Full ASVAB Practice Form 7: Astronomy, Steering and Pulleys

Answer: B

Correct answer: At rest. Motion is always measured relative to a reference point. Inside the transport, the soldier's position does not change, so she is at rest relative to the vehicle, even though both move at 20 m/s relative to the road.

• A: That is the soldier's motion relative to the road, not relative to the vehicle she is riding in.
• B (correct): The soldier keeps the same position inside the transport, so relative to the transport she is not moving.
• C: The road appears to move backward relative to the transport, but the seated soldier does not.
• D: The transport moves at a steady speed in a straight line, and the soldier stays in her seat, so nothing here shows acceleration.

Answer: A

Correct answer: 32. The number after the element name is the mass number, which counts protons plus neutrons. Neutrons =

• A (correct): Neutrons equal mass number minus atomic number: 60 − 28 = 32.
• B: This is the number of protons, given by the atomic number.
• C: This is the mass number, the total of protons and neutrons together.
• D: This adds the two numbers instead of subtracting the protons from the mass number.

Answer: C

Correct answer: Peroxisome. Peroxisomes are small sacs that break down fatty acids and certain toxins. Their reactions produce hydrogen peroxide, which an enzyme inside the peroxisome quickly converts to water and oxygen.

• A: Lysosomes digest worn-out parts and engulfed particles with acidic enzymes; they are not named for hydrogen peroxide.
• B: The Golgi modifies, sorts and packages proteins and lipids; it does not break down fatty acids.
• C (correct): Peroxisomes break down fatty acids and neutralize toxins, and an enzyme inside them turns hydrogen peroxide into water and oxygen.
• D: Smooth ER makes lipids and detoxifies drugs, but the hydrogen peroxide breakdown happens in peroxisomes.

Answer: D

Correct answer: Neptune. The Kuiper Belt is the icy outer region beyond Neptune, home to Pluto and many similar bodies. Do not confuse it with the main asteroid belt, which lies mostly between Mars and Jupiter.

• A: Beyond Mars lies the main asteroid belt of rocky bodies, which is a different region from the Kuiper Belt.
• B: Jupiter marks the outer edge of the main asteroid belt, not the start of the icy Kuiper Belt.
• C: Nothing like the Kuiper Belt sits just past Earth; the next planet out is Mars.
• D (correct): The Kuiper Belt is an outer region of icy objects past the eighth planet, Neptune.

Answer: D

Correct answer: It loses its supply of warm ocean water and moisture. Hurricanes draw their energy from warm ocean water: evaporated moisture rises, condenses and releases latent heat that sustains the storm. Over land that supply of warmth and moisture is cut off, so the storm weakens, although its rain can still cause inland flooding.

• A: Earth's rotation affects motion over land and sea alike; the Coriolis effect does not switch off.
• B: Land is heated by the Sun, often strongly; this does not explain the loss of the storm's fuel.
• C: Pressure over land varies; this is not why hurricanes weaken.
• D (correct): Hurricanes are fueled by warm water and moisture whose latent heat drives the circulation, so cutting off that supply weakens them.

Answer: A

Correct answer: 3.0 m. A plane mirror forms an image as far behind the mirror as the object is in front of it. The image is 1.5 m behind the mirror, so the total distance from the sailor to his image is

• A (correct): The image appears 1.5 m behind the mirror, and the sailor is 1.5 m in front, so they are 3.0 m apart.
• B: This is the distance from the mirror to the image, not from the sailor to the image.
• C: This halves the distance; a plane mirror image is as far behind the mirror as the object is in front.
• D: The image is not on the mirror's surface; it appears behind the mirror.

Answer: B

Correct answer: Chemical weathering. Weathering acts in place, while erosion and deposition involve moving material. Because the iron-bearing minerals are reacting with oxygen and water to form rust, the minerals' chemistry is changing, which makes it chemical weathering.

• A: Mechanical weathering breaks rock into smaller pieces without changing its minerals; the rusting shows a chemical change.
• B (correct): Oxidation of iron minerals changes their chemical makeup in place, which is chemical weathering.
• C: Erosion moves weathered material elsewhere, but the stem says the material stayed in place.
• D: Deposition is the settling of transported material, and nothing here was transported.

Answer: D

Correct answer: Analogous structures, showing similar solutions evolved independently. Ask whether the similarity comes from shared ancestry or from a shared job. Bat and fly wings share only their function, not their construction, so they are analogous structures.

• A: Homologous structures share an inherited underlying design; a bat wing and a fly wing do not.
• B: Similar function without shared design does not point to recent common ancestry.
• C: Traits gained through use during life are not inherited, and this does not describe how wings arose.
• D (correct): Features that do a similar job but evolved separately, without a shared design, are analogous.

Answer: B

Correct answer: Magnesium chloride and water. Acid plus base gives a salt plus water. Combine the metal ion from the base (magnesium) with the negative ion from the acid (chloride) to get magnesium chloride, and

supplies the water.

• A: Hydrogen gas forms when an acid reacts with a reactive metal, not with a metal hydroxide.
• B (correct): The acid's hydrogen ions join the base's hydroxide ions to make water, and magnesium ions pair with chloride ions as the salt.
• C: Hydrogen chloride is the acid that is used up, so it cannot be the product of the reaction.
• D: Neutralization makes a salt and water; it does not release chlorine gas or form an oxide.

Answer: A

Interpolation estimates a value between measured points and is usually fairly safe. Extrapolation goes beyond the measured range, here from week 6 to week 30, and is riskier because conditions such as the plant's growth limit may change.

• A (correct): Week 4.5 lies between measured points, while week 30 is far beyond the data, where growth conditions may change.
• B: This reverses the terms; estimating between measured points is interpolation, and going beyond them is extrapolation.
• C: A steady trend inside the measured range does not guarantee it continues far outside it; the plant may stop growing.
• D: Both estimates use the same data; the farther an estimate goes beyond the tested range, the less trustworthy it is.

Answer: C

Correct answer: Its core will collapse in a supernova, leaving a neutron star or black hole. A star's fate depends mainly on its mass. Sun-like stars become red giants and then white dwarfs, but a star of about 20 solar masses ends with core collapse and a supernova, leaving a neutron star or black hole.

• A: That gentle path fits stars of roughly the Sun's mass, not stars many times more massive.
• B: No star fuses hydrogen forever, and more massive stars actually use up their core fuel faster.
• C (correct): Very massive stars end in core collapse, and the remnant is a neutron star or black hole.
• D: A star's remnant does not become a planet; planets form differently and shine by reflected light.

Answer: A

Correct answer: 8 m/s. Net force: 2,700 N − 900 N = 1,800 N. Acceleration:

Starting from rest, speed after 4 s is 2 m/s² × 4

• A (correct): Net force is 1,800 N, giving 2 m/s² of acceleration, and 2 m/s² for 4 s gives 8 m/s.
• B: This uses the full 2,700 N pull and ignores the 900 N of resistance.
• C: This adds the resistance to the pull instead of subtracting it.
• D: This is the acceleration in m/s², not the speed reached after 4 s.

Answer: B

Correct answer: Field B's yield is about 9.5% higher than Field A's. Read the real values from the axis, not the bar sizes, because the baseline is 80 kg rather than 0.

Field B's yield is only about 9.5% higher, even though its bar looks three times as tall.

• A: This compares the bar heights by eye; the bars only measure 4 kg and 12 kg above the 80 kg baseline, not the full yields.
• B (correct): The difference is 92 minus 84, or 8 kg, and 8 divided by the reference value 84 is about 0.095, a 9.5% increase.
• C: The 8 is a difference in kilograms, not a percent; it must still be divided by the original value of 84 kg.
• D: This divides the 8 kg difference by 92 instead of 84, using the wrong reference value for an increase from Field A.

Answer: A

Correct answer: 45. Use change = (births + immigrants) − (deaths + emigrants). The herd grew by

Solving gives I = 45 immigrants.

• A (correct): Net change is +60, so 140 + I − 95 − 30 = 60, which gives I = 45.
• B: This leaves out the 30 emigrants, who are a loss that must be made up by more immigrants.
• C: This swaps the roles of births and deaths, treating the 140 births as a loss and the 95 deaths as a gain.
• D: This is the net change in herd size, not the number of immigrants; births, deaths and emigration also changed the herd.

Answer: A

Correct answer: ADH rises, the kidneys reabsorb more water, and urine becomes small in volume and dark. The hypothalamus senses blood that is too concentrated, and the pituitary releases more ADH. ADH makes kidney tubules reabsorb more water, so urine is small in volume and dark. This negative feedback opposes the water loss.

• A (correct): Low body water triggers more ADH, which makes kidney tubules return more water to the blood, leaving concentrated urine.
• B: This is the response to extra body water, the opposite of the dehydrated worker's situation.
• C: ADH causes more water reabsorption, not less, so it cannot produce a large volume of dilute urine.
• D: The body adjusts ADH to water balance, and the kidneys keep filtering blood even when water is short.

