Full ASVAB Practice Form 4: Ohm's Law, Forces and Springs

Answer: A

Correct answer: Divergent. Plates that pull apart form a divergent boundary. Magma rises to fill the gap and builds new crust, which is what happens along mid-ocean ridges.

• A (correct): At a divergent boundary plates pull apart and new crust forms from rising magma.
• B: At a convergent boundary plates collide, and one may sink beneath the other.
• C: At a transform boundary plates grind past each other sideways without creating new crust.
• D: Subduction happens where one plate sinks under another, the opposite of plates moving apart.

Answer: B

Correct answer: Sublimation. Name the start and end states. The snow starts as solid ice and disappears into the air as vapor with no liquid stage, and solid directly to gas is sublimation.

• A: Melting turns a solid into a liquid, but no liquid water forms here.
• B (correct): The ice crystals go straight from solid to water vapor, skipping the liquid stage.
• C: Evaporation is liquid turning to gas at the surface, and there is no liquid in this case.
• D: Deposition is the reverse change, gas going directly to solid, as when frost forms.

Answer: B

Correct answer: Transpiration. Plants take up water through their roots and release it as vapor from their leaves; this is transpiration. Together with evaporation from open water, it moves water from the land into the air.

• A: Condensation is water vapor cooling into liquid droplets, such as clouds, the opposite direction.
• B (correct): Transpiration is the process in which plants give off water vapor through their leaves.
• C: Precipitation is water falling from clouds as rain, snow, sleet or hail.
• D: Infiltration is water soaking into the ground, not vapor leaving leaves.

Answer: A

Correct answer: It is a negative control. A negative control gets no treatment and is expected to show no effect from it. Comparing the treated dishes with this sterile-water dish shows whether the disinfectant made any difference.

• A (correct): It receives no treatment and is expected to show ordinary growth, giving a baseline for what happens without the disinfectant.
• B: A positive control uses something already known to work, such as a proven disinfectant; sterile water is not expected to stop growth.
• C: The dependent variable is the measured outcome, such as the amount of bacterial growth, not a dish or group.
• D: Controlled variables are factors held constant across all dishes, such as temperature; this dish is a comparison group.

Answer: A

Correct answer: During differentiation, each cell type switches on some genes and switches off others. Nearly all of a person's body cells contain the same DNA. Through differentiation, each cell turns certain genes on and others off, so a nerve cell builds long extensions for signaling while a skin cell builds a protective covering.

• A (correct): Differentiation lets cells with identical DNA use different sets of genes and take on specialized forms.
• B: Almost every body cell keeps the same full set of DNA; specialization comes from which genes are used, not from losing genes.
• C: Human body cells carry the same 46 chromosomes; the chromosome number does not explain specialization.
• D: All of a person's body cells descend from one fertilized egg by cell division, which is why their DNA matches.

Answer: C

Correct answer: The same amount of product forms sooner, because the energy barrier is lower. A catalyst lowers the activation energy, so more collisions succeed and the reaction goes faster. It is not used up, and it changes neither the final amount of product nor the overall energy change.

• A: A catalyst is not a reactant and does not raise the final yield; it only changes the speed.
• B: A catalyst does not change the overall energy released or absorbed by the reaction.
• C (correct): A catalyst provides a pathway with lower activation energy, so the reaction finishes faster with the same final yield.
• D: A catalyst speeds a reaction and is regenerated by the end, so it is not consumed.

Answer: B

Correct answer: 0.5 J. Use

• A: This skips squaring the compression, computing ½ × 400 × 0.05 instead of using 0.05².
• B (correct): Elastic energy = ½ × 400 × (0.05)² = ½ × 400 × 0.0025 = 0.5 J.
• C: This squares the compression but leaves out the factor of ½.
• D: This simply multiplies k by x, which gives a force in newtons, not stored energy.

Answer: D

Correct answer: Have the nurses rate itching without knowing which patients used the cream. Observer bias happens when what researchers expect affects what they record. In a blind study the people measuring results do not know which subjects received the treatment, so their expectations cannot shape the ratings.

• A: Repeated ratings by people who still know the groups can repeat the same bias; averaging does not remove it.
• B: A larger sample makes averages more reliable but does not stop nurses from seeing what they expect.
• C: Self-selection makes the groups less fair; it does nothing about the nurses' expectations.
• D (correct): Blinding the people who record results keeps their expectations from influencing what they record.

Answer: A

Correct answer: 32 m. For steady braking to rest,

Check: stopping takes

s at an average of 8 m/s, and 8 x 4 = 32 m.

• A (correct): Using the braking formula, 16 squared is 256, and 256 divided by 2 x 4 = 8 gives 32 m.
• B: This divides 256 by 4 and leaves out the 2 in the denominator of the braking formula.
• C: This is 16 divided by 4, which is the stopping time in seconds, not a distance.
• D: This divides 256 by 2 only, forgetting to include the 4 m/s² deceleration.

Answer: D

Correct answer: 15 kg. Newton's second law is

• A: This multiplies force by acceleration; mass is force divided by acceleration.
• B: This divides acceleration by force, which flips the relationship upside down.
• C: Adding force and acceleration mixes two different units and has no physical meaning.
• D (correct): Rearranging the second law gives mass = net force / acceleration = 45 / 3 = 15 kg.

