Full ASVAB Practice Form 6: Power, Brakes and Hydraulics

Answer: D

Correct answer: A well-tested explanation that ties together many observations. In science, a theory is a broad, well-tested explanation, such as plate tectonics, that ties together many observations. A law describes a pattern, a hypothesis is a testable proposed explanation, and all of them can be revised if new evidence requires it.

• A: This is the everyday meaning of theory; in science an untested idea is closer to a hypothesis.
• B: Describing a pattern is the job of a scientific law, and both laws and theories can be refined by new evidence.
• C: One experiment cannot prove an idea; theories build confidence through many repeated tests.
• D (correct): A scientific theory has survived repeated attempts to disprove it and explains why many observations happen.

Answer: D

Correct answer: Carbon dioxide. A compound contains two or more elements chemically bonded in a fixed ratio. Carbon dioxide always has one carbon atom for every two oxygen atoms. Copper is an element, and air and sweetened tea are mixtures whose proportions can change.

• A: Air is a mixture of gases such as nitrogen and oxygen in proportions that can vary.
• B: Copper is an element made of only one kind of atom.
• C: Sweetened tea is a mixture; you can add more or less sugar.
• D (correct): Carbon dioxide is carbon and oxygen chemically bonded in a fixed ratio, which makes it a compound.

Answer: D

Correct answer: Radio waves. The electromagnetic spectrum, from lowest to highest frequency, runs radio, microwave, infrared, visible, ultraviolet, X-ray and gamma. Radio waves are at the low-frequency, long-wavelength end.

• A: Gamma rays sit at the opposite end of the spectrum, with the highest frequency and shortest wavelength.
• B: Ultraviolet is beyond violet, the high-frequency end of visible light, so its frequency is high.
• C: Microwaves have low frequency, but they come just after radio waves, which are lower still.
• D (correct): Radio waves begin the spectrum order and have the lowest frequency and longest wavelength.

Answer: C

Correct answer: Lava. Magma and lava are the same kind of molten material in different places: magma is underground, and lava is molten rock after it erupts onto the surface.

• A: Magma is molten rock still beneath the surface; once it erupts, it gets a different name.
• B: Basalt is a solid extrusive igneous rock that forms after lava cools, not the molten material itself.
• C (correct): Molten rock that has reached the surface is lava; the term describes its location above ground.
• D: Sediment is loose weathered particles carried by water, wind or ice, not molten rock.

Answer: C

Correct answer: Proteins. An enzyme is a biological catalyst that is usually a protein. Do not confuse the enzyme with its substrate: amylase acts on starch, a carbohydrate, but amylase itself is a protein.

• A: Starch, the substrate amylase acts on, is a carbohydrate, but the enzyme itself is not.
• B: Lipids such as fats and phospholipids store energy and form membranes; they do not usually act as enzymes.
• C (correct): Most enzymes, including amylase, are proteins: chains of amino acids folded into a shape with an active site.
• D: DNA and RNA store and carry genetic information; the enzyme is coded by a gene but is not a nucleic acid.

Answer: A

Correct answer: G-C-T-A-A-C. In DNA, A pairs with T and G pairs with C. Working base by base: C gives G, G gives C, A gives T, T gives A, T gives A, G gives C, so the partner strand is G-C-T-A-A-C.

• A (correct): Each base is replaced by its partner: C with G, G with C, A with T and T with A.
• B: This uses uracil, which appears only in RNA; a DNA strand pairs A with T.
• C: This simply repeats the original strand instead of pairing each base with its partner.
• D: This pairs C with A and G with T, mixing up the two base-pairing rules.

Answer: A

Correct answer: 20,000 years. Convert to the same unit first: 1 km = 1,000 m = 100,000 cm.

Time = distance ÷ rate = 100,000 cm ÷ 5 cm per year = 20,000 years.

• A (correct): 1 km = 100,000 cm, and 100,000 cm ÷ 5 cm per year = 20,000 years.
• B: This uses 10,000 cm for 1 km; a kilometer is 1,000 m, or 100,000 cm.
• C: This uses 1,000,000 cm for 1 km, ten times too large.
• D: This treats 1 km as 1,000 cm, confusing kilometers with centimeters and meters.

Answer: B

Correct answer: The adrenal medulla, releasing epinephrine. Sudden stress triggers the fight-or-flight response. Nerve signals reach the inner part of each adrenal gland, the medulla, which releases epinephrine (adrenaline), raising heart rate, opening the airways and freeing fuel for muscles.

• A: Cortisol from the adrenal cortex supports blood glucose during longer stress, not the response within seconds.
• B (correct): Nerve signals trigger the adrenal medulla to release epinephrine within seconds, raising heart rate and opening the airways.
• C: Insulin lowers blood glucose after a meal and has nothing to do with sudden fear.
• D: Thyroid hormone sets the long-term metabolic rate; it does not cause a racing heart within seconds.

Answer: A

Correct answer: About 2.5 km. Light arrives almost instantly, so the delay is the sound's one-way travel time. Sound in air travels about 343 m/s, roughly 1 km every 3 s.

Distance ≈ 7.5 s ÷ 3 s per km = 2.5 km (343 × 7.5 ≈ 2,570 m).

• A (correct): Sound covers about 1 km every 3 s, so 7.5 s ÷ 3 s per km gives about 2.5 km.
• B: This halves the distance as if it were an echo; thunder travels only one way from the strike to the listener.
• C: This multiplies the delay by 3 instead of dividing; it takes about 3 s per kilometer, not 3 km per second.
• D: This assumes sound travels 1 km each second; sound in air is closer to 343 m/s, about 1 km every 3 s.

Answer: A

Correct answer: 395 g. Rearrange

to

Then m = 0.79 g/mL × 500 mL = 395 g, which makes sense because the alcohol is a little less dense than water.

• A (correct): Mass equals density times volume: 0.79 g/mL × 500 mL = 395 g.
• B: This divides the volume by the density instead of multiplying, so the result does not even have units of mass.
• C: This assumes the liquid has the density of water, 1.0 g/mL, instead of 0.79 g/mL.
• D: This misplaces the decimal point; 0.79 × 500 is 395, not 39.5.

Answer: C

Correct answer: Oxygen gas, O₂. A molecule is two or more atoms bonded together; a compound needs two or more different elements. O₂ has two bonded oxygen atoms but only one element, so it is a molecule that is not a compound.

• A: Water is a molecule, but it contains two different elements, so it is also a compound.
• B: Sodium chloride is an ionic compound that forms a lattice of ions rather than separate molecules.
• C (correct): O₂ is two bonded atoms, making it a molecule, but it contains only one element, so it is not a compound.
• D: Neon exists as single, unbonded atoms, so it is neither a molecule nor a compound.

Answer: B

Legumes such as alfalfa host nitrogen-fixing bacteria in root nodules that turn nitrogen gas into ammonium. When the alfalfa residue is decomposed, ammonium is released, and nitrifying bacteria convert it to nitrate, which corn roots absorb, so less fertilizer is needed.

• A: Plants cannot break the triple bond in nitrogen gas; the alfalfa relies on bacteria in its root nodules to fix it.
• B (correct): This links fixation by nodule bacteria, release by decomposers and nitrification into a usable form for the next crop.
• C: Denitrification runs the other way, turning nitrate back into nitrogen gas that escapes to the air.
• D: Phosphorus is a separate nutrient with its own cycle; it cannot substitute for the nitrogen that corn needs.

Answer: A

Correct answer: It moves faster, and sunlight heating its nucleus makes a coma and tails likely. In an elliptical orbit, a body moves faster near the Sun and slower far away. Close to the Sun, sunlight warms the icy nucleus so gas and dust escape, forming a coma and tails that point generally away from the Sun. Far out and cold, the comet may show no tail at all.

• A (correct): Objects in elliptical orbits move fastest nearest the Sun, and solar heating there drives off gas and dust.
• B: The pull is strongest near the Sun, and the comet is moving fastest there, not slowest.
• C: Only an ideal circular orbit keeps constant speed; elliptical orbits speed up near the Sun.
• D: The speed part is right, but comet tails point generally away from the Sun, not simply behind the comet's motion.

Answer: B

Correct answer: C_2H_5OH + 3O_2 → 2CO_2 + 3H_2O. Ethanol has 2 C, 6 H and 1 O. Carbon: write 2 in front of carbon dioxide. Hydrogen: 6 H needs 3 water molecules. Oxygen on the right is

ethanol supplies 1, so 6 more must come from 3 oxygen molecules.

• A: Six water molecules hold 12 hydrogen atoms, but one ethanol molecule has only 6.
• B (correct): Each side has 2 carbon, 6 hydrogen and 7 oxygen atoms, so every atom is accounted for.
• C: This forgets the oxygen atom inside ethanol: the left side has 16 oxygen atoms but the right has 14.
• D: Carbon and hydrogen match, but the left side has only 5 oxygen atoms while the right has 7.

Answer: C

Correct answer: 2 s; 20 m. Gravity slows the ball by 10 m/s every second, so it reaches 0 m/s at the top after

Its speed changes evenly from 20 to 0 m/s, so its average speed is 10 m/s, and 10 m/s x 2 s = 20 m.

• A: The time is right, but 20 m/s x 2 s assumes the ball kept its full launch speed the whole way up; its average speed is only 10 m/s.
• B: The height is right, but 4 s is the time for the whole trip up and back down, not just the rise.
• C (correct): The ball loses 10 m/s each second, so it stops after 2 s, and its average speed of 10 m/s over 2 s gives 20 m.
• D: This uses the round-trip time and multiplies it by the launch speed, making both values too large.