Answer: C

Correct answer: $4.40. Divide the cost by the number of pounds:

so the beef costs $4.40 per pound.

• A: This rounds the weight up to 4 pounds before dividing, which understates the price per pound.
• B: This multiplies the price by the weight instead of dividing.
• C (correct): Price per pound is dollars divided by pounds: 15.40 divided by 3.5 is 4.40.
• D: This divides pounds by dollars, which gives pounds per dollar, not dollars per pound.

Answer: B

Correct answer: $630. Add the expenses:

Subtract from income:

• A: This is the total of the expenses, not the amount left over.
• B (correct): Expenses total 725 + 310 + 140 + 95 = $1,270, and 1,900 − 1,270 = $630.
• C: This is an addition slip; the expenses total $1,270, not $1,170.
• D: This is a slip that adds an extra $100 to the expenses.

Answer: B

Correct answer: 2/5. Work = rate x time. The rate is $\frac{1}{10}$ of the road per day, so in 4 days the crew finishes

of the road.

• A: This is the fraction still left to regrade, not the fraction already done.
• B (correct): The crew does 1/10 per day, and 4 days times 1/10 equals 4/10, which simplifies to 2/5.
• C: This is the fraction done in one day, not in 4 days.
• D: This inverts the number of days worked instead of multiplying the rate by the time.

Answer: C

Correct answer: 202. Differences from 200: +3, −3, +5, −1, +6, which sum to +10.

Average difference:

Mean:

• A: This adds the full sum of the differences, +10, to the baseline without dividing it by 5.
• B: 203 is the middle value when the counts are put in order, which is the median, not the mean.
• C (correct): The differences from 200 are +3, −3, +5, −1, and +6, which total +10; 10 divided by 5 is +2, so the mean is 202.
• D: 200 is only the baseline; the differences above it outweigh those below it.

Answer: D

Correct answer: 17.05 kg. Line up the decimal points and fill empty places with zeros:

Estimate check:

• A: This lines up 4.3 by its right-hand digit, treating it as 0.43 instead of 4.30.
• B: This treats 12 as 0.12 by lining up its digits on the right instead of at the decimal point.
• C: This drops the 0 placeholder in the tenths place; 0.75 + 0.30 is 1.05, not 1.5.
• D (correct): Lining up the points as 12.00 + 0.75 + 4.30 gives 17.05.

Answer: B

Correct answer: 52. Multiplication and division come before subtraction, and divisions are done left to right:

Then

• A: This divides 6 ÷ 2 first and then 48 ÷ 3 = 16, which breaks the left-to-right rule.
• B (correct): 7 × 8 = 56, then 48 ÷ 6 = 8 and 8 ÷ 2 = 4 from left to right, so 56 − 4 = 52.
• C: This stops after 48 ÷ 6 = 8 and never divides by 2.
• D: This adds the 4 instead of subtracting it.

Answer: B

Correct answer: 4 hours 40 minutes. Add the rates over a common denominator:

of the job per hour.

Invert to get the time:

which is 4 hours 40 minutes.

• A: This is half of the faster deckhand's time, which would only be true if both worked as fast as the faster one.
• B (correct): The combined rate is 3/14 of the job per hour, so the time is 14/3 hours, which is 4 hours 40 minutes.
• C: This averages the two times; a team is always faster than either worker alone.
• D: This adds the two times instead of adding the rates.

Answer: D

Correct answer: 2.4 hours. Time equals total divided by rate: $0.288÷0.12$. Move both decimal points two places right:

Check:

• A: This shifts the divisor two places but the dividend three places, which makes the answer ten times too large.
• B: This misplaces the decimal point in the quotient; 0.12 times 0.24 is only about 0.03 liter.
• C: This multiplies the rate by the total instead of dividing the total by the rate.
• D (correct): Shifting both points two places gives 28.8 divided by 12, which is 2.4.

Answer: A

Correct answer: 2,400 words. Find the rate per minute:

words per minute.

Scale to an hour:

words per hour. Or divide by 0.75 hour:

• A (correct): Her rate is 1,800 / 45 = 40 words per minute, and 40 x 60 = 2,400 words per hour.
• B: This is her rate per minute, not per hour.
• C: This treats 45 minutes as 0.45 hour; 45 minutes is 0.75 hour.
• D: This multiplies the words by the minutes instead of dividing to find a rate.

Answer: C

Correct answer: 1,692. Break 36 into 30 and 6 and multiply each part by 47:

Add the partial products:

An estimate of

shows the answer is a little under 1,800.

• A: This forgets to shift the tens partial product, adding 141 instead of 1,410 to 282.
• B: This drops a carry when adding the partial products.
• C (correct): 47 × 30 = 1,410 and 47 × 6 = 282, and 1,410 + 282 = 1,692.
• D: This adds an extra 100 while combining the partial products.

Answer: C

Correct answer: $15,000. Remove the base pay to get the commission: 1,150 minus 400 is $750.

Sales equal commission divided by the rate:

Check: 5 percent of 15,000 is 750, plus 400 is 1,150.

• A: This divides the whole $1,150 by 0.05 without first removing the $400 base pay.
• B: This divides by 0.5 instead of 0.05; 5 percent is 0.05.
• C (correct): The commission was 1,150 minus 400, or 750, and 750 divided by 0.05 is 15,000.
• D: This takes 5 percent of the commission; the commission is the part, so you must divide by the rate.

Answer: D

Correct answer: $80.00. Run the steps forward: cost × 1.20 = marked price, and marked price × 0.90 = $86.40.

So cost × 1.08 = $86.40, and cost =

Check:

and 90% of $96 is $86.40.

• A: This undoes only the 20% markup and forgets to undo the 10% discount.
• B: This undoes only the 10% discount, giving the marked price instead of the store's cost.
• C: This treats the two changes as a net 10% to remove by subtracting; percent changes are undone by dividing by each multiplier.
• D (correct): Cost × 1.20 × 0.90 = cost × 1.08 = $86.40, so the cost is $86.40 ÷ 1.08 = $80.00.

Answer: A

Correct answer: $480. Work in order, each fraction applying to what remains. Rent:

Food:

leaving 1,200.

Savings:

so she saves $480.

• A (correct): Rent leaves $1,600, food (1/4 of $1,600) leaves $1,200, and 2/5 of $1,200 is $480.
• B: This takes 2/5 of the full $2,400, but the savings fraction applies to what is left after rent and food.
• C: This takes 2/5 of the $1,600 left after rent and skips the food step.
• D: This is the amount left after saving (3/5 of $1,200), not the amount saved.

Answer: B

Correct answer: 8 minutes 20 seconds. To lap the slower runner, the faster one must gain a full 400 meters. She gains

meter each second, so it takes

Since 480 seconds is 8 minutes, 500 seconds is 8 minutes 20 seconds.

• A: This adds the speeds, which applies only to runners heading toward each other.
• B (correct): The faster runner gains 0.8 m/s, so a 400-meter gain takes 500 seconds.
• C: This is how long the faster runner takes to run one lap, not how long she takes to gain a lap.
• D: This reads 8.33 minutes as 8 minutes 33 seconds instead of converting 0.33 minute to 20 seconds.

Answer: B

Correct answer: 60. Sand is 5 parts and equals 20 bags, so one part is

bags.

The mix has

parts, so the batch uses

bags (8 cement, 20 sand, 32 gravel).

• A: This is only the gravel, 8 × 4 bags.
• B (correct): One part is 20 ÷ 5 = 4 bags, and the 15 total parts make 15 × 4 = 60 bags.
• C: This adds cement and gravel (8 + 32) but leaves out the 20 bags of sand.
• D: This multiplies 20 by the 15 total parts, treating the 20 bags as one part instead of five.

Answer: D

Correct answer: unproductive. Split fruitless into fruit (a result or yield) plus -less (without). A fruitless search or effort yields no results, so it is unproductive.

• A: Fruity means tasting of fruit; it ignores the -less ending entirely.
• B: Abundant means plentiful, which is closer to the opposite, fruitful.
• C: This describes fruit that is not ready yet, a literal reading that misses the sense of no results.
• D (correct): Fruit here means a result, and -less means without, so a fruitless effort produces nothing.

Answer: D

Correct answer: loud noise. The result "made it hard to hear the phone" tells you RACKET is about sound. A racket from jackhammers is a loud noise.

• A: A racket can be a strung paddle used in tennis, but jackhammers do not produce one.
• B: Racket can mean a dishonest business, a real meaning that does not fit jackhammers or hearing.
• C: Jackhammers do create dust, but dust would not make it hard to hear a phone.
• D (correct): Jackhammers are noisy, and a loud noise is exactly what would drown out a phone.

Answer: D

Correct answer: sufficient. Adequate means enough or satisfactory for a purpose. Sufficient matches in meaning and degree; excellent and extra overstate it, and lacking is the opposite.

• A: Excellent is far stronger than adequate, which means only good enough.
• B: This is the opposite; lacking means not enough.
• C: Extra means more than is needed, which overstates adequate.
• D (correct): Adequate means enough for the need, which is what sufficient means.

