly compressible' describes gases, which is why air in a brake line makes the pedal feel spongy. 'Nearly free of friction' is wrong because liquids have internal friction (viscosity) and hydraulic systems do lose some energy to it. 'Highly viscous' is wrong too: hydraulic fluid is chosen to flow easily, and a thick fluid would make the system slower, not stronger.

Correct answer: Transmitted equally in all directions

Under Pascal's principle, pressure applied to a confined fluid is transmitted equally in all directions, undiminished, to every part of the fluid and the walls of its container. That is why a hydraulic line can deliver force to a cylinder far from the pedal or lever. 'Transmitted only in the direction of the push' treats the fluid like a solid rod. 'Weakened as it spreads outward' assumes the pressure fades with distance, but in a confined fluid at rest the applied pressure is the same everywhere. 'Absorbed as the fluid is compressed' treats the liquid like a spring, but hydraulic fluid is practically incompressible.

Correct answer: Larger force over a shorter distance

The large output piston produces a larger force over a shorter distance. Pressure is the same throughout the fluid, so the bigger area turns it into a bigger force, but the fluid pushed by the small piston spreads over the large area and lifts it only a little. 'Larger force over a longer distance' would create work from nothing. 'Smaller force over a longer distance' describes the small piston's side of the trade, and 'smaller force over a shorter distance' would mean the press loses on both counts, which no frictionless hydraulic press does.

Correct answer: 5

The mechanical advantage is 5: output area divided by input area, 10 square inches / 2 square inches = 5. The answer 8 comes from subtracting the areas instead of dividing them. The answer 25 comes from squaring the ratio, a step that applies only when the problem gives piston diameters rather than areas. The answer 64 makes both mistakes, subtracting the areas and then squaring the difference.

Correct answer: Inclined plane

A screw is an inclined plane wrapped around a cylinder: its thread is a long, gentle spiral ramp, so a small turning effort moves a load a short distance along the axis with a large force. A wedge is the closest wrong answer, but a wedge is a double ramp driven straight into a gap, not one wound around a shaft. A wheel and axle describes the screwdriver handle that turns the screw, not the screw itself, and a lever and fulcrum is a rigid bar pivoting on a point, with no ramp at all.

Correct answer: On the wheel, at its outer edge

The effort goes on the wheel, at its outer edge. Turning force equals force times radius, so pushing at the rim of the large wheel, as a hand does on a doorknob, gives the effort the longest lever arm and lets a small force produce a strong twist at the small axle. 'On the wheel, close to its center' throws away most of that radius. 'On the axle, at its outer edge' and 'on the axle, close to its center' both apply the effort at the small radius, which gains speed or distance at the wheel but no force advantage.

Correct answer: It spreads the same rise across more distance

A longer ramp to the same height needs less force because it spreads the same rise across more distance: the work of raising the load is fixed, so pushing it along a longer path takes less force at every step. 'It makes the load weigh less on the slope' is wrong because the load's weight does not change; only the share of it you must push against does. 'It spreads the same weight across more surface' is wrong because the load rests on the same small patch of ramp at any moment, whatever the ramp's length, and spreading weight lowers pressure, not the force needed to push. 'It makes the friction drop on the slope' is wrong because a gentler slope presses the load harder against the surface, so friction rises slightly rather than drops.

Correct answer: The ramp's sloped length to its height

The ideal mechanical advantage of an inclined plane compares the ramp's sloped length to its height: a 12-foot ramp rising 3 feet has a mechanical advantage of 4. 'The ramp's width to its height' brings in the width, which has no effect on how much force it takes to push a load up the slope. 'The ramp's rise to its run' is the slope or grade of the ramp, a different measurement. 'The ramp's sloped length to its horizontal run' compares two measurements that are nearly equal on a gentle ramp, so it says almost nothing about the force saved.

Correct answer: Efficiency is reduced by friction in the pulleys

The system's efficiency is reduced by friction in the pulleys: an actual advantage of 4 against an ideal of 5 means some of the input work goes into friction instead of lifting the load. 'Ideal mechanical advantage is reduced by friction in the pulleys' is wrong because the ideal value is fixed by the number of supporting rope segments and stays 5. 'Rope must be pulled farther because of friction' is wrong because the ratio of rope pulled to load raised is also set by the rope geometry; friction raises the force needed, not the distances. 'Output force falls below input force because of friction' confuses force with work: friction makes the work put out less than the work put in, but an actual advantage of 4 still means the output force is four times the input force.

Correct answer: A second-class lever that increases force

A nutcracker is a second-class lever that increases force: the hinge is the fulcrum at one end, the nut (the load) sits in the middle, and the hands push at the far ends, so the effort arm is always longer than the load arm. 'A first-class lever that increases force' and 'a first-class lever that increases distance' both need the fulcrum between the effort and the load, as in a seesaw or a pry bar. 'A third-class lever that increases distance' needs the effort in the middle, as with tweezers, which gains speed and distance but gives up force.

Correct answer: Turning the output shaft faster

A large gear driving a small gear is better for turning the output shaft faster: the small gear must make several turns for each turn of the large one, so speed rises while torque falls. 'Turning the output shaft with more torque' is what the opposite setup, a small gear driving a large one, is for. 'Turning the output shaft with less effort' is wrong because trading torque for speed means the driver needs more effort for the same output load, not less. 'Turning the output shaft the other way' is no advantage of either setup, since any directly meshed pair reverses direction.