Answer: A

Correct answer: 4 hours. Opposing rates subtract: net buildup =

per hour.

Time =

• A (correct): The snow depth grows by 3 - 1 = 2 inches per hour, and 8 / 2 = 4 hours.
• B: This adds the melting rate to the snowfall rate instead of subtracting it.
• C: This uses the snowfall rate alone and ignores the melting.
• D: This divides by the melting rate of 1 inch per hour, which does not measure the buildup.

Answer: C

Correct answer: $16.09. Line up the decimal points and add:

Two $20 bills are $40.00, so the change is

• A: This is the total cost of the items; the question asks for the change from $40.
• B: This comes from a borrowing slip when subtracting 23.91 from 40.00.
• C (correct): The items total 14.65 + 6.89 + 2.37 = $23.91, and 40.00 − 23.91 = $16.09.
• D: This reverses the cents digits; 40.00 − 23.91 leaves 9 cents, not 91 cents.

Answer: A

Correct answer: 1,200. Use the friendly factor 25: multiplying by 25 is the same as multiplying by 100 and dividing by 4.

• A (correct): Since 4 × 25 = 100, divide 48 by 4 to get 12 and multiply by 100 to get 1,200.
• B: This drops a zero; 25 × 48 must be more than 25 × 40 = 1,000.
• C: This adds an extra zero; the product is far smaller than 25 × 500.
• D: This misplaces digits; a correct product of 25 × 48 ends in 00 because 48 is a multiple of 4.

Answer: B

Correct answer: 55 miles per hour. Distance:

in 2 hours. Average speed:

per hour.

When equal time is spent at each speed, the simple average of the speeds gives the same answer.

• A: 110 is the total distance in miles; it must be divided by the 2 hours.
• B (correct): Equal times were spent at each speed, so the simple average works: 110 miles in 2 hours is 55.
• C: This treats the legs as equal distances; here the times are equal, so the speeds are not weighted differently.
• D: 65 is only the speed of the second hour, not the average for the whole drive.

Answer: D

Correct answer: 16 times. Each length is multiplied by k = 4. Area depends on two lengths, so it is multiplied by

• A: This applies the scale factor to area as if it were a length.
• B: This doubles the scale factor instead of squaring it.
• C: This cubes the scale factor, which is how volume changes, not area.
• D (correct): Area changes by the square of the scale factor, 4 × 4 = 16.

Answer: B

Correct answer: 456. Total made:

loaves.

Rejected: 5% of

Good loaves:

• A: This is the number of rejected loaves, an intermediate value.
• B (correct): The line makes 80 × 6 = 480 loaves; 5% of 480 is 24, and 480 − 24 = 456.
• C: This is the total made before any loaves are rejected.
• D: This adds the 24 rejected loaves instead of subtracting them.

Answer: B

Correct answer: $2,800. Use

and solve for P:

The deposit was $2,800.

• A: This divides by the rate alone and ignores the 3 years, so it finds the principal for one year's interest.
• B (correct): Solving I = P × r × t for P gives 378 ÷ (0.045 × 3) = 378 ÷ 0.135 = $2,800.
• C: This uses 0.45 instead of 0.045 for 4.5%, which makes the answer ten times too small.
• D: This adds the interest to the principal; the question asks for the original deposit only.

Answer: C

Correct answer: 12 miles per hour. Times:

Average speed:

per hour, below the simple average because more time is spent at 10 miles per hour.

• A: 12.5 averages the two speeds, but she spends 3 hours at the slower speed and only 2 at the faster one.
• B: This divides one 30-mile leg by the total time instead of the full 60 miles.
• C (correct): She rides 60 miles in 2 + 3 = 5 hours, and 60 divided by 5 is 12.
• D: This adds the two speeds instead of finding total distance over total time.

Answer: C

Correct answer: $64.90. Tip:

Total: 55 plus 9.90 is $64.90, the same as $55\times 1.18$.

• A: This is only the tip; the question asks for the bill plus the tip.
• B: This adds 18 dollars instead of 18 percent of the bill.
• C (correct): The tip is 0.18 times 55, or 9.90, and 55 plus 9.90 is 64.90.
• D: This uses 0.018 for 18 percent; 18 percent is 0.18.

Answer: C

Correct answer: 2:00 p.m. Moving in opposite directions, they separate at

per hour. Time =

so they are 540 miles apart at 2:00 p.m.

• A: This uses only the slower helicopter's speed: 540 ÷ 120 = 4.5 hours.
• B: This uses only the faster helicopter's speed: 540 ÷ 150 = 3.6 hours.
• C (correct): They separate at 270 mph, and 540 ÷ 270 = 2 hours after noon.
• D: This subtracts the speeds to get 30 mph, which applies to a chase, not to opposite directions.

Answer: B

Correct answer: 8 hours. Add the rates:

One-eighth of the job per hour means the job takes 8 hours.

• A: This averages the two times; a team is always faster than its faster member.
• B (correct): The rates 1/10 and 1/40 add to 5/40 = 1/8 job per hour, so the job takes 8 hours.
• C: This assumes a second worker halves the faster worker's time, which is true only if both work equally fast.
• D: This adds the times instead of adding the rates.

Answer: D

Correct answer: 26. Let the sister's age be s. Marcus is $2s-4$, and the sum is

So

Marcus:

Check:

• A: This is the sister's age, an in-between value rather than Marcus's age.
• B: This doubles the sister's age but forgets the "4 years less."
• C: This simply subtracts 4 from the sum of their ages.
• D (correct): With sister = s, Marcus = 2s - 4, so s + 2s - 4 = 41 gives s = 15 and Marcus = 26.

Answer: A

Correct answer: 1/2. Start:

The trip uses

leaving 3 gallons.

After adding 9 gallons there are 12 gallons, and

of the tank.

• A (correct): The tank goes from 18 gallons to 18 - 15 = 3 gallons, then up to 12 gallons, and 12/24 = 1/2.
• B: This takes 5/8 of the fuel in the tank (18 gallons) rather than 5/8 of a full tank.
• C: This counts only the 9 added gallons and ignores the 3 gallons already in the tank.
• D: This is the fraction left after the trip; the 9 gallons added afterward were left out.

Answer: C

Correct answer: The 3.2-pound bag, by $0.09 per pound. Find each unit price. Small bag:

per pound. Large bag:

per pound.

The 3.2-pound bag is cheaper by

dollar per pound.

• A: This finds the right difference but picks the wrong bag; $2.74 per pound is the higher price.
• B: This compares the total prices, 8.48 - 6.85, instead of the prices per pound.
• C (correct): The 2.5-pound bag costs $2.74 per pound and the 3.2-pound bag costs $2.65, a difference of $0.09.
• D: This subtracts the weights (3.2 - 2.5) instead of comparing unit prices.

Answer: D

Correct answer: 20%. Profit is 75 minus 60, or $15. The question says percent of the selling price, so the selling price is the whole.

which is 20 percent. Dividing by the cost instead would give the 25 percent markup.

• A: This divides the $15 profit by the cost of $60, which gives the markup on cost, not the percent of the selling price.
• B: This is the cost as a percent of the selling price, not the profit.
• C: This treats the $15 profit as the percent without dividing by any whole.
• D (correct): The profit is $15, and the selling price of $75 is the whole here, so 15 divided by 75 is 20 percent.

Answer: B

Correct answer: sends out for sale. Ex means out and port means carry. A country that exports grain carries it out to sell to other nations.

• A: Bringing goods in from abroad is import; the prefix im-, in, reverses the direction.
• B (correct): Ex means out and port means carry, so exporting is carrying goods out of the country.
• C: Farming grows the grain, but port, carry, shows it is being shipped away.
• D: Storing keeps grain in place, while export moves it out of the country.

Answer: B

Correct answer: easily carried. The root port means carry, and -able means able to be. Together, portable means able to be carried, such as a portable radio.

• A: Heavy things are hard to carry, which works against the meaning.
• B (correct): The root port means carry, and -able means able to be, so portable means able to be carried.
• C: This confuses the root port with the noun port, a harbor.
• D: Fixed in place is the opposite of something you can move around.

Answer: C

Correct answer: leave out. Define the word first, then apply the not: to OMIT is to leave something out. The phrase leave out states that meaning; include is what the whole sentence asks for, not what the word means, and admit is a sound-alike.

• A: Include is the opposite of omit; the sentence asks you not to omit, which means it wants you to include the number.
• B: Admit sounds similar but means to confess or let in.
• C (correct): Leave out is the exact meaning of omit.
• D: Writing something twice repeats it, which is unrelated to leaving something off a form.

Answer: D

Correct answer: piece. A fragment is a small part broken or separated from a whole, such as a fragment of glass. Piece matches; whole is the opposite, and crack and copy describe different things.

• A: This is the opposite; a fragment is only part of something.
• B: A crack is a break line in an object, not a separated piece of it.
• C: A copy is a duplicate of something, not a broken-off part.
• D (correct): A fragment is a small part broken off from something larger, which is a piece.

Answer: D

Correct answer: overjoyed. Match the degree to the evidence: a life-or-death outcome and laughing while weeping show intense joy. Ecstatic means overwhelmingly happy, so overjoyed fits, while pleased is too weak.