Answer: C

Correct answer: extremely small. Micro means small, and a microscope is used to see tiny things. Cracks that can be spotted only under a bright lamp are extremely small.

• A: This is the meaning of macro, the opposite root that test writers use as a trap.
• B: Depth is not part of the word; micro is about size, and the hard-to-see cracks point to small.
• C (correct): Micro means small, and the cracks could be seen only under a bright lamp, so they were tiny.
• D: Cracks can be dangerous, but the word itself tells how small they are, not how risky.

Answer: A

Correct answer: likely. On the evidence scale, possible is weakest, then plausible, then probable, then certain. Fresh tracks raise the idea above merely possible but short of proof, so likely is the match.

• A (correct): Probable means more likely than not, a judgment supported by some evidence, such as the boot prints.
• B: Proven means certain beyond doubt; boot prints make the conclusion likely but do not confirm it.
• C: The evidence points toward the shed, so unlikely reverses the deputy's judgment.
• D: Imaginable means merely possible, too weak for a conclusion backed by fresh tracks.

Answer: D

Correct answer: crash. Collision comes from collide, with the d changing to s before -ion. The ending forms a noun naming an act, so a collision is the act of hitting, a crash. The damage to both trucks confirms it.

• A: Collide is the verb base; after "The" the sentence needs a noun.
• B: This is the meaning of collusion, a lookalike word with a different base.
• C: A near miss means the vehicles did not touch, yet both were damaged.
• D (correct): Collide plus -sion names the act of colliding, which is a crash.

Answer: C

Correct answer: illnesses. "Such as" introduces examples, and what colds, ear infections and stomach bugs share is that they are sicknesses. AILMENTS means illnesses.

• A: This is only one example from the list, not the category that covers all of them.
• B: Medicines treat these problems, but the list names the problems themselves.
• C (correct): Colds, ear infections and stomach bugs are all minor sicknesses, so the word names that whole group.
• D: The clinic treats patients, but the list names conditions, not people.

Answer: B

Correct answer: orderly. Organized follows was and describes the toolbox, so it is an adjective naming a result: arranged in order. Organizational would mean relating to an organization. The answer is orderly.

• A: This is the meaning of organizational, a family member about organizations rather than tidiness.
• B (correct): Organized describes something arranged neatly, like a toolbox where every socket has its place.
• C: Cluttered means messy, the opposite of a toolbox where she can find anything.
• D: Nothing in the sentence concerns cost; the clue is about how easily she finds things.

Answer: B

Correct answer: aimed. TRAINED has the object "flashlight" and the phrase "on the open gate" shows direction. Train here means aim; taught is the primary-definition trap.

• A: Taught is the familiar sense, but a flashlight cannot be taught.
• B (correct): To train a light on something is to point it there, and "aimed his flashlight on the gate" fits.
• C: Switching on a light is a different action; "trained on the open gate" tells where the beam went.
• D: Practicing is part of training a skill, which does not fit an object like a flashlight.

Answer: B

Correct answer: save. The flood is the threat and most of the tools is what survived, so the crew rescued them. SALVAGE means to save something from loss or damage.

• A: Selling is a possible later action, but the sentence only says the tools were recovered.
• B (correct): Save fits: the crew rescued the tools from the flood damage.
• C: Flooded tools may need cleaning, but that adds a step the sentence never mentions.
• D: Discard is the opposite of rescuing the tools.

Answer: A

Correct answer: still. The result clue, reflecting like a mirror, means no waves or ripples. PLACID means calm and peaceful, so still is the precise match.

• A (correct): Still fits: a surface smooth enough to mirror the trees is calm and undisturbed.
• B: A lake's depth has nothing to do with reflecting like a mirror; this is a loosely related idea.
• C: Dawn might be cold, but temperature does not explain the mirror-like surface.
• D: Stormy is the opposite; rough water could not reflect clearly.

Answer: D

Correct answer: easily influenced. Impress, impression, impressive, and impressionable share a root but not a meaning. The suffix -able here means able to receive an impression, so an impressionable person is easily influenced, as the context of adopting others' opinions confirms. Impressive is the family false friend.

• A: Impressive is a different member of the impress family; it means causing admiration, not being shaped by others.
• B: This confuses the word with making a lasting impression; the volunteers are the ones affected, not memorable.
• C: This is the opposite; the volunteers changed their opinions quickly.
• D (correct): The sentence shows these volunteers taking on whatever opinion they heard last, which is being easily influenced.

Answer: B

Correct answer: Misinterpreted. Mis- marks a mistake in an action, and construe means to interpret or understand. Taking a joke as criticism is interpreting it wrongly, so misconstrued means misinterpreted.

• A: Built badly reads construe as construct and treats the prefix like mal-; the error is in understanding, not in making something.
• B (correct): Mis- means wrongly, and construe means interpret, so to misconstrue is to interpret wrongly.
• C: Refused to hear treats mis- as refusal; mis- marks a mistaken action, not a decision to decline.
• D: Explained clearly drops the error that mis- signals, and her worry shows something went wrong.

Answer: A

Correct answer: attack from the side. Flank has more than one sense, so let the sentence decide. Troops sent "around its left end" while others hold the front are hitting the line from the side, so FLANK means attack from the side.

• A (correct): Sending troops around the end of a line is moving to strike it from the side.
• B: The third company holds the front; the companies going around the end are not striking from the front.
• C: Flank can mean to be next to something, as guards flank a door, but these troops move around the line to attack it.
• D: Moving around the enemy's end to strike it is the opposite of pulling back.

Answer: A

Correct answer: hinted at something unpleasant. The clue without naming anyone shows the accusation was indirect, and blaming a coworker for theft is negative. Insinuate means to imply something unflattering indirectly, which separates it from assert, demonstrate, and deny.

• A (correct): Insinuate means to suggest something, usually negative, in an indirect way, as the shift lead does without naming anyone.
• B: Declaring openly is asserting; the clue without naming anyone shows the accusation was indirect.
• C: This is demonstrate; the sentence gives no proof, only a suggestion.
• D: Denying would reject the idea; the shift lead is putting the idea forward, not rejecting it.

Answer: C

Correct answer: Marcus was getting ready for an early-morning fitness test. Evidence: an early bedtime, a 4:30 alarm, gym clothes by the door and a note about a 0600 fitness test. Bridge: people prepare like this before an important early event. Conclusion: Marcus was getting ready for the test. The wrong answers add past results, habits or feelings the passage never mentions.

• A: No earlier test result appears anywhere in the passage; this invents a past event.
• B: The passage says he went to bed earlier than usual, which suggests this schedule is unusual, not a daily habit.
• C (correct): The early alarm, the laid-out gym gear and the note about a 0600 test at the track all point to preparation for the test.
• D: Nothing describes his feelings about running; this assigns a motive the passage never signals.

Answer: C

Correct answer: Read the size printed on the old filter's frame. The passage follows process order, marked by first, next, before, then and finally. After the old filter comes out, the very next step is to read the size printed on its frame, before it is thrown away and before the new filter goes in.

• A: Turning the furnace off is the first step, done before the filter door is even opened.
• B: Inserting the new filter comes after the size has been checked, so it is not the step right after removal.
• C (correct): The passage says to check the printed size before throwing the old filter away, right after pulling it out.
• D: This is the final step of the process, not the one that follows removing the old filter.

Answer: A

Correct answer: become weaker. The crew had to wait because the wind was too strong. The following sentence says the gusts died down to a light breeze, and then the lift went ahead. That restatement shows abate means become weaker; putting it back in, wait for the wind to become weaker, fits the sentence.

• A (correct): The next sentence restates what happened: the gusts died down to a light breeze, which is the wind becoming weaker.
• B: Direction is never mentioned; the passage stresses that the wind went from strong gusts to a light breeze.
• C: This is the opposite; stronger wind would have kept the crane idle, but the crew finished the lift after the wind changed.
• D: The wind speed is given, but the crew was waiting for the wind to calm, not for someone to measure it.

Answer: D

Correct answer: The heaters are alike in most ways but differ in a key safety feature. The passage lists several similarities and then turns, with however, to the one difference it cares about: the automatic tip-over shutoff. When a comparison stresses one meaningful difference, that difference is the main idea, and the similarities are only background.

• A: This repeats similarities that only set the scene; it leaves out the difference the passage stresses.
• B: The passage never gives fire statistics; this comes from outside the paragraph.
• C: The passage suggests choosing the heater with a shutoff, not avoiding heaters; this reverses its advice.
• D (correct): The similarities lead up to the turn word however, and the rest of the passage explains why the tip-over shutoff matters.

Answer: D

The routine schedule starts with breakfast at 6 a.m., but "however" introduces an exception for federal holidays. On those days breakfast and lunch become one brunch from 9 a.m. to 1 p.m., so that is the first meal. The exception, not the routine, controls the answer.

• A: These are the normal breakfast hours, but on federal holidays breakfast is replaced by brunch.
• B: These are the normal lunch hours, which the holiday brunch also replaces.
• C: These are dinner hours, which do not change, but dinner is not the first meal of the day.
• D (correct): On federal holidays the first meal is the single brunch, served from 9 a.m. to 1 p.m.

Answer: B

Correct answer: Route 14 is shorter and toll-free, while Highway 6 is usually plowed sooner in winter storms. Sort each feature to its own side: Route 14 is 32 miles, free, and has town traffic lights; Highway 6 is 41 miles, has a $3 toll, no lights, and is plowed first. The supported statement keeps every feature on the right route and makes no overall ranking or time claim.

• A: Highway 6 has the toll and no lights, but it is the longer route at 41 miles, so this swaps a feature.
• B (correct): Each feature is matched to the correct route: Route 14 is 32 miles and free, and Highway 6 is plowed first.
• C: The passage compares separate traits and never ranks one route as better overall.
• D: Travel time is never stated, and the towns' traffic lights and 25 mph limits could slow Route 14, so always faster adds a claim.

Answer: D

Correct answer: Leather usually resisted cuts better, and synthetic kept hands drier in every wet trial. Keep each qualifier with its own subject. The leather gloves did better in most cut tests, not all of them, and the synthetic gloves stayed drier in every wet trial. Only the statement that keeps usually for leather and every time for synthetic matches.

• A: The passage says most tests, and it notes a few where the synthetic gloves held up just as well.
• B: This weakens an absolute claim; the passage says the synthetic gloves stayed drier in every wet-weather trial.
• C: Both features are swapped between the two kinds of gloves.
• D (correct): This keeps the qualifier most for the leather gloves and the absolute every for the synthetic gloves, just as the passage does.

Answer: A

Correct answer: Every student in the class eventually passed the practical exam. Track each quantity word: all 25 took the exam, most passed the first time, a few did not, and every one of those passed in May. Linking the last two facts shows that all students passed eventually, while no student passed only partly or never.

• A (correct): Most passed the first time, and the passage says every student who retook the exam passed, so all 25 passed in the end.
• B: The passage says a few students did not pass the first time, so "every" overstates the first-attempt result.
• C: This reverses the numbers: most passed the first time, and only a few needed a retake.
• D: This misreads the passage; the few who failed at first all passed on the second try.

Answer: B

Correct answer: They could not afford enough hay at its higher price. Map the chain: dry spring, then a small hay harvest, then a sharp price rise, then ranchers unable to afford hay, then the cattle sale. A question about the most direct cause wants the link right before the sale, which is that the ranchers could not afford the expensive hay.

• A: The dry spring started the chain, but it led to the sale only through the poor harvest and the price rise.
• B (correct): This is the last link in the chain, the step right before the sale, and the passage connects the sale to it directly.
• C: The small harvest is a middle link; it raised prices, and the high price is what the ranchers could not afford.
• D: The passage says nothing about cattle prices; this cause is invented.

Answer: D

Correct answer: The robot may have helped, but the drop in errors cannot yet be credited to it alone. Ask who says each opinion. The error-free claim is the seller's and the praise is the head of nursing's. The only unattributed judgment is the last sentence, which says the two changes cannot be separated, so the author is cautious: the robot might deserve some credit, but the evidence cannot show how much.

• A: This repeats the seller's claim, which the author does not adopt, and the numbers themselves show 9 errors remained.
• B: This glowing judgment belongs to the head of nursing; quoting it does not mean the author agrees.
• C: This swings too far the other way; the author says the two changes cannot be separated yet, not that the labels were responsible.
• D (correct): The final, unattributed sentence is the author's voice; it accepts that errors fell but says the cause is still unclear because two changes happened together.

Answer: D

Correct answer: 12 units. Both points have y = 4, so they lie on a horizontal line. The distance is the difference of the x-values:

units.

• A: This subtracts 7 from 5, dropping the negative sign of -7.
• B: This adds the two y-values, but the points lie on the same horizontal line, so y does not change.
• C: This subtracts in the opposite order and keeps the sign, but a distance is never negative.
• D (correct): The points share y = 4, so subtract the x-values: 5 - (-7) = 12.

Answer: D

Correct answer: 64. An exponent counts repeated factors:

Doubling step by step gives 2, 4, 8, 16, 32, 64.

• A: This multiplies the base by the exponent, 2 times 6, instead of repeating the factor.
• B: This uses 2 as a factor only five times, which is 2^5.
• C: This uses 2 as a factor seven times, which is 2^7.
• D (correct): Using 2 as a factor six times gives 2, 4, 8, 16, 32, 64.

Answer: A

Correct answer: (3, 12). Substitute y = 4x into the second equation:

so 5x = 15 and x = 3. Then

Check:

• A (correct): With x = 3 and y = 12, both y = 4x and x + y = 15 are true.
• B: This reverses the order; with x = 12, y would have to be 48 for y = 4x.
• C: This pair adds to 15 but 10 is not 4 times 5, so it fits only one equation.
• D: Here y is 4 times x, but 2 + 8 = 10, not 15, so it fits only one equation.

Answer: C

Correct answer: −9. Work inside the bars first: |−9| = 9 because −9 is 9 units from zero. The minus sign in front then takes the opposite: −9.

• A: This finds |−9| = 9 but ignores the minus sign written outside the bars.
• B: This treats the two minus signs as canceling to zero; −|−9| means the opposite of 9.
• C (correct): |−9| = 9, and the minus sign outside the bars makes the result −9.
• D: This squares 9; absolute value is a distance, not a power.

Answer: B

Correct answer: x ≥ 5. Distribute on both sides:

Subtract 5x and add 2: 3x ≥ 15. Divide by 3: x ≥ 5. Check x = 5: 38 ≥ 38 is true, so 5 is included.

• A: This distributes to the first term only, writing 8x − 1 and 5x + 2.
• B (correct): Distributing gives 8x − 2 ≥ 5x + 13, so 3x ≥ 15 and x ≥ 5.
• C: This reverses the sign, but dividing by positive 3 does not change direction.
• D: This forgets to move the −2 on the left, solving 3x ≥ 13.

Answer: A

Correct answer: (-4, 0). On the x-axis, y = 0. Solve

so the line crosses at (-4, 0).

• A (correct): Setting y = 0 gives 3x = -12, so x = -4.
• B: This is the y-intercept, where x equals 0, not where the line meets the x-axis.
• C: This loses the negative sign when moving 12 to the other side of the equation.
• D: This finds the correct value -4 but puts it in the y position; x-intercepts have the form (x, 0).

Answer: A

Correct answer: 360 square inches. The diagonals of a rhombus are perpendicular, so the area is half the product of the full diagonals.

The sign covers 360 square inches.

• A (correct): Half of 30 times 24 is 360 square inches.
• B: This multiplies the diagonals but forgets the factor of one half.
• C: This divides the product by 4, as if half-diagonals were multiplied and then halved again.
• D: This adds the two diagonals instead of multiplying them.

Answer: C

Correct answer: 2,124. Test 4 with the last two digits and 8 with the last three digits. For 2,124, 24 is a multiple of 4, but 124 leaves a remainder of 4 when divided by 8, so 2,124 is divisible by 4 only.

• A: It is divisible by 4, but 416 = 8 × 52, so it is also divisible by 8.
• B: Its last two digits, 34, are not a multiple of 4.
• C (correct): Its last two digits, 24, are a multiple of 4, but its last three digits, 124, are not a multiple of 8 (124 ÷ 8 = 15.5).
• D: Its last two digits, 30, are not a multiple of 4.

Answer: D

Correct answer: {(4, 1), (5, 1), (6, 1)}. A relation is a function when no input is paired with two different outputs. In {(4, 1), (5, 1), (6, 1)} each input appears once; sharing the output 1 is allowed.

• A: The input 1 is paired with both 4 and 5, so this is not a function.
• B: The input 3 is paired with both 2 and −2, so this is not a function.
• C: The input 0 is paired with both 1 and 5, so this is not a function.
• D (correct): Each input has exactly one output; different inputs may share the same output.

Answer: D

Correct answer: 8 meters. Write the formula and substitute.

So h = 104 divided by 13 = 8 meters.

• A: This divides 104 by the sum of the bases, 26, forgetting the one half.
• B: This divides 104 by only the longer base, 16.
• C: This divides 104 by only the shorter base, 10.
• D (correct): The average base is 13, and 104 divided by 13 is 8.

Answer: A

Correct answer: 2x. Distribute:

and the minus before the second group flips both signs: $-x+6$. Combine:

so the result is $2x$. Checking with x = 1: the original is

which matches.

• A (correct): 3x - 6 - x + 6 gives 2x, and the constants cancel.
• B: This flips only the first sign in the second group, writing -x - 6 instead of -x + 6.
• C: This multiplies 3 by x only, writing 3x - 2 instead of 3x - 6.
• D: This drops the minus sign in front of the second group and adds x - 6.

Answer: D

Correct answer: x = 11. The LCD of 2 and 5 is 10. Multiply every term, including the 5:

Distribute:

3x = 33 and x = 11.