• A: Pleased means mild satisfaction, far too weak for laughing and weeping with relief over a child's survival.
• B: The weeping comes from overwhelming joy at good news, not distress; the news itself is happy.
• C: She may be surprised, but surprise is not a feeling of joy; ecstatic names the joy itself.
• D (correct): Ecstatic is the top of the happiness scale, overwhelming joy, which fits a mother learning her son survived.

Answer: B

Correct answer: solid. The collocation "structurally sound" plus "after checking for cracks" points to condition, not noise. SOUND here means solid and free of defects.

• A: Sound as a noun is something you hear, but "structurally sound" describes the bridge's condition.
• B (correct): Sound as an adjective means in good condition, and "structurally solid" fits an inspection with no cracks.
• C: Fragile is the opposite of what an inspector would declare about a bridge that passed a crack check.
• D: The bridge is old, but "structurally" describes its strength, not its age.

Answer: C

Correct answer: joint. A concerted effort is one carried out jointly by several people or groups. The clue 'from three towns' supports joint; musical is a spelling association, and desperate and sincere describe feelings rather than cooperation.

• A: This is an association with the look-alike word concert, not the meaning of concerted.
• B: The effort might have been urgent, but desperate describes feeling hopeless, not working together.
• C (correct): Concerted means planned or carried out together, which matches joint.
• D: Sincerity describes honesty of feeling, not people acting together.

Answer: A

Correct answer: awaiting a decision. Pend means hang, and in modern use a pending matter is left hanging, not yet decided. The list waits for the June meeting, so it is awaiting a decision.

• A (correct): Pend means hang, and a pending matter is still hanging, not yet settled, until the board meets.
• B: This takes pend, hang, too literally; the list is undecided, not physically hung.
• C: This is the opposite; the board has not met yet.
• D: Nothing has been ended; the decision is simply waiting.

Answer: D

Correct answer: carefully considered. A week of comparing pay, benefits, and commute times shows careful thought before acting. Deliberate means done thoughtfully and on purpose, so carefully considered matches.

• A: Hasty is the opposite: done too quickly without enough thought.
• B: Hesitant means unsure and holding back; Marcus took time but ended by making a firm decision.
• C: Luck means chance, but the sentence shows careful planning rather than chance.
• D (correct): Deliberate describes a decision made slowly and on purpose after thought, which a week of comparing details shows.

Answer: A

Correct answer: flush out. In a shop setting the technical sense applies. The phrase after the comma explains what happens: leftover fuel is forced out with nitrogen. PURGE means flush out.

• A (correct): Forcing leftover fuel out of the line with nitrogen is flushing it out.
• B: This is the opposite; the goal is to remove what is inside the line, not add to it.
• C: Sealing would trap the leftover fuel inside instead of forcing it out.
• D: This is the political sense of purge, which does not fit a gas line in a welding shop.

Answer: A

Correct answer: occurring at certain times of year. Cover -al to find season. The ending -al forms an adjective meaning relating to the base, so seasonal means tied to a season. The fall harvest example confirms work done only at certain times of year.

• A (correct): Season plus -al means relating to a season, so seasonal work happens only during part of the year.
• B: Season is the noun base; the target describes work, so it is an adjective.
• C: This is the opposite of work tied to one season, such as the harvest.
• D: This confuses seasonal with seasoned, which describes food with added flavor.

Answer: D

Correct answer: line; quarrel. In A, the partners "seats" and "of the theater" give a line. In B, "a loud row over" a chore is a quarrel. Check the order: line first, quarrel second.

• A: Both meanings are right but in reverse order, the classic trap in two-sentence items.
• B: Paddling a boat is a verb sense, but in B row is a noun after "a loud" with no boat.
• C: A has no oars or boat; "front row of the theater" names a line of seats.
• D (correct): A uses the sense rhyming with "go" (a line of seats), and B uses the sense rhyming with "cow" (a noisy argument).

Answer: C

Correct answer: difference. Variation follows "a slight," so it is a noun. From vary, to differ, a variation is a difference or slightly different version. Variable and varied are related forms with different meanings.

• A: Changeable is the meaning of variable, an adjective; it cannot follow a slight as a noun here.
• B: A wide assortment fits varied, describing a group of many kinds, not one small gap between two colors.
• C (correct): A variation is a change or a slightly different version, so a slight variation in color is a slight difference.
• D: A perfect match is the opposite of the doors differing in color.

Answer: C

Correct answer: Impossible to challenge. Break it into un- (not), assail (attack) and -able (able to be): not able to be attacked. Three cameras confirming the account make any challenge hopeless, so the full-strength meaning, impossible to challenge, beats the weaker hard to challenge.

• A: Being popular is not the meaning; un- + assail + -able means no one can successfully attack it.
• B: Not yet challenged adds a time idea that the prefix does not carry; the point is that no challenge could succeed.
• C (correct): Un- (not) plus assail (attack) plus -able (able to be) means not able to be attacked, which fits three matching recordings.
• D: Openly attacked keeps the base assail but drops the negative prefix, reversing the meaning.

Answer: C

Correct answer: false. Two steps: the colon introduces evidence, and the evidence shows the cables held only half the claimed load. Claims contradicted by testing are false, so spurious means false, not merely a little exaggerated.

• A: Snapping at half the advertised load is far more than a small overstatement; this choice gets the degree wrong.
• B: Nothing suggests the claims were secret; they were advertised openly.
• C (correct): The test results after the colon show the claims were simply untrue, so spurious means false.
• D: The clue is about whether the claims were true, not about price.

Answer: A

Correct answer: A 10-year-old wearing the green wristband from the swim test. The rule requires an adult for every child under 12, with one exception: a child who passed the deep-water test and wears the green wristband. Only the 10-year-old with the wristband meets that exception.

• A (correct): This child is under 12 but meets the exception: the test was passed and the wristband is being worn.
• B: Lessons are not the lifeguards' test, so the exception does not apply and an adult must watch her.
• C: A 10-year-old is not an adult, so this child still needs adult supervision.
• D: The rule makes no exception for shallow water; only passing the swim test removes the adult requirement.

Answer: A

Correct answer: 21 pints. A difference question calls for subtraction: 84 pints minus 63 pints equals 21 pints.

• A (correct): Subtracting the Thursday total from the Monday total gives 84 - 63 = 21 pints.
• B: This adds the two days together (84 + 63) instead of finding how far apart they are.
• C: This is a subtraction slip; 84 - 63 is 21, not 29.
• D: This is simply Thursday's total, not the difference between the two days.

Answer: D

Correct answer: The alert system will save lives. Separate the speaker's words from the writer's. The prediction that the system "will save lives" sits inside quotation marks and is credited to the director. The enrollment number, the registration rule, and the description of the alerts are all stated by the writer.

• A: The writer reports this enrollment figure directly, outside any quotation.
• B: The writer states the registration rule as a fact in the final sentence.
• C: The writer describes what the system does in the first sentence, as reported fact.
• D (correct): These words appear only inside the director's quotation, so they are the speaker's view, not something the writer confirms.

Answer: B

Correct answer: She wants customers to see the worn parts before they approve repairs. When a passage states a purpose, use it. The sign says the photos let customers see the problem before approving the work. The drop in phone calls happened afterward, so it is an effect, not the stated reason, and claims about higher charges or a state law invent a motive or an outside fact.

• A: Nothing in the passage mentions prices, so this invents a hidden motive.
• B (correct): The sign at the counter states this purpose directly, so it is the best-supported reason.
• C: The passage never mentions any law; this relies on an outside fact that the text does not supply.
• D: Fewer calls is a result the passage reports, but the stated reason on the sign is letting customers see the problem.

Answer: D

Correct answer: to celebrate the team's achievement. Ask which direction the details push. First time in its history, more crates than any other, no penalties and a leadership award all praise the students, and no sentence recommends, explains a process or raises a risk. The purpose is to celebrate the win.

• A: The borrowed garage is mentioned as a detail of the team's effort; the passage never says the school should provide anything.
• B: Design and coding are mentioned only in passing; no process is explained.
• C: Cost is never mentioned; the trip to Houston is reported as good news.
• D (correct): The passage highlights a first-ever title, a perfect final round and an individual award, all details that praise what the team accomplished.

Answer: C

Correct answer: The shoulders along the stretch were made wider. Separate reported events from predictions. The repaving, the wider shoulders and the new lane lines are described as finished work. Words like expect, should and will mark hopes and plans, so fewer accidents, fewer complaints and the review have not been reported as happening.

• A: Officials only expect this; expect marks a prediction, not a reported result.
• B: Should cut down is a forecast, and the passage reports no change in complaints.
• C (correct): The passage reports that crews widened both shoulders by two feet as part of the finished work.
• D: The review will take place next year, so it has not happened yet.

Answer: C

Correct answer: thick and hard to see through. Use cause and effect as a clue, then ask what the word describes. Because the fog was dense, the captain could not see her own bow, so dense means thick and hard to see through. The held departures are a result of that thickness, not its definition.

• A: Delayed departures are a result of the fog, not the meaning of dense; this mistakes a consequence for a definition.
• B: Fog may be cold and damp, but the clues are all about not being able to see, which is what dense describes here.
• C (correct): The captain could not see her own bow, and departures waited until the shore came into view, so the fog was thick enough to block sight.
• D: The fog did last until nine, but the word describes how thick it was, shown by the hidden bow, not how long it stayed.