Check:

• A: This comes from multiplying the fractions by 10 but leaving the 5 on the right side unchanged, giving 3x + 17 = 5.
• B: This comes from writing −2(x − 1) as −2x − 2, forgetting that a negative times −1 gives +2.
• C: This comes from multiplying only the x by −2 and writing −2(x − 1) as −2x − 1.
• D (correct): Multiplying every term by 10 gives 5(x + 3) − 2(x − 1) = 50, so 3x + 17 = 50 and x = 11.

Answer: B

Correct answer: 74°. Angles 4 and 5 lie between the rails on opposite sides of the brace, so they are alternate interior angles and are equal:

which gives 3x = 45 and x = 15. Angle

°.

Angle 2 sits directly above angle 4 on the same straight brace, so they form a linear pair: angle

°.

• A: 106° is angle 4 (and angle 5); angle 2 forms a linear pair with angle 4, so it is supplementary, not equal.
• B (correct): Angle 4 is 106°, and angle 2 is its linear-pair partner, so 180 - 106 = 74°.
• C: 15 is x, not an angle measure.
• D: This subtracts x from 180; the value of x must first be used to find an angle.

Answer: C

Correct answer: 225π square cm. A radius drawn to the point of contact meets the tangent at a right angle, so the radius, the tangent segment and the 25 cm distance form a right triangle with hypotenuse 25.

The area is π(15)^2 = 225π square cm.

• A: This is the circumference, 2π times 15, not the area.
• B: This uses the 25 cm distance as the radius; that distance is the hypotenuse, from the center to an outside point.
• C (correct): The right triangle gives r = 15, and π times 15 squared is 225π square cm.
• D: This uses the 20 cm tangent segment as the radius; the radius is the other leg of the right triangle.

Answer: A

Correct answer: 56°. Interior angle

°. Angles B and C are the base angles opposite the equal sides, so angle C = 62°. Then angle

°. (Check with the exterior angle theorem:

)

• A (correct): With both base angles 62°, angle A = 180 - 124 = 56°.
• B: 62° is each base angle; angle A is the vertex angle between the equal sides.
• C: 124° is the sum of the two base angles, not angle A.
• D: This splits the exterior angle in half, but the two remote angles A and C are not equal.

Answer: B

Correct answer: To reverse the rotor coil current every half turn so the torque keeps one direction. Fed with steady DC, a rotor coil would turn until its sides faced the poles and then be pushed back. The segmented commutator, with brushes sliding across it, reverses the coil current every half turn so the force keeps turning the rotor the same way.

• A: Raising voltage is a transformer's job, and a transformer needs AC; the commutator does not change voltage.
• B (correct): Switching the coil connections at the right moment keeps the coil from rocking back, so the rotor keeps turning.
• C: That is the job of the bearings, not the commutator.
• D: Running current is limited by back emf, not the commutator; at start-up there is little back emf to limit it.

Answer: A

Correct answer: Semiconductor. Pure silicon conducts poorly because its four outer electrons are locked into covalent bonds, yet a small energy boost from heat or light frees some of them to carry current. Adding tiny amounts of impurities, called doping, raises conductivity in a controlled way, which is what makes transistors and solar cells possible. The tempting mistake is calling silicon a conductor because it is used in electronics; metals conduct far better, and silicon's usefulness comes from controllable, not high, conductivity.

• A (correct): Silicon's resistivity lies between that of conductors and insulators, and doping can control its conductivity.
• B: Insulators such as dry porcelain or PVC have very high resistivity and cannot be made to conduct by doping.
• C: Good conductors are metals such as silver, copper, and aluminum with many free electrons.
• D: Ionic conductors are electrolytes such as salt water, where ions carry the charge.

Answer: B

Correct answer: The field is stronger near that end. In a field diagram, the closer the lines, the stronger the field. Lines crowded near the end mean the field there is stronger than at the middle of the side.

• A: Field lines never cross, because a point cannot have two field directions.
• B (correct): Crowded lines show a stronger field and spread-out lines show a weaker one.
• C: This reverses the rule; closer lines mean a stronger field, not a weaker one.
• D: Line spacing shows strength, not direction; direction is given by the arrows.

Answer: B

Correct answer: The current is the same through both resistors. In series there is only one path, so charge cannot pile up or leak away between parts. Every series component carries the same current; what differs is the voltage drop, which is larger across the 100 ohm resistor.

• A: Larger resistance does not draw more current, and in series the current cannot differ anyway.
• B (correct): Series parts form a single path, so the same current passes through each one regardless of its resistance.
• C: Unequal currents happen in parallel branches; a single series path cannot have different currents.
• D: Current is not consumed; the current leaving a resistor equals the current entering it.

Answer: D

Correct answer: P-type silicon with holes as majority carriers. A three-valence-electron dopant can form only three complete bonds in the silicon crystal. Each missing electron is a hole, so the dopant is an acceptor and the result is p-type silicon with holes as the majority carriers. The material is still electrically neutral overall.

• A: N-type doping needs a dopant with five valence electrons that donates an extra electron; gallium has only three.
• B: Even a few dopant atoms per million raise silicon's conductivity greatly; that is the purpose of doping.
• C: The holes act as positive carriers, but each is balanced by a fixed negative acceptor ion, so the material stays neutral.
• D (correct): Gallium completes only three of silicon's four bonds, leaving holes, so it is an acceptor and makes p-type material.

Answer: C

Correct answer: 12 V. Think in shares of resistance. With three resistors of R and one of 2R, the total is 5R.

The larger resistor gets

and each smaller one gets 6 V. Check:

• A: This is each resistor’s share before the change, one-fourth of 30 V.
• B: This doubles the old 7.5 V share without allowing for the larger total resistance.
• C (correct): The shares are now 1, 1, 1 and 2 out of 5, so the larger resistor takes 2/5 of 30 V.
• D: This is the new drop across each of the three smaller resistors.

Answer: B

Correct answer: 30 W. Input power equals output divided by efficiency:

Check: 90 percent of 30 W is 27 W, and the other 3 W is lost as heat.

• A: This multiplies by 0.90, which would make the input smaller than the output.
• B (correct): Dividing the useful output by the efficiency, 27 divided by 0.90, gives 30 W of input.
• C: This adds 10 percent of the output instead of dividing by the efficiency.
• D: This is the power lost as heat, not the input power.

Answer: B

Correct answer: 3 A. Power, voltage and current are linked by

Check: 12 V times 3 A gives back 36 W.

• A: This multiplies the power by the voltage; current comes from dividing power by voltage.
• B (correct): From P = VI, the current is 36 W divided by 12 V, which is 3 A.
• C: This divides voltage by power, which is the formula turned upside down.
• D: Adding 36 and 12 combines unlike quantities and has no meaning.

Answer: C

Correct answer: The fuse opens, because 0.3 A is more than its 0.25 A rating. Convert the rating first: 250 mA = 250 × 0.001 A = 0.25 A. A steady 0.3 A is above that rating, so the fuse is expected to melt and open the circuit, stopping current in that path.

• A: This compares the numbers without converting units; 250 mA is only 0.25 A.
• B: A fuse protects against excess current, melting when the current through it is too high.
• C (correct): Converting 250 mA gives 0.25 A, so 0.3 A is an overload and the fuse link should melt and open the path.
• D: Resetting describes a circuit breaker; a fuse is sacrificial and must be replaced after it opens.

Answer: D

Correct answer: Conventional current flows from anode to cathode, while electrons move from cathode to anode. In a forward-biased diode, conventional current flows in the direction the symbol's triangle points, from anode to cathode. Electrons, being negative, travel the opposite way, from cathode to anode.

• A: Conventional current goes from anode to cathode; it is electrons that move from cathode to anode.
• B: Electrons carry negative charge, so they move opposite to conventional current.
• C: This reverses both directions; conventional current follows the symbol's triangle toward the bar.
• D (correct): Conventional current follows the triangle from the p-side anode to the n-side cathode, and electrons move the opposite way.

Answer: B

Correct answer: The current returns on the neutral, so outgoing and return currents stay equal. A GFCI compares current leaving on the hot conductor with current returning on the neutral. Current that flows from hot through a person to neutral still returns on the neutral, so there is no imbalance to detect. That is a key limit of GFCI protection.

• A: A GFCI does not trip on total current; it reacts to a few milliamperes of imbalance.
• B (correct): A GFCI only senses an imbalance; current through a person from hot to neutral still comes back on the neutral.
• C: Detecting arcing is the job of an AFCI, not a GFCI.
• D: The mat blocks a path to ground, but the hand-to-hand path between hot and neutral is still complete.

Answer: A

Correct answer: A wave that swings between −1 V and +12 V. Classify by a change of sign, not a change of size. Only the wave that goes from −1 V up to +12 V crosses to the opposite side of zero. The others stay on one side, even the rectified humps that merely touch zero.

• A (correct): It dips below zero and then returns above it, so its direction really reverses.
• B: It changes size but never crosses zero, so it is varying DC.
• C: Touching zero is not reversing; each hump returns on the same positive side, which is pulsating DC.
• D: It stays on the negative side and never changes sign, so it is steady DC.

Answer: B

Correct answer: 12 Ω. Total current is

The 8 Ω branch carries

so the other branch carries

Its resistance is 24 V divided by 2 A, or 12 Ω. Check: 8 parallel with 12 is

and 24 squared divided by 4.8 is 120 W.

• A: 24 squared divided by 120 W gives the equivalent resistance of the whole pair, not the unknown branch.
• B (correct): The total current is 5 A, the 8 Ω branch takes 3 A, and the remaining 2 A at 24 V means 12 Ω.
• C: Subtracting 4.8 Ω from 8 Ω treats the resistances as if they combined in series.
• D: Adding the 3 A branch current to the 5 A total instead of subtracting it gives 8 A and the wrong resistance.

Answer: C

Correct answer: 4 hours. Stored energy:

Wh. Battery output needed:

Runtime:

• A: This multiplies the load by 0.8, making the battery supply less than the load uses.
• B: This applies the 80 percent efficiency twice, once to the stored energy and once to the load.
• C (correct): The battery must supply 48 W divided by 0.8, or 60 W, and 240 Wh divided by 60 W is 4 hours.
• D: This divides 240 Wh by the 48 W load and ignores the inverter loss.

Answer: A

Correct answer: 6 V and 4 s. Treat this as two separate definitions. Voltage is energy per charge, so 72 J divided by 12 C gives 6 V. Current is charge per time, so time is charge divided by current: 12 C divided by 3 A gives 4 s. Check that each number carries the correct unit; swapping volts and amperes or seconds is a frequent error when several quantities appear in one problem.

• A (correct): V = $\frac{72}{12}$ = 6 V; t = $\frac{12}{3}$ = 4 s.
• B: The numerical values are paired with wrong quantities and units.
• C: 72−12 and 12×3 are invalid substitutions.
• D: This confuses energy/current and time.

Answer: A

Correct answer: Alternator. The battery supplies the burst of energy needed for cranking. After the engine starts, the belt-driven alternator powers the vehicle's electrical loads and recharges the battery, which is why running voltage is normally about 13.5 to 14.7 V.

• A (correct): The engine-driven alternator takes over the electrical load once the engine runs and recharges the battery.
• B: The starter only cranks the engine and stops working once the engine runs.
• C: The coil produces high voltage for spark plugs; it does not charge the battery.
• D: A resistor uses up voltage; it cannot produce electrical energy.

Answer: D

Correct answer: How the oil performs in cold-temperature viscosity tests. In a multi-grade label the number before the W (winter) rates how the oil flows in cold tests, and the number after the dash rates viscosity when hot. In 10W-40, the 10 is the cold rating and the 40 is the hot rating.

• A: The grade says nothing about change intervals; those come from the manufacturer's schedule.
• B: That is the number after the dash, the 40 in this label.
• C: W means winter here, not weight in pounds; the label is a viscosity rating.
• D (correct): The W stands for winter, and the number before it rates cold flow; a lower number flows better when cold.

Answer: D

Correct answer: 45 bar. Pressure is force over area: 1,800 N ÷ 4 cm² = 450 N/cm². Since 1 N/cm² equals 10 kPa, that is 4,500 kPa. One bar is 100 kPa, so

bar.

• A: This divides by 100 directly from N/cm², skipping the step that 1 N/cm² equals 10 kPa.
• B: This treats 1 N/cm² as equal to 1 bar, but 1 bar is 10 N/cm².
• C: This is the value in kilopascals; it still has to be divided by 100 to get bar.
• D (correct): 1,800 ÷ 4 = 450 N/cm², which is 4,500 kPa, and 4,500 ÷ 100 = 45 bar.

Answer: A

Correct answer: Less body roll, but tires that skip over bumps more, reducing grip and comfort. Spring rate is a compromise. Stiffer springs cut roll and dive on smooth pavement, but on rough ground they let the tire bounce off bumps instead of following them, so grip can drop and the ride becomes harsher.

• A (correct): Stiff springs limit roll, but on rough surfaces the tire cannot follow the bumps as well, so grip and ride suffer.
• B: Stiffer springs can help on smooth roads, but on rough roads they can reduce tire contact.
• C: A stiffer spring compresses less under the same load, so it would not lower the car.
• D: Spring rate strongly affects comfort; dampers only control how fast the springs move, so they do not set comfort alone.

Answer: A

Correct answer: Neutral releases the clutches and bands so no drive path exists; use park and the parking brake. In neutral the transmission does not connect its input shaft to its output shaft, so engine torque stops inside the gearbox. Because nothing is locked, the vehicle is free to roll, so a parked vehicle should rely on park and the parking brake.

• A (correct): In neutral the gear-selecting clutches and bands are released, breaking the torque path, so the truck can roll unless park and the parking brake hold it.
• B: Neutral does not lock anything; it only breaks the path, which is why a vehicle in neutral can roll.
• C: The engine still turns the converter impeller in neutral; neutral alone does not hold a vehicle in place.
• D: The differential is not what breaks the path in neutral, and the foot brakes are not a parking device.

Answer: D

Correct answer: It increases. Compression ratio is (swept volume plus clearance volume) divided by clearance volume. With swept volume fixed, shrinking the clearance volume makes the denominator fall faster than the numerator, so the ratio rises.

• A: Shrinking the bottom of the ratio, the clearance volume, raises the ratio rather than lowering it.
• B: Compression ratio depends on clearance volume, so changing that volume changes the ratio.
• C: The ratio rises, but by how much depends on how much clearance is removed; there is no automatic doubling.
• D (correct): The swept volume is unchanged, so a smaller clearance volume makes the ratio of total volume to clearance volume larger.

Answer: D

Correct answer: Whether the tire has been run underinflated or overloaded. An underinflated or overloaded tire sags, so its edges carry more of the load and both shoulders wear faster. Center wear suggests overinflation and one-edge wear suggests alignment, so both-shoulder wear points to checking pressure and load first.

• A: Overinflation tends to wear the center of the tread, not both shoulders.
• B: Imbalance is linked to vibration and cupping, not even wear on both shoulders.
• C: Camber or toe problems usually wear only one edge, not both edges equally.
• D (correct): Wear on both shoulders points toward low pressure or too much load, though it is a clue, not proof.

Answer: A

Correct answer: So the strut and spring can rotate as the wheels are turned. On a steered strut, the whole strut and spring turn with the knuckle as the driver steers. The bearing in the strut mount lets that rotation happen smoothly; a worn mount can cause binding, creaks or a popping sound when steering.

• A (correct): The strut turns with the knuckle during steering, and the bearing lets it rotate smoothly against the body.
• B: The wheel bearing in the knuckle handles hub rotation as the car rolls, not the strut mount.
• C: Damping over bumps happens inside the strut as oil is forced through valves, not in the mount.
• D: Toe is set by tie rod length; the mount bearing does not change it.

Answer: D

Correct answer: 120 W. Each parallel branch sees the full 12 V. Branch currents are

A and

so the total is 10 A.

As a check, the equivalent resistance is 1.2 ohms, and

• A: This adds the resistances to 5 ohms as if the parts were in series, but parallel branches each get the full 12 V.
• B: This counts only the seat heater branch (12 V x 6 A) and leaves out the fan.
• C: This counts only the fan branch (12 V x 4 A) and leaves out the seat heater.
• D (correct): The branches draw 12/2 = 6 A and 12/3 = 4 A, so the feed carries 10 A and 12 V x 10 A = 120 W.

Answer: C

Correct answer: 10 degrees, retarded. Treat BTDC angles as positive and ATDC angles as negative: 8 degrees BTDC is +8 and 2 degrees ATDC is -2.

The spark now fires later in the piston's travel, so the timing was retarded by 10 crankshaft degrees.

• A: Subtracting 2 from 8 treats both readings as before TDC; the second reading is after TDC, so the two angles add.
• B: The size is right, but moving from before TDC to after TDC makes the spark later, which is retarded.
• C (correct): The spark moves 8 degrees to reach TDC and 2 more past it, a total of 10 degrees later, which is retarded.
• D: This both subtracts the angles incorrectly and reverses the direction; firing after TDC is later, not earlier.

Answer: B

Correct answer: Cabin air filter. Weak airflow and odors from the vents point to the cabin air filter, which cleans air entering the passenger compartment. The engine air filter is a separate part that affects engine performance.

• A: This filter feeds air to the engine; when clogged it affects engine performance, not vent airflow.
• B (correct): This filter cleans air entering the passenger compartment, and a clogged one causes weak vent airflow and odors.
• C: The oil filter cleans engine oil and has nothing to do with air delivered to the passenger compartment.
• D: The fuel filter cleans fuel going to the engine, not air for the heating and air-conditioning system.

Answer: A

Correct answer: Sliding bevel gauge. A sliding bevel has a blade that can be set to any angle and then locked. Set it against the existing cut, lock it, and transfer the same angle to the new boards without ever reading degrees.