Answer: B

Correct answer: A weak snow layer buried under several feet of new snow. Separate the trigger from the enabling condition. The cornice falling set off the avalanche, but the weak layer buried under several feet of new snow is what allowed an avalanche that large. The question asks what made it possible, so the enabling condition is the answer.

• A: The falling cornice is the trigger that started the avalanche, not the condition that allowed one so large.
• B (correct): The weak December layer under heavy January snow set up the slope to fail, which is the enabling condition.
• C: The passage never mentions skiers on the slope; the section was closed and the avalanche began with the cornice.
• D: The cold, dry spell happened in December, not on the morning of the avalanche, and it built the weak layer rather than starting the avalanche.

Answer: D

Correct answer: Faster ways to buy tickets helped fix the ferry's late departures. This is a problem-and-solution passage told in time order. The main idea must connect both halves: long lines delayed the boats, and faster ticketing fixed it. The plan for a third boat is simply the last event, and naming only the problem covers half the passage.

• A: This is the last event mentioned, but the final item in a sequence is not automatically the point; it is a future plan, not the change and result the passage explains.
• B: This names the problem but leaves out the fix and the improvement that the rest of the passage describes.
• C: This stretches one ferry's experience into a claim about all transportation, and the passage never says apps are best.
• D (correct): This links the problem (long lines and delays) to the response (app sales and a second booth) and its result (on-time departures).

Answer: D

Correct answer: Slip 6 at 2 p.m. Sort the facts by boat: the Tidewater normally leaves Slip 9 at 2 p.m. The exception says that from December through February it uses Slip 6, and nothing changes its time. Both parts of the answer must match, so the Tidewater leaves Slip 6 at 2 p.m.

• A: This is the Tidewater's usual slip, but the exception for December through February moves it to Slip 6.
• B: Slip 6 is right for January, but 6 a.m. is the Sea Lark's departure time, not the Tidewater's.
• C: 1:30 p.m. is when Tidewater passengers must check in, thirty minutes before the boat actually departs.
• D (correct): January falls in the December-through-February exception, so the Tidewater moves to Slip 6, and its departure time stays 2 p.m.

Answer: C

Correct answer: Scalene. No two of the side lengths are equal, so the triangle is scalene.

• A: An isosceles triangle needs at least two equal sides, and no two of these lengths are equal.
• B: An equilateral triangle needs all three sides equal.
• C (correct): All three side lengths are different.
• D: Right describes angles, and these sides fail anyway: 144 + 225 = 369, not 400.

Answer: C

Correct answer: Concave. A convex polygon has every interior angle under 180 degrees. An angle over 180 degrees makes a corner point inward, creating a dent, so the polygon is concave.

• A: A convex polygon must have every interior angle below 180 degrees, and 200 is above that.
• B: A regular polygon is convex with all angles equal, so it cannot have an angle above 180 degrees.
• C (correct): An interior angle above 180 degrees creates an inward dent, which is what makes a polygon concave.
• D: A polygon may have an angle over 180 degrees as long as its straight sides close up without crossing.

Answer: C

Correct answer: 81°. Vertical angles sit directly across from each other at an intersection and are always equal, so the vertical angle also measures 81°.

• A: 99° is the measure of each neighboring angle (180 - 81), not of the vertical angle.
• B: 9° is the complement of 81°; vertical angles are equal, not complementary.
• C (correct): Vertical angles are equal, so the angle across from 81° is also 81°.
• D: 279° is what remains of a full turn after 81°, not the angle across from it.

Answer: A

Correct answer: 169. A perfect square is a whole number times itself. Squares near these values are

Only 169 is on that list.

• A (correct): 169 = 13 x 13, so it is the square of a whole number.
• B: 160 lies between 144 (12 squared) and 169 (13 squared), so it is not a perfect square.
• C: 150 also lies between 144 and 169, so its square root is not a whole number.
• D: 125 is a perfect cube (5 cubed), but it lies between 121 and 144, so it is not a perfect square.

Answer: C

Correct answer: −1.4. Rewrite the subtraction of a negative as addition: −4.75 + 2.3 + 1.05. Then

• A: This subtracts 1.05 instead of adding it.
• B: The size is right, but −2.45 + 1.05 is still below zero.
• C (correct): −4.75 + 2.3 = −2.45, and subtracting −1.05 adds 1.05, giving −1.4.
• D: This treats every term as negative: −4.75 − 2.3 − 1.05.

Answer: C

Correct answer: 2 is the only even prime number. A prime is a whole number greater than 1 with exactly two factors. Any even number above 2 is divisible by 1, 2 and itself, so it is composite. That leaves 2 as the only even prime.

• A: 1 has only one factor, so it is neither prime nor composite; the smallest prime is 2.
• B: Odd numbers such as 9, 15 and 21 are composite.
• C (correct): Every other even number has 2 as a factor, so it has more than two factors.
• D: A prime has exactly two factors, 1 and itself.

Answer: C

Correct answer: -3/4. Subtract in the same order on top and bottom.

A quick sketch agrees: the line falls from left to right.

• A: This subtracts in one order on top and the opposite order on the bottom, losing the negative sign.
• B: This divides the run by the rise; slope is rise over run.
• C (correct): The rise is 2 - 8 = -6 and the run is 5 - (-3) = 8, so the slope is -6/8, or -3/4.
• D: This adds the coordinates instead of subtracting them.

Answer: B

Correct answer: Multiplying 3 by x but not by −4. The correct work is

2x = 10 and x = 5. If the 3 multiplies only the x, you get

so 2x = 2 and x = 1. Substituting x = 1 into the original gives

on the left but 9 on the right, so the check exposes the error.

• A: No step in this equation requires dividing by a negative number, so this error cannot occur here.
• B (correct): Writing 3x − 4 + 10 = x + 8 gives 2x + 6 = 8, so x = 1; the correct work gives x = 5.
• C: There is no minus sign in front of the parentheses here; the 3 is positive.
• D: Changing only the left side gives 3x − 12 = x + 8, which leads to x = 10, not x = 1.

Answer: D

Correct answer:

Divide both sides by −2 and reverse the sign:

Read from the x side, this is

Check x = 0: 8 ≥ 0 is true, and

• A: This divides by −2 but keeps the original direction instead of reversing it.
• B: This flips the sign but drops the negative when dividing 8 by −2.
• C: This divides by 2 instead of −2, losing both the negative and the needed flip.
• D (correct): Dividing both sides by −2 flips the sign: −4 ≤ x, which reads x ≥ −4.

Answer: B

Correct answer: 43. Build the terms in order:

• A: This is the third term; one more step is needed to reach the fourth.
• B (correct): Repeating "multiply by 4, then subtract 1" three times from 1 gives 3, 11, 43.
• C: This is the fifth term, one step too many.
• D: This plugs n = 4 into 4n − 1 instead of using the previous term.

Answer: D

Correct answer: 9/10·w. Rewrite both coefficients over the common denominator 10:

Add the numerators:

so the result is $\frac{9}{10}w$.

• A: This adds the tops and the bottoms separately, which is not how fractions add.
• B: This multiplies the fractions instead of adding them.
• C: This changes 1/2 to 5/10 but keeps 2 as the top of the second fraction instead of 4.
• D (correct): With tenths, 5/10 + 4/10 = 9/10.

Answer: C

Correct answer: $150. Let t be the truck cost and a the ATV cost:

Adding gives

Subtracting the first from the second gives

Adding these, 2t = 300, so t = $150 (and a = $70; check

).

• A: This is the cost of one ATV, not one truck.
• B: This is the combined cost of one truck plus one ATV, found by adding the equations and dividing by 5.
• C (correct): With t = 150 and a = 70, both receipts check: 300 + 210 = 510 and 450 + 140 = 590.
• D: This splits the truck-plus-ATV total of $220 evenly, ignoring that a truck costs $80 more than an ATV.

Answer: C

Correct answer:

·C + 32. Undo the operations on F in reverse order. Multiply both sides by 9/5, the reciprocal of 5/9: (9/5)

Add 32 to both sides:

C + 32.

Check with C = 100: (9/5)

the boiling point of water in Fahrenheit.

• A: This adds 32 correctly but keeps 5/9 instead of multiplying by its reciprocal 9/5.
• B: This uses the reciprocal correctly but subtracts 32 instead of adding it to undo F − 32.
• C (correct): Multiplying both sides by 9/5 gives (9/5)C = F − 32, and adding 32 isolates F.
• D: This adds 32 before undoing the 5/9 factor, so 32 is wrongly multiplied by 9/5.

Answer: C

Correct answer: 1080 cubic inches. Area scales by k squared, so k squared = 9 and k = 3. Volume scales by k cubed = 27.

• A: This multiplies the volume by 9, the area factor, but volume scales by k cubed, not k squared.
• B: This multiplies by the length factor 3 only; volume grows by 3 cubed.
• C (correct): Area grew by 9, so k is 3; volume grows by 3 cubed, 27, and 40 times 27 is 1080.
• D: This multiplies by 9 squared, 81, treating 9 as the length factor instead of the area factor.

Answer: A

Correct answer: 72 - 18π square inches. Each hole spans the 6-inch width, so its diameter is 6 and its radius is 3. Each hole is π(3)^2 = 9π, so two holes are 18π.

The remaining metal is 72 - 18π square inches.