• A (correct): Its blade can be locked at any angle, so it copies and transfers an unknown angle directly.
• B: A try square only provides a fixed 90-degree angle.
• C: A standard combination square head gives fixed 90- and 45-degree references, not an arbitrary angle.
• D: A framing square is a large fixed right-angle tool and cannot be locked to copy an odd angle.

Answer: A

Correct answer: Chlorides break down the protective chromium oxide film in spots. Stainless steel stays clean because chromium forms a self-repairing oxide film. Chlorides from salt water or pool chemicals can break that film in small spots, causing pitting, so the grade must be matched to the environment.

• A (correct): Stainless resists rust through a thin oxide film, but chlorides from salt or pool chemicals can attack it locally and cause pitting.
• B: Stainless steel is corrosion resistant, not rust-proof; real stainless grades can still pit in chlorides.
• C: Fatigue produces cracks that grow from stress raisers under cycling loads, not scattered corrosion pits.
• D: Chromium is added for corrosion resistance; surface hardness does not explain pits that form only in the pool area.

Answer: D

Correct answer: 9.525 mm. Change the fraction to a decimal, then multiply by the exact factor of 25.4 mm per inch:

A quick magnitude check (a bit under 10 mm) catches a backwards conversion.

• A: This divides 0.375 by 25.4 instead of multiplying, so the conversion was done backwards.
• B: This misplaces the decimal point; a 3/8 in hole cannot be almost 100 mm wide.
• C: This uses 25 mm per inch instead of the exact 25.4 mm per inch.
• D (correct): 3/8 in = 0.375 in, and 0.375 × 25.4 = 9.525 mm.

Answer: B

Correct answer: 120 mm/min. Multiply feed per revolution by rotational speed so the revolution units cancel:

• A: This adds the RPM and the feed per revolution instead of multiplying them.
• B (correct): Feed per revolution times revolutions per minute gives 0.15 x 800 = 120 mm/min.
• C: This divides 800 by 0.15; the two quantities must be multiplied so revolutions cancel.
• D: This is a decimal-place slip; 0.15 x 800 is 120, not 12.

Answer: C

Correct answer: 5 board feet. Board feet = thickness x width x length (all in inches) / 144.

• A: 720 is the volume in cubic inches; it still has to be divided by 144 cubic inches per board foot.
• B: Dividing 720 by 12 treats a board foot as 12 cubic inches instead of 144.
• C (correct): 2 x 10 x 36 = 720 cubic inches, and 720 / 144 = 5 board feet.
• D: This ignores the 2-inch thickness, using only 10 x 36 / 144, which is a face area, not a volume.

Answer: B

Correct answer: Springback. After plastic bending, some elastic strain remains and recovers when the load is removed, so the bend opens a little. Shops plan for springback by bending slightly past the target angle.

• A: Thermal expansion is a size change caused by temperature, not a bent part opening up after release.
• B (correct): Elastic recovery that lets a bent part relax partly toward its original shape is called springback.
• C: Fracture means the material cracks or breaks; this strip stayed in one piece.
• D: Malleability is the ability to be shaped under compression, not the partial return after bending.

Answer: C

Correct answer: A self-locking nut. Locking features such as self-locking nuts or suitable thread-locking compounds address loosening. A plain flat washer distributes load but does not lock the nut.

• A: A flat washer mainly spreads bearing load; it is not a positive locking device.
• B: A dowel pin locates and aligns parts; it does not keep a nut from turning.
• C (correct): A self-locking nut has a built-in feature, such as an insert or deformed thread, that resists loosening.
• D: Extra length does not add a locking feature or stop the nut from backing off.

Answer: A

Correct answer: 78 N·m. Only the perpendicular part of the force counts:

• A (correct): Torque is 200 × 0.45 × sin 60°, or 90 × 0.866, which is about 78 N·m.
• B: This treats the push as perpendicular; at 60 degrees only part of the force turns the fastener.
• C: This uses 0.5 as the factor, which is the sine of 30 degrees, not 60 degrees.
• D: This divides by sin 60° instead of multiplying; an angled push can never give more torque than a perpendicular one.

Answer: A

Correct answer: 360 N. Torque depends on the actual lever arm, which is where the hand pushes: 0.25 m. Rearranging

• A (correct): With the hand 0.25 m from the bolt, 90 N·m divided by 0.25 m requires 360 N.
• B: This uses the full 0.30-m wrench length, but the effective arm is only where the force is applied.
• C: This multiplies torque by the arm length instead of dividing.
• D: This multiplies 90 by the 0.30-m wrench length, which uses both the wrong operation and the wrong arm.

Answer: A

Correct answer: The spring constant k. The slope of a force-extension line is $\Delta F/\Delta x$, which is the spring constant. A steeper line means a stiffer spring, and the area under the line gives the stored energy.

• A (correct): Slope is the change in force divided by the change in extension, which is exactly the stiffness k.
• B: Stored energy is the area under the line, not its slope.
• C: Natural length is a property of the unloaded spring and is not read from the slope of this graph.
• D: The graph describes the spring's response to loads; its own weight does not appear as the slope.

Answer: A

Correct answer: Deliver more work out than is put in. A simple machine can change the size, direction, or distance of a force, but it cannot create energy. In the ideal case work out equals work in, and friction makes real output smaller.

• A (correct): Work output can never exceed work input; at best the two are equal in an ideal machine.
• B: Machines commonly lengthen the effort path in exchange for a smaller force.
• C: Lowering the needed force is the main purpose of these machines.
• D: A wedge turns a forward push into sideways pushes, so direction can change.

Answer: D

Correct answer: 180 N. The movable pulley is held up by two rope segments, so the IMA is 2. Effort = 360

• A: Multiplying the load by 2 instead of dividing gives a force larger than the load, which a pulley that helps cannot require.
• B: This treats the pulley as fixed; a movable pulley has two segments sharing the load.
• C: Dividing by 3 assumes a third supporting segment that this simple system does not have.
• D (correct): Two segments pull up on the movable pulley, so each carries half of 360 N.

Answer: A

Correct answer: A flow of oil. A pump moves oil from the reservoir into the system, so it creates flow. Pressure appears only when that flow is resisted, for example by a load on a cylinder.

• A (correct): A pump creates flow, and pressure rises only as that flow meets resistance such as a loaded cylinder.
• B: Pressure builds only when the flow meets resistance; with no load the oil circulates at low pressure.
• C: Heat is shed mainly at the reservoir and coolers, not produced as cooling by the pump.
• D: A pump converts the energy of its drive into fluid power; it cannot create energy.

Answer: A

Correct answer: 130 m. Displacement is the straight line from start to finish. The legs are perpendicular, so use the Pythagorean theorem.

• A (correct): The two legs are at right angles, so the displacement is √(50² + 120²) = √16,900 = 130 m.
• B: This is the total distance flown along the path, not the straight-line displacement.
• C: This subtracts the legs as if they lay along one line in opposite directions.
• D: This averages the two legs, which has no meaning for displacement.

Answer: D

Correct answer: 30 cm. Every point on the rigid handle turns through the same angle, so each point moves in proportion to its distance from the pivot.

Bristle travel = 10 cm ×

This third-class lever trades force for a larger, faster motion at the far end.

• A: This flips the ratio; the bristles are farther from the pivot, so they move more than the hand, not less.
• B: Points at different distances from the pivot move different amounts; only the angle of rotation is the same.
• C: This measures the bristle distance from the lower hand (0.80 m) instead of from the pivot, giving a ratio of 2.
• D (correct): The bristles are three times as far from the pivot as the lower hand, so they move three times as far.

Answer: B

Correct answer: About 20 hp. At steady speed the engine force equals the resisting force, so

Convert to horsepower: 15,000 ÷ 746 ≈ 20 hp.

• A: This multiplies 15 kW by 0.746 instead of dividing the watts by 746.
• B (correct): Power is 600 × 25 = 15,000 W, and 15,000 ÷ 746 is about 20 hp.
• C: This divides the force by the speed, 600 ÷ 25, which is not a power at all.
• D: This treats 15 kW as if it were 15 hp; a horsepower is about 746 W, not 1,000 W.

Answer: C

Correct answer: 3 m/s². Weight and normal force:

Friction:

• A: This divides the full 120 N push by the mass, forgetting to subtract friction.
• B: This divides the 75 N friction force by the mass instead of the net force.
• C (correct): Friction on the bin is 0.5 × 150 = 75 N, net force is 120 − 75 = 45 N, and 45 ÷ 15 = 3 m/s².
• D: This adds friction to the push; kinetic friction opposes the sliding, so it must be subtracted.

Answer: A

Correct answer: About 2.1 mm. Use the temperature change, not a single reading: ΔT =

That is about 2.1 mm.

• A (correct): The temperature change is 50°C, and 17 × 10⁻⁶ × 2.5 × 50 = 0.002125 m, about 2.1 mm.
• B: This uses the final temperature, 70°C, as the change; only the 50 degree rise counts.
• C: This uses the starting temperature, 20°C, as the change instead of the 50 degree rise.
• D: This slips a power of ten when converting 0.002125 m to millimeters.

Answer: A

Correct answer: 300 N. Only the vertical part of each tension holds the sign up, and with the angle measured from vertical that part is $T\cos \theta$.

Tilted segments always need more tension than the 240 N they would carry hanging straight.

• A (correct): Each segment's vertical share is $T\cos 37^{\circ }$, so $2\times 0.80T=480$ N and T = 300 N.
• B: This is the tension if the segments hung straight down; tilting them means each needs more tension than half the load.
• C: This multiplies the straight-hanging share by cos 37 degrees; you must divide by the cosine, which raises the tension.
• D: This uses sin 37 degrees, but the angle is measured from vertical, so the vertical part of the tension uses the cosine.

Answer: B

Correct answer: 98 N. Convert mass to weight:

The ramp's IMA is

• A: This divides the mass, 40 kg, by the IMA; mass must first be converted to weight in newtons.
• B (correct): The weight is 40 times 9.8 = 392 N, the IMA is 3.0/0.75 = 4, and 392/4 = 98 N.
• C: This is the generator's full weight; the ramp's IMA of 4 cuts the needed effort to one quarter of it.
• D: This multiplies the weight by the IMA; a helping machine divides the load by its mechanical advantage.

Answer: D

Correct answer: It sinks, and keeps sinking, because it is squeezed smaller and displaces less water. A balloon is compressible. Deeper water squeezes it, so it displaces less water and its buoyant force falls below its weight. Sinking deeper squeezes it more, so it keeps sinking faster.

• A: Neutral buoyancy held only at 5 m; at 6 m the balloon is compressed and no longer balanced.
• B: Buoyancy depends on displaced volume, which shrinks as the balloon is compressed.
• C: Greater depth adds pressure on all sides; for a squeezable balloon it reduces lift rather than adding it.
• D (correct): Higher pressure compresses the balloon, cutting its displaced volume and buoyancy, so it sinks further and is squeezed even more.

Answer: A

Correct answer: 900 N. The acceleration points opposite the velocity because the elevator is slowing, so it points upward. Then

• A (correct): Slowing a downward motion means the acceleration points up, so N = 75 × (10 + 2) = 900 N.
• B: This is the true weight, which the scale reads only at constant speed.
• C: This counts only the 75 × 2 needed for the acceleration, not the full normal force.
• D: This uses g − a, but slowing down while moving down is an upward acceleration.

Answer: B

Correct answer: 165 N. Potential energy gained:

Work against friction:

Total push work = 990 J, so the push force is

• A: This subtracts friction, but friction opposes the push and must be added.
• B (correct): Total work 750 J + 240 J = 990 J, and 990 ÷ 6 = 165 N.
• C: This covers only the potential energy gain and ignores the energy lost to friction.
• D: This is the total work in joules, not the force; it must be divided by 6 m.

Answer: C

Correct answer: 54 N·m. Stage ratios are

N·m.

• A: This is the ideal torque from the 12:1 ratio; it skips the 90 percent efficiency.
• B: This adds the stage ratios (3 + 4 = 7) instead of multiplying them, then applies the efficiency.
• C (correct): The stage ratios multiply, 3 times 4 = 12, so ideal torque is 60 N·m, and 90 percent of that is 54 N·m.
• D: This adds the stage ratios to get 7 and also ignores the efficiency.

Answer: C

Check one letter at a time. Point X is at a wide corner of the diamond, and point Y is at the middle of the bottom side of the house shape. 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 X is at a wide corner and it meets the house shape at a bottom corner, but point Y is at the middle of the bottom side.
• B: The line ends in the wrong place: it meets the diamond at the middle of a side, but point X is at a wide corner.
• C (correct): The line joins a wide corner of the diamond to the middle of the bottom side of the house shape, the same spots as points X and Y 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 house shape at the peak of the roof, but point Y is at the middle of the bottom side.

Answer: C

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 a corner of the short side of the trapezoid. 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 half-circle at a corner of the flat side, but point J is at the top of the curved side and it meets the trapezoid at the middle of the short side, but point K is at a corner of the short side.
• B: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point K is at a corner of the short side.
• C (correct): The line joins the top of the curved side of the half-circle to a corner of the short side of the trapezoid, the same spots as points J and K 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 half-circle at the middle of the flat side, but point J is at the top of the curved side.

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 trapezoid.

• A: This figure is a parallelogram. The pieces in the left box do not have these shapes, so they cannot fill this outline without gaps or overlaps.
• B (correct): This trapezoid is made of exactly the 2 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 68% of the shape, but the matching piece in the left box covers about 78%.
• D: This figure has 3 pieces, but the left box has 2. Every piece must be used once, and nothing may be added.

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 square.

• A: A cut is in a different place, so the pieces do not match: one piece here covers about 41% of the shape, but the matching piece in the left box covers about 49%.
• B (correct): This square is made of exactly the 2 pieces in the left box, each only turned and slid into place.
• C: 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.
• D: This figure has 3 pieces, but the left box has 2. Every piece must be used once, and nothing may be added.

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 parallelogram.

• A: 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.
• B: This figure has 4 pieces, but the left box has 3. Every piece must be used once, and nothing may be added.
• C: A cut is in a different place, so the pieces do not match: one piece here covers about 29% of the shape, but the matching piece in the left box covers about 18%.
• D (correct): This parallelogram is made of exactly the 3 pieces in the left box, each only turned and slid into place.

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 pentagon.

• A (correct): This pentagon is made of exactly the 3 pieces in the left box, each only turned and slid into place.
• B: 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.
• 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 55% of the shape, but the matching piece in the left box covers about 46%.

Answer: D

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

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 trapezoid.

• A (correct): This trapezoid is made of exactly the 3 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 32% of the shape, but the matching piece in the left box covers about 22%.
• 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 14% of the shape, but the matching piece in the left box covers about 22%.

Answer: B

Check one letter at a time. Point X is at a wide corner of the diamond, and point Y is at a corner of the long side of the trapezoid. 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 middle of a side, but point X is at a wide corner and it meets the trapezoid at the middle of the long side, but point Y is at a corner of the long side.
• B (correct): The line joins a wide corner of the diamond to a corner of the long side of the trapezoid, the same spots as points X and Y 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 X is at a wide corner.
• D: The line ends in the wrong place: it meets the trapezoid at the middle of the short side, but point Y is at a corner of the long side.

Answer: D

Check one letter at a time. Point P is at the top of the curved side of the half-circle, and point Q is at the middle of a side of the hexagon. 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 pentagon, but the left box has a hexagon. Joining parts never changes a shape.
• B: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point P is at the top of the curved side.
• C: The line ends in the wrong place: it meets the hexagon at a corner, but point Q is at the middle of a side.
• D (correct): The line joins the top of the curved side of the half-circle to the middle of a side of the hexagon, the same spots as points P and Q in the left box; turning a shape does not move a point on it.

Answer: B

Check one letter at a time. Point J is at a corner of the rectangle, and point K 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 rectangle at the center, but point J is at a corner.
• B (correct): The line joins a corner of the rectangle to a wide corner of the diamond, 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 diamond at the middle of a side, but point K is at a wide corner.
• D: One of the shapes here is a square, but the left box has a rectangle. Joining parts never changes a shape.

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 is a half-circle. The pieces in the left box do not have these shapes, so they cannot fill this outline without gaps or overlaps.
• B: A cut is in a different place, so the pieces do not match: one piece here covers about 46% of the shape, but the matching piece in the left box covers about 29%.
• C (correct): This trapezoid is made of exactly the 4 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 38% of the shape, but the matching piece in the left box covers about 29%.

Answer: C

Check one letter at a time. Point V is at a corner of the hexagon, and point W is at a corner of the flat side of the half-circle. 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 hexagon at the center, but point V is at a corner.
• B: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point W is at a corner of the flat side.
• C (correct): The line joins a corner of the hexagon to a corner of the flat side of the half-circle, the same spots as points V and W in the left box; turning a shape does not move a point on it.
• D: One of the shapes here is a pentagon, but the left box has a hexagon. Joining parts never changes a shape.

Answer: C

Check one letter at a time. Point V is at a corner where the roof meets a wall of the house shape, and point W 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 slanted side, but point W is at the sharpest corner.
• B: The line ends in the wrong place: it meets the house shape at the middle of a wall, but point V is at a corner where the roof meets a wall.
• C (correct): The line joins a corner where the roof meets a wall of the house shape to the sharpest corner of the right triangle, the same spots as points V and W 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 house shape at the middle of the bottom side, but point V is at a corner where the roof meets a wall and it meets the right triangle at the middle of the slanted side, but point W 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 pentagon.

• A: 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 28%.
• B: 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.
• C: A cut is in a different place, so the pieces do not match: one piece here covers about 51% of the shape, but the matching piece in the left box covers about 38%.
• D (correct): This pentagon is made of exactly the 4 pieces in the left box, each only turned and slid into place.