• A (correct): Each hole has radius 3 and area 9π; the plate's 72 square inches minus 18π remains.
• B: This removes only one hole; the plate has two.
• C: This subtracts the two circumferences, 6π each, which are lengths, not areas.
• D: This computes the plate as 6 by 6; the plate is 12 by 6, or 72 square inches.

Answer: D

Correct answer: A capacitor. Two equal-length parallel plates represent a capacitor, which stores energy in an electric field and is rated in farads. Unequal plates would instead mean a battery cell.

• A: A cell's two lines are of unequal length, with the longer line marking the positive terminal.
• B: A resistor is drawn as a zigzag or a small rectangle.
• C: A fuse is usually a small rectangle or a wavy line between terminals, not two equal plates.
• D (correct): Two equal parallel plates separated by a gap is the standard capacitor symbol.

Answer: C

Correct answer: Reversing the direction of the coil current. Wrap your right-hand fingers in the direction of the conventional current and your thumb points to the north end. If the current flows the other way around the coil, your thumb points the other way, so the poles flip. Turns, current size and core material only change strength.

• A: More turns raise the ampere-turns and make the magnet stronger, but the field direction stays the same.
• B: More current strengthens the field without changing which end is north.
• C (correct): By the right-hand coil rule, reversing the current reverses the field, so the ends trade poles.
• D: A different core changes how strong the magnet is and how much magnetism it keeps, not which end is north.

Answer: A

Correct answer: 1.25 kW. One kilowatt is 1,000 W, so divide by 1,000:

• A (correct): Dividing 1,250 W by 1,000 gives 1.25 kW.
• B: This divides by 100 instead of 1,000.
• C: This divides by 10,000, moving the decimal one place too far.
• D: This divides by 10 instead of 1,000.

Answer: B

Correct answer: Resistivity. Resistivity, symbol $\rho$, describes how strongly a material opposes current regardless of size or shape. Resistance then depends on that resistivity together with length and area, through

• A: Resistance belongs to a particular object and changes with its length and cross-sectional area.
• B (correct): Resistivity is a material property in ohm-meters; every copper wire at one temperature has the same value.
• C: Current depends on the applied voltage and the circuit's resistance, not just on the material.
• D: A wire's voltage drop depends on its resistance and the current it carries.

Answer: A

Correct answer: 0.4 A. For a fixed resistance, current is directly proportional to voltage. The voltage changes by

so the current does too: 0.6 times

Check:

• A (correct): With constant resistance, current scales with voltage: 0.6 A times 6/9 is 0.4 A.
• B: This uses the ratio upside down; lowering the voltage must lower the current.
• C: The current would stay the same only if the voltage stayed the same.
• D: This squares the voltage ratio, which is how power changes, not current.

Answer: B

Correct answer: It switches very fast and has no moving contacts to wear out. A relay moves physical contacts, which limits its speed and causes wear. A transistor switches electronically with no moving parts, so it can turn a load on and off thousands or even millions of times per second without wearing out.

• A: Complete isolation is an advantage of a relay, whose coil and contacts are separate circuits.
• B (correct): Transistors have no moving parts, so they can switch millions of times per second without contact wear or arcing.
• C: Relays are generally more tolerant of brief overloads than semiconductor switches.
• D: Closed relay contacts have very low resistance; this is a relay strength, not a transistor one.

Answer: A

Correct answer: 18 V. Total resistance is

kΩ, so the current is 24 V ÷ 8 kΩ = 3 mA. The drop across the 6 kΩ resistor is 3 mA × 6 kΩ = 18 V, and the 2 kΩ resistor gets the other 6 V, adding up to 24 V.

• A (correct): The current is 24/8000 = 3 mA, and 3 mA × 6 kΩ = 18 V.
• B: This is the drop across the 2 kΩ resistor; the larger resistor takes the larger share.
• C: Series drops split in proportion to resistance, not equally between the two parts.
• D: The full source voltage appears across one part only if the loop is open; here both resistors share it.

Answer: A

Correct answer: About 377 W. Convert speed first:

rad/s.

Then

• A (correct): $\omega =2\pi \times 900/60\approx 94.2$ rad/s, and $4\times 94.2\approx 377$ W.
• B: This multiplies torque by rpm directly, skipping the conversion to radians per second.
• C: This converts rpm to revolutions per second but forgets the $2\pi$ radians in each revolution.
• D: This uses only $\pi$ instead of $2\pi$ radians per revolution, giving half the true power.

Answer: A

Correct answer: 150 W. Because the current is already given as an RMS value, use it directly in the resistive power formula.

• A (correct): $P=I_{\text{rms}}^{2}R=5^2\times 6=150$ W.
• B: This is $I\times R$, which gives the 30 V RMS voltage across the element, not its power.
• C: This halves the correct power, applying an extra RMS correction to a value that is already RMS.
• D: This converts 5 A to a peak of about 7.07 A and uses the peak in $I^{2}R$; RMS values should be used directly.

Answer: C

Correct answer: The lamp goes dark while the current in the wires rises sharply. The wire is a short circuit: an unintended low-resistance path around the load. Almost all the current takes that easy path, so the lamp goes dark, and with so little resistance in the loop the current becomes very large, heating the wires and draining the battery. Fuses and breakers exist to open the circuit in this situation.

• A: The new wire gives current an easier path around the lamp, not into it, so the lamp receives little or none.
• B: A short adds a path rather than breaking one; current increases instead of stopping.
• C (correct): The low-resistance wire bypasses the lamp, so current skips the lamp and grows large, heating the wires.
• D: Current takes the path available to it, and a near-zero-resistance wire carries most of it.

Answer: B

Correct answer: 3 Ω. Use 18 as the common denominator:

Flip the result:

which is below the smallest branch.

• A: This adds the three values as if they were in series.
• B (correct): The reciprocals add to 3/18 + 2/18 + 1/18 = 1/3, so the equivalent is 3 Ω.
• C: This averages the three values, which is not a parallel rule.
• D: This stops at the sum of reciprocals, 1/3, without taking the reciprocal again.

Answer: A

Correct answer: 4.5 J. Find the energy at each current with

then subtract.

The increase is

• A (correct): Final energy 4.8 J minus starting energy 0.3 J gives an increase of 4.5 J.
• B: This squares the change in current, 3 A; the energy formula must be applied to each current and then subtracted.
• C: This is the total energy stored at 4 A; the coil already held 0.3 J at 1 A.
• D: This uses the current change without squaring it; inductor energy grows with the square of the current.

Answer: D

Correct answer: 294 Wh. Find each stage separately. Warm-up: 6 minutes is 0.1 h, so

Wh. Printing:

Wh.

Total:

Wh.

• A: This multiplies 240 W by 6 without converting the minutes to hours.
• B: This averages the two powers even though the stages last very different times.
• C: This simply adds the two power ratings, which gives watts, not energy.
• D (correct): The warm-up uses 240 W times 0.1 h, or 24 Wh, and the printing uses 270 Wh, for 294 Wh in all.

Answer: A

Correct answer: Twice as much. Halving the length of the same wire halves its resistance. At a fixed voltage, use

with V unchanged and R halved, the power doubles. The shorter element draws twice the current at the same voltage, so it heats more, not less.

• A (correct): Half the length gives half the resistance, and at fixed voltage P = V squared over R, so power doubles.
• B: This assumes less wire means less heat, but at a fixed voltage a smaller resistance draws more current and more power.
• C: Power would stay the same only if the resistance stayed the same, but halving the length halves R.
• D: Power scales as 1/R at fixed voltage, not 1/R squared; halving R doubles the power.

Answer: A

Correct answer: 48 W. Total resistance is

so the current is

A through both resistors.

With a shared current, use

• A (correct): The series current is 32 divided by 16, or 2 A, and $2^2\times 12=48$ W.
• B: This applies the full 32 V to the 12 Ω resistor alone, but it only has part of the source voltage.
• C: This is the total power delivered by the source, not the share in the 12 Ω resistor.
• D: This is the power in the 4 Ω resistor, not the 12 Ω resistor.

Answer: D

Correct answer: It turns electrical energy from the battery into rotation that spins the engine. The starter is a motor: electrical energy in, mechanical rotation out, and only during starting. Its small pinion turns the flywheel ring gear to spin the crankshaft. The alternator does the reverse job, which is why the two are easy to mix up.

• A: That describes the alternator, a generator that works in the opposite direction from the starter.
• B: Storing energy is the battery's job, not the starter's.
• C: Holding voltage steady is the job of the voltage regulator in the charging system.
• D (correct): The starter is an electric motor that spends stored battery energy to crank the engine fast enough to fire.

Answer: B

Correct answer: The bead. The beads are loops of steel wire at the tire's inner edges. Air pressure pushes them against the rim, sealing the air in and locking the tire in place.

• A: The shoulder is the rounded edge where tread meets sidewall, not the part that seals on the rim.
• B (correct): The beads are wire loops at the tire's inner edges that seal against and grip the rim.
• C: Steel belts lie under the tread to give it strength; they do not touch the rim.
• D: The sidewall is the flexible side between shoulder and rim; the bead is at its inner edge.

Answer: A

Correct answer: To keep the rear wheels from locking before the fronts as weight shifts forward. When a car decelerates, load shifts toward the front axle, so the front tires grip better and the rear tires lose some grip. Limiting rear pressure keeps the lightly loaded rear wheels from locking first, which could make the car spin.

• A (correct): Braking unloads the rear tires, so they have less grip and would lock first if they got full pressure.
• B: Weight transfer moves load to the front, so the front tires gain grip and the rears lose some.
• C: Limiting rear pressure is about wheel lock and grip, not fluid boiling point.
• D: The parking brake is applied mechanically or by electric motors; it is not what the proportioning valve controls.

Answer: B

Correct answer: It packs more air mass into each cylinder to burn more fuel. A naturally aspirated engine fills its cylinders with atmospheric pressure alone. A boosted engine forces air in above atmospheric pressure, so each cylinder holds more air, can burn more fuel each cycle and produces more power from the same displacement.

• A: A turbo engine still uses intake, compression, power and exhaust, with one power stroke per cylinder per cycle.
• B (correct): Boost raises intake pressure above atmospheric, filling the same cylinder with denser air that supports burning more fuel.
• C: Swept volume comes from bore and stroke, which a turbo does not change.
• D: No combustion happens in the turbo; exhaust flow spins its turbine, which drives the compressor.

Answer: A

Correct answer: It is denser, so each volume holds more oxygen and needs more fuel. Air temperature changes air density. Cold air is denser and packs more oxygen into each unit of volume, so the ECM uses the IAT reading to estimate a larger air mass and inject matching fuel.

• A (correct): Cold air is denser, so the same volume carries more air mass and oxygen, and the ECM adds fuel to match.
• B: This reverses the relationship; hot air is the thinner, less dense air.
• C: Air is about 21 percent oxygen regardless of temperature; cold changes its density, not its makeup.
• D: In speed-density systems the ECM needs IAT to estimate air mass, and it also uses IAT for spark timing.

Answer: B

Correct answer: 275 ft. Convert the speed:

/s.

Then use distance equals speed times time.

• A: This multiplies 75 by 2.5 without converting miles per hour into feet per second.
• B (correct): 75 mph is 110 ft/s, and 110 ft/s times 2.5 s is 275 ft.
• C: This uses 88 ft/s, which is the conversion for 60 mph, not 75 mph.
• D: This divides the speed by the time instead of multiplying them.

Answer: A

Correct answer: It would be cut in half. In

the rate is inversely proportional to thickness. Doubling d divides P by 2, so heat gets through the thicker wall half as fast.

• A (correct): Thickness d is in the denominator, so doubling it halves the rate.
• B: This treats thickness as if it were in the numerator; a thicker wall slows conduction.
• C: Only k, A, and ΔT were held constant; d changed, so the rate changes.
• D: That would need d squared in the formula; d appears only to the first power.

Answer: C

Correct answer: Have a trained technician do it with proper, undamaged equipment and the maker's procedure. A compressed coil spring stores a large amount of energy even when the vehicle is lifted, and careless release can make it fly apart. Spring and strut removal should be done by a trained technician using proper equipment and the manufacturer's procedure, and a vehicle must never be supported by a jack alone.

• A: A compressed spring can release with deadly force, and a vehicle should never rest on a jack alone.
• B: Cutting a loaded spring can release its stored energy violently and is extremely dangerous.
• C (correct): Spring and strut removal stores dangerous energy, so it belongs to trained technicians following the manufacturer's steps.
• D: Even with the wheel hanging, the spring stays compressed and still stores a great deal of energy.

Answer: C

Correct answer: 8.0 m/s². Reaction distance: 20 m/s x 1.5 s = 30 m at full speed, so only

m remain for braking.

Rearranging

• A: This uses the whole 55 m as braking distance, forgetting the 30 m covered during the reaction time.
• B: This subtracts the reaction distance but leaves out the 2 in a = v²/2d.
• C (correct): Reaction distance is 20 x 1.5 = 30 m, leaving 25 m to brake, so a = 20² ÷ (2 x 25) = 8.0 m/s².
• D: This divides 20² by 55, ignoring both the reaction distance and the 2 in the formula.

Answer: D

Correct answer: About 1,284 N·m. Overall ratio =

Total torque = 220 × 13.26 × 0.88 ≈ 2,567 N·m.

An open differential sends equal torque to each axle, so each gets about 2,567 ÷ 2 ≈ 1,284 N·m.

• A: This is the total torque at the differential; it is not split between the two axles.
• B: This splits the torque correctly but leaves out the 88 percent efficiency.
• C: This adds the ratios (3.4 + 3.9 = 7.3) instead of multiplying them.
• D (correct): Total axle torque is 220 × 3.4 × 3.9 × 0.88 ≈ 2,567 N·m, and an open differential splits it equally, about 1,284 N·m per axle.

Answer: A

Correct answer: Nitrile. Each elastomer resists different things: nitrile handles oil and fuel, silicone handles heat, and EPDM handles weather and ozone. For an oil and gasoline seal, nitrile is the right choice.

• A (correct): Nitrile rubber is the elastomer known for handling oil and fuel.
• B: EPDM is chosen for weather and ozone resistance, but it swells in oil and fuel.
• C: Silicone is valued for heat resistance, not for resistance to fuel and oil.
• D: Natural rubber is stretchy and tough but is attacked by oils and fuels.

Answer: B

Correct answer: Tapped holes. Since the screws engage the housing itself, the housing holes must carry internal threads. Those are tapped holes, cut or formed with a tap.

• A: Clearance holes let a bolt pass through without engaging the wall, which would require a nut.
• B (correct): Tapped holes have internal threads, so the screws can thread straight into the housing.
• C: A countersink shapes the hole's top for a flush head but adds no threads for the screw to grip.
• D: Dowel pins locate parts; they leave no threaded hole for the screws.

Answer: D

Correct answer: 0.79 mm. Tooth spacing is the reciprocal of TPI, then convert inches to millimeters.

• A: 0.031 is the spacing in inches (1/32); the unit was never converted to millimeters.
• B: This divides 32 by 25.4, which inverts the conversion.
• C: This multiplies 25.4 by 32, giving a length far larger than one inch of blade.
• D (correct): Spacing is 1/32 inch, and 25.4 / 32 is about 0.79 mm.

Answer: A

Correct answer: Cut away from the body and retract the blade when not cutting. Cut away from your body and hands on a stable surface, and retract or guard the blade whenever it is not in use.

• A (correct): Directing the cut away from the body and guarding the blade between cuts keeps a slip from causing injury.
• B: If the blade slips, it travels straight into the worker.
• C: An exposed blade can cut anyone who picks up or brushes against the knife.
• D: A hand in the blade path can be cut if the knife slips.

Answer: D

Correct answer: 4 MPa. Find the bonded area first: 50 mm x 15 mm = 750 mm². Then stress = force / area =

N/mm², or 4 MPa.

This is only a nominal average; real joints have edge and peel stresses.

• A: This divides the load by the 15 mm length alone instead of by the overlap area.
• B: This divides the load by the 50 mm width alone instead of by the overlap area.
• C: This divides area by load (750 / 3,000); stress is load divided by area.
• D (correct): Area = 50 x 15 = 750 mm², and 3,000 N / 750 mm² = 4 N/mm², which is 4 MPa.

Answer: A

Correct answer: 45 3/4 inches. Needed length = total of the pieces + (number of cuts x kerf).

• A (correct): 6 x 7 1/2 = 45 inches of blocks plus 6 x 1/8 = 3/4 inch of kerf gives 45 3/4 inches.
• B: This counts only the blocks and ignores the material turned into sawdust by the six cuts.
• C: This allows kerf for only five cuts, but the plan states six full separation cuts.
• D: This uses 1/4 inch per cut, double the stated 1/8-inch kerf.

Answer: A

Correct answer: Torque each bolt to 40 N·m in order, then use an angle gauge to add 90 degrees. This is torque-angle tightening. Bring each bolt to 40 N·m with a torque wrench in the specified pattern, then turn each one 90 degrees more, measured with an angle gauge, in the same order so the head clamps evenly.

• A (correct): Torque-angle tightening uses a torque wrench for the first stage and an angle gauge to measure the extra turn, following the set order.
• B: Degrees of rotation cannot be converted into an added torque figure; the procedure calls for a measured angle.
• C: An impact wrench gives no reliable torque, and estimating the angle by eye skips the measurement the procedure requires.
• D: Ignoring the listed sequence can clamp the head unevenly and warp it.

Answer: C

Correct answer: 11.87 mm. Read the sleeve first: 11 mm plus the visible half-millimeter line gives 11.50 mm. Then add the thimble:

The reading is

• A: This misses the half-millimeter line on the sleeve, an error of exactly 0.50 mm.
• B: This treats each thimble division as 0.001 mm instead of the stated 0.01 mm.
• C (correct): The sleeve gives 11.50 mm and the thimble adds 0.37 mm, for 11.87 mm.
• D: This treats each thimble division as 0.1 mm, adding 3.7 mm to the 11.50-mm sleeve value.

Answer: B

Correct answer: Four 1.5 mm chamfers, each at 45°. The letter X has two uses here. 4X means the feature occurs four times, while 1.5 × 45° gives the chamfer's leg length and angle. So each of the four corners gets a 1.5 mm, 45° chamfer.

• A: The 4X is a quantity, not a multiplier for the 1.5 mm size.
• B (correct): 4X gives four occurrences, and 1.5 × 45° describes a 1.5 mm bevel at 45 degrees.
• C: There is no Ø symbol, so the feature is a chamfer, not a hole.
• D: A round would be marked with R; a size with an angle describes a beveled chamfer.

Answer: D

Correct answer: The work rest must be adjusted, but the tongue-guard gap is acceptable. Convert each fraction to a decimal and compare it with its own limit.

Work rest:

which is more than the 0.125-inch (1/8) maximum, so it must be adjusted using a safe shutdown. Tongue guard:

which is less than the 0.250-inch (1/4) maximum, so it is acceptable.

• A: This ignores that 5/32 inch (0.156 in.) is larger than the one-eighth-inch (0.125 in.) work-rest maximum.
• B: This swaps the two limits; the tongue guard allows up to one-quarter inch, and the rest allows only one-eighth inch.
• C: Only the rest gap is too large; 7/32 inch (0.219 in.) is less than the one-quarter-inch (0.250 in.) tongue-guard maximum.
• D (correct): 5/32 in. = 0.156 in. exceeds the 0.125 in. rest limit, while 7/32 in. = 0.219 in. is within the 0.250 in. tongue-guard limit.

Answer: A

Correct answer: It is the same. In the dry-friction model,

The coefficient and the normal force are unchanged, so the friction force is the same at any sliding speed.

• A (correct): Kinetic friction equals the kinetic coefficient times the normal force, and neither depends on sliding speed.
• B: This treats dry friction like slow fluid drag, which grows in proportion to speed.
• C: This treats dry friction like fast air drag, which grows roughly with the square of speed.
• D: Sliding faster does not reduce dry friction in the simple model; the force stays fixed.

Answer: D

Correct answer: 18 kg. Water has a density of 1,000 kg/m³, which is the same as 1 kg per liter.

Mass = density × volume = 1 kg/L × 18 L = 18 kg.

• A: This slips a decimal place; each liter of water is about 1 kg, not 0.1 kg.
• B: This multiplies by 10 as if converting to weight in newtons; 180 would be the weight in N, not the mass in kg.
• C: This converts liters to cubic meters but then forgets to multiply by the density of 1,000 kg/m³.
• D (correct): Fresh water has about 1 kg of mass in every liter, so 18 L has a mass of about 18 kg.

Answer: C

Correct answer: Excess backlash between mating teeth. Backlash is the small gap between the back of one tooth and the face of its mating tooth. When the input reverses, the teeth must cross that gap before they push again, so the output lags and may clunk. Some backlash is normal, but wear makes it grow.

• A: Thrust from helical teeth pushes a gear along its shaft; it does not cause a lag on reversal.
• B: Slip belongs to smooth belt drives; meshing teeth cannot slip past each other.
• C (correct): The gap between teeth lets the input turn a little before it engages the output after a reversal.
• D: Self-locking stops a wheel from driving a worm backward; it does not produce a short delay and clunk.

Answer: D

Correct answer: 1. Ideal mechanical advantage is effort arm ÷ load arm. With the pivot centered, the two arms are equal, so the ratio is 1. The balance gives no force gain and no distance gain; it only reverses the direction of motion.

• A: A ratio of two equal, nonzero lengths cannot be zero; the balance still passes force from one side to the other.
• B: This is the value for an effort arm half as long as the load arm, not for equal arms.
• C: This would need an effort arm twice as long as the load arm; centered arms are equal.
• D (correct): Equal arms make the ratio of effort arm to load arm exactly 1.

Answer: C

Correct answer: $27.00. Convert power to kilowatts: 1,500 W = 1.5 kW. Total time: 4

h.

Energy =

kWh, and cost =

• A: This multiplies 1,500 W instead of 1.5 kW, forgetting to convert watts to kilowatts.
• B: This is the cost for only one day of running, not the full 30 days.
• C (correct): Energy is 1.5 kW × 120 h = 180 kWh, and 180 × $0.15 = $27.00.
• D: This slips a decimal place in the final multiplication of 180 kWh by $0.15.

Answer: A

Correct answer: 300 N/m. The spring constant is the slope of the line.

• A (correct): The slope is the change in force over the change in extension: 18 N divided by 0.06 m gives 300 N/m.
• B: This divides 18 N by 6 without converting centimeters to meters; 3 N per cm equals 300 N/m.
• C: This mixes the two points, dividing 30 N by 0.04 m; each force must be paired with its own extension.
• D: This divides the force change by the final 0.10 m extension instead of by the change in extension.

Answer: C

Correct answer: 300 m. Match the units first: 90 km/

Then d = vt =

• A: This multiplies 90 by 12 without converting km/h to m/s, mixing hours and seconds.
• B: This multiplies by 3.6 to convert, but going from km/h to m/s requires dividing by 3.6.
• C (correct): Converting 90 km/h gives 25 m/s, and 25 × 12 = 300 m.
• D: This slips a decimal place after the correct conversion to 25 m/s.

Answer: C

Correct answer: 150 N. In an ideal machine, work in equals work out:

The distance ratio

also shows the IMA is 3, and

• A: This multiplies the load by the distance ratio instead of dividing, which would make the effort larger than the load.
• B: This is the full load; it ignores that pulling three times as far as the load rises cuts the force to one third.
• C (correct): Work in equals work out: the effort times 2.4 m must equal 450 N times 0.8 m, which is 360 J, so the effort is 150 N.
• D: 360 is the output work in joules, not a force; it still has to be divided by the 2.4 m of rope pulled.

Answer: A

Correct answer: 1.0 mm. Find strain from Young's modulus, then multiply by the length.

Stretch:

m = 1.0 mm.

• A (correct): Strain is 100 MPa ÷ 200 GPa = 0.0005, and 0.0005 × 2 m = 0.001 m, or 1.0 mm.
• B: This is the strain read as millimeters per meter but not multiplied by the 2 m length.
• C: This divides the 0.0005 strain by the 2 m length; stretch is strain multiplied by length.
• D: This slips a power of ten when combining megapascals and gigapascals.

Answer: C

Correct answer: 320 N. The weight splits into $W\sin \theta$ along the slope and $W\cos \theta$ into the surface. With no friction, the holding force must balance the slope component.

• A: This is $W\cos \theta$, the part pressing into the ramp surface, not the part pulling down the slope.
• B: This is the full weight; on a 30 degree ramp only part of the weight acts along the slope.
• C (correct): The part of the weight pulling down along the slope is $W\sin \theta =640\times 0.50=320$ N, so that much force holds it.
• D: This uses the tangent of 30 degrees; the component of weight along the slope uses the sine.

Answer: B

Correct answer: 500 N. Only the vertical parts of the two tensions hold up the weight, so 2T sin θ = W.

• A: This simply splits the weight in half, which is right only for vertical cables; angled cables must pull harder.
• B (correct): Solving 2T sin 60° = 870 gives T = 870 ÷ 1.74 = 500 N.
• C: This uses cos 60° in place of sin 60°; the vertical part of a cable's pull uses the sine of its angle above horizontal.
• D: This divides the weight by sin 60° but forgets that two cables share the load.

Answer: C

Correct answer: 250 N and 24 cm. Square the diameter ratio to get the area ratio:

Force shrinks by the area ratio and travel grows by the same ratio, so work in equals work out.

• A: This uses the diameter ratio of 4 for both force and travel; area, which sets both, grows with the square of the diameter.
• B: The force correctly uses the area ratio of 16, but the travel uses the diameter ratio of 4 instead of the same area ratio.
• C (correct): The area ratio is (6.0/1.5) squared = 16, so the input force is 4,000/16 = 250 N and the input travel is 16 times 1.5 = 24 cm.
• D: The travel correctly uses the area ratio of 16, but the force uses the unsquared diameter ratio of 4.

Answer: B

Correct answer: About 43 N·m. Output power =

Output speed =

rad/s.

Torque = power ÷ angular velocity = 1,350 ÷ 31.4 ≈ 43 N·m.

• A: This uses the full 1,500 W; a 90 percent efficient gearbox delivers only 1,350 W.
• B (correct): Output power 1,350 W divided by about 31.4 rad/s gives about 43 N·m.
• C: This is the motor's torque reduced for losses; it leaves out the 6:1 torque gain.
• D: This divides power by rpm; power must be divided by angular velocity in rad/s.

Answer: C

Correct answer: 12.6 s. Find the piston area from the diameter, then the volume, then divide by the flow rate.

The flow is

cubic centimeters per second, so

• A: This squares the diameter but leaves out the $\pi /4$ factor, overstating the area as 64 square centimeters.
• B: This uses $\pi d^2$ without dividing by 4, making the area and the oil volume four times too large.
• C (correct): Piston area is $\pi (8.0{)}^2/4\approx 50.3$ square centimeters, so the stroke takes about 2,513 cubic centimeters; at 200 cubic centimeters per second that is about 12.6 s.
• D: This uses the 8.0 cm diameter as if it were the area; area grows with the square of the diameter.

Answer: B

Correct answer: 100 N. Take moments about the pivot. The bag makes

N·m on the left. The plank's center is at 2.5 m, which is 1.0 m right of the pivot, so its weight makes

N·m on the right and already helps.

The right end is

m from the pivot:

so F = 100 N.

• A: This ignores the plank's weight; its center lies on the right side of the pivot and helps balance the bag.
• B (correct): The plank's own weight supplies 100 N·m on the right, leaving 350 N·m for the end force: 350 ÷ 3.5 = 100 N.
• C: This adds the plank's moment to the bag's side, but the plank's center is right of the pivot, so it works against the bag.
• D: This divides by the full 5.0 m plank length instead of the 3.5 m distance from the pivot to the right end.

Answer: A

Check one letter at a time. Point K is at the top of the curved side of the half-circle, and point L is at the sharpest corner of the right triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the top of the curved side of the half-circle to the sharpest corner of the right triangle, the same spots as points K and L in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the right triangle at the right-angle corner, but point L is at the sharpest corner.
• C: The line ends in the wrong place: it meets the right triangle at the middle of the slanted side, but point L is at the sharpest corner.
• D: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point K is at the top of the curved side and it meets the right triangle at the middle of the longer leg, but point L is at the sharpest corner.

Answer: D

Count the pieces first: every figure must use each piece exactly once, with nothing added. Then pick one distinctive piece, such as the largest one or one with a curved or sharply pointed edge, and look for it in each figure; pieces may be turned but never flipped over. A figure whose cut lines are in different places has pieces of different sizes and can be crossed out. Here the pieces fit together into a rectangle.

• A: A cut is in a different place, so the pieces do not match: one piece here covers about 73% of the shape, but the matching piece in the left box covers about 61%.
• B: This figure has 3 pieces, but the left box has 2. Every piece must be used once, and nothing may be added.
• C: This figure is a square. The pieces in the left box do not have these shapes, so they cannot fill this outline without gaps or overlaps.
• D (correct): This rectangle is made of exactly the 2 pieces in the left box, each only turned and slid into place.

Answer: B

Check one letter at a time. Point E is at a corner of the long side of the trapezoid, and point F is at a wide corner of the diamond. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the trapezoid at the middle of a slanted side, but point E is at a corner of the long side and it meets the diamond at a sharp corner, but point F is at a wide corner.
• B (correct): The line joins a corner of the long side of the trapezoid to a wide corner of the diamond, the same spots as points E and F in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the diamond at the center, but point F is at a wide corner.
• D: The line ends in the wrong place: it meets the diamond at the middle of a side, but point F is at a wide corner.

Answer: A

Count the pieces first: every figure must use each piece exactly once, with nothing added. Then pick one distinctive piece, such as the largest one or one with a curved or sharply pointed edge, and look for it in each figure; pieces may be turned but never flipped over. A figure whose cut lines are in different places has pieces of different sizes and can be crossed out. Here the pieces fit together into a circle.

• A (correct): This circle is made of exactly the 2 pieces in the left box, each only turned and slid into place.
• B: A cut is in a different place, so the pieces do not match: one piece here covers about 43% of the shape, but the matching piece in the left box covers about 27%.
• C: A cut is in a different place, so the pieces do not match: one piece here covers about 85% of the shape, but the matching piece in the left box covers about 73%.
• D: This figure has 3 pieces, but the left box has 2. Every piece must be used once, and nothing may be added.

Answer: C

Count the pieces first: every figure must use each piece exactly once, with nothing added. Then pick one distinctive piece, such as the largest one or one with a curved or sharply pointed edge, and look for it in each figure; pieces may be turned but never flipped over. A figure whose cut lines are in different places has pieces of different sizes and can be crossed out. Here the pieces fit together into a trapezoid.

• A: This figure has 4 pieces, but the left box has 3. Every piece must be used once, and nothing may be added.
• B: A cut is in a different place, so the pieces do not match: one piece here covers about 35% of the shape, but the matching piece in the left box covers about 43%.
• C (correct): This trapezoid is made of exactly the 3 pieces in the left box, each only turned and slid into place.
• D: A cut is in a different place, so the pieces do not match: one piece here covers about 13% of the shape, but the matching piece in the left box covers about 26%.

Answer: A

Count the pieces first: every figure must use each piece exactly once, with nothing added. Then pick one distinctive piece, such as the largest one or one with a curved or sharply pointed edge, and look for it in each figure; pieces may be turned but never flipped over. A figure whose cut lines are in different places has pieces of different sizes and can be crossed out. Here the pieces fit together into a parallelogram.

• A (correct): This parallelogram is made of exactly the 3 pieces in the left box, each only turned and slid into place.
• B: This figure is a rectangle. The pieces in the left box do not have these shapes, so they cannot fill this outline without gaps or overlaps.
• C: A cut is in a different place, so the pieces do not match: one piece here covers about 62% of the shape, but the matching piece in the left box covers about 40%.
• D: This figure has 4 pieces, but the left box has 3. Every piece must be used once, and nothing may be added.

Answer: C

Check one letter at a time. Point M is at a corner of the rectangle, and point N is at the center of the pentagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the pentagon at a corner, but point N is at the center.
• B: The line ends in the wrong place: it meets the rectangle at the center, but point M is at a corner.
• C (correct): The line joins a corner of the rectangle to the center of the pentagon, the same spots as points M and N in the left box; turning a shape does not move a point on it.
• D: One of the shapes here is a hexagon, but the left box has a pentagon. Joining parts never changes a shape.

Answer: A

Check one letter at a time. Point T is at a sharp corner of the diamond, and point U is at the middle of a side of the triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins a sharp corner of the diamond to the middle of a side of the triangle, the same spots as points T and U in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the diamond at a wide corner, but point T is at a sharp corner and it meets the triangle at a corner, but point U is at the middle of a side.
• C: The line ends in the wrong place: it meets the triangle at the center, but point U is at the middle of a side.
• D: The line ends in the wrong place: it meets the diamond at the middle of a side, but point T is at a sharp corner.

Answer: B

Count the pieces first: every figure must use each piece exactly once, with nothing added. Then pick one distinctive piece, such as the largest one or one with a curved or sharply pointed edge, and look for it in each figure; pieces may be turned but never flipped over. A figure whose cut lines are in different places has pieces of different sizes and can be crossed out. Here the pieces fit together into a circle.

• A: A cut is in a different place, so the pieces do not match: one piece here covers about 39% of the shape, but the matching piece in the left box covers about 46%.
• B (correct): This circle is made of exactly the 3 pieces in the left box, each only turned and slid into place.
• C: This figure has 4 pieces, but the left box has 3. Every piece must be used once, and nothing may be added.
• D: A cut is in a different place, so the pieces do not match: one piece here covers about 63% of the shape, but the matching piece in the left box covers about 46%.

Answer: A

Check one letter at a time. Point G is at the middle of a side of the triangle, and point H is at the middle of a long side of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the middle of a side of the triangle to the middle of a long side of the rectangle, the same spots as points G and H in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the triangle at the center, but point G is at the middle of a side.
• C: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the rectangle at the center, but point H is at the middle of a long side.

Answer: C

Check one letter at a time. Point G is at a sharp corner of the diamond, and point H is at a corner of the triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the diamond at the center, but point G is at a sharp corner.
• B: The line ends in the wrong place: it meets the triangle at the middle of a side, but point H is at a corner.
• C (correct): The line joins a sharp corner of the diamond to a corner of the triangle, the same spots as points G and H in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the triangle at the center, but point H is at a corner.

Answer: B

Check one letter at a time. Point J is at the top of the curved side of the half-circle, and point K is at the sharpest corner of the right triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the right triangle at the middle of the shorter leg, but point K is at the sharpest corner.
• B (correct): The line joins the top of the curved side of the half-circle to the sharpest corner of the right triangle, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point J is at the top of the curved side.
• D: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point J is at the top of the curved side and it meets the right triangle at the middle of the shorter leg, but point K is at the sharpest corner.

Answer: D

Check one letter at a time. Point E is at the middle of a short side of the rectangle, and point F is at a wide corner of the diamond. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• B: The line ends in the wrong place: it meets the rectangle at a corner, but point E is at the middle of a short side.
• C: The line ends in the wrong place: it meets the rectangle at the middle of a long side, but point E is at the middle of a short side.
• D (correct): The line joins the middle of a short side of the rectangle to a wide corner of the diamond, the same spots as points E and F in the left box; turning a shape does not move a point on it.

Answer: B

Count the pieces first: every figure must use each piece exactly once, with nothing added. Then pick one distinctive piece, such as the largest one or one with a curved or sharply pointed edge, and look for it in each figure; pieces may be turned but never flipped over. A figure whose cut lines are in different places has pieces of different sizes and can be crossed out. Here the pieces fit together into a circle.

• A: A cut is in a different place, so the pieces do not match: one piece here covers about 49% of the shape, but the matching piece in the left box covers about 39%.
• B (correct): This circle is made of exactly the 4 pieces in the left box, each only turned and slid into place.
• C: A cut is in a different place, so the pieces do not match: one piece here covers about 30% of the shape, but the matching piece in the left box covers about 39%.
• D: This figure is a hexagon. The pieces in the left box do not have these shapes, so they cannot fill this outline without gaps or overlaps.

Answer: B

Count the pieces first: every figure must use each piece exactly once, with nothing added. Then pick one distinctive piece, such as the largest one or one with a curved or sharply pointed edge, and look for it in each figure; pieces may be turned but never flipped over. A figure whose cut lines are in different places has pieces of different sizes and can be crossed out. Here the pieces fit together into a rectangle.

• A: A cut is in a different place, so the pieces do not match: one piece here covers about 60% of the shape, but the matching piece in the left box covers about 40%.
• B (correct): This rectangle is made of exactly the 4 pieces in the left box, each only turned and slid into place.
• C: A cut is in a different place, so the pieces do not match: one piece here covers about 32% of the shape, but the matching piece in the left box covers about 40%.
• D: This figure is a square. The pieces in the left box do not have these shapes, so they cannot fill this outline without gaps or overlaps.