Answer: A

Correct answer: Two identical cells, each with 12 chromosomes. Mitosis is used for growth and repair. The DNA is copied first and then split evenly, so one cell becomes two identical cells that keep the full diploid number of 12.

• A (correct): Mitosis keeps the chromosome number the same and produces two genetically identical daughter cells.
• B: This describes meiosis, which halves the number and makes gametes, not repair cells.
• C: Mitosis does not halve the chromosome number; halving happens only in meiosis I.
• D: Mitosis is a single division producing two cells, not four.

Answer: B

Correct answer: About 10 minutes. One-way time is distance divided by speed: 90,000,000 km ÷ 300,000 km/s = 300 s.

The signal must go out and the reply must come back, so the total is 2 × 300 s = 600 s. Dividing by 60 gives 10 minutes.

• A: This is the one-way travel time only; the reply must also cross the same 90 million km back to Earth.
• B (correct): Each leg takes 300 s, so the round trip is 600 s, which is 10 minutes.
• C: This treats the 600 s round-trip time as if it were already in minutes instead of dividing by 60.
• D: This doubles the round-trip time a second time, counting each leg twice.

Answer: D

Correct answer: 5,200 years. Count the halvings: 1 → 1/2 → 1/4 → 1/8 → 1/16 is 4 half-lives.

Age = 4 × 1,300 years = 5,200 years.

• A: This multiplies the half-life by 16; 1/16 remaining means 4 half-lives, not 16.
• B: This is 2 half-lives, which would leave 1/4 of the parent isotope, not 1/16.
• C: This counts 8 half-lives by halving 16; the number of halvings to reach 1/16 is 4.
• D (correct): Halving four times gives 1/16 (1 → 1/2 → 1/4 → 1/8 → 1/16), and 4 × 1,300 = 5,200 years.

Answer: D

Correct answer: 10 m/s. Only the drop in height matters: 20 m − 15 m = 5 m. With no friction, lost potential energy becomes kinetic energy, so

and the mass cancels.

• A: This uses the 15 m height of the second hill as the drop; the car has only fallen 20 − 15 = 5 m.
• B: This is the speed at ground level after a full 20 m drop, not at the top of a 15 m hill.
• C: This is the value of 2gh = 100 before taking the square root; the speed is the square root of that.
• D (correct): The car has dropped 5 m, so each kilogram has gained 50 J of kinetic energy, giving a speed of 10 m/s.

Answer: C

A vaccine presents a harmless form of an antigen, so the person's own immune system makes antibodies and memory cells: active immunity. Ready-made antibodies protect right away but the body did not make them and forms no memory cells: passive immunity.

• A: These labels are reversed: making your own response is active, and receiving finished antibodies is passive with no memory cells.
• B: Having antibodies is not enough; immunity is active only when the body's own B cells make them.
• C (correct): The vaccine's antigen makes the body build its own antibodies and memory cells, while donated antibodies work at once but build no memory.
• D: A vaccine presents a harmless antigen, and the second soldier received antibodies, so the roles are swapped.

Answer: D

Correct answer: 2,451. A number is divisible by 3 when the sum of its digits is a multiple of 3.

For 2,451:

so 2,451 is divisible by 3.

• A: Its digits add to 19, which is not a multiple of 3.
• B: Its digits add to 8, which is not a multiple of 3.
• C: Its digits add to 10, which is not a multiple of 3; ending in 3 does not matter.
• D (correct): Its digits add to 2 + 4 + 5 + 1 = 12, a multiple of 3.

Answer: A

Correct answer: 8 miles. Use

Hours cancel, leaving miles.

• A (correct): Distance is rate times time: 3.2 times 2.5 is 8.
• B: This adds the rate and the time instead of multiplying them.
• C: This divides the rate by the time; distance needs multiplication.
• D: This uses only the 2 whole hours and leaves out the last half hour.

Answer: D

Correct answer: $720. Add the parts:

One part is

Larger share:

Check:

• A: This is the smaller share (2 parts), not the larger one.
• B: This divides by 3 instead of by the 5 total parts.
• C: This takes 2/3 of the total, treating the ratio 2:3 as a fraction of the whole.
• D (correct): There are 5 parts of $240 each, and the larger share is 3 × $240 = $720.

Answer: A

Correct answer: 45 minutes. In a chase the gap shrinks by the difference of the speeds:

Time =

• A (correct): The motorcycle gains 16 mph, so 12 ÷ 16 = 0.75 hour, which is 45 minutes.
• B: This adds the speeds to get 104 mph, which is the rule for vehicles moving toward each other.
• C: This divides the gap by the motorcycle's full speed of 60 mph instead of by the 16 mph it gains.
• D: This reads 0.75 hour as 75 minutes instead of multiplying by 60.

Answer: C

Correct answer: 153 pounds. Differences from 150: −2, +3, +6, −1, +2, +10, which sum to +18.

Average difference:

Mean:

• A: This adds the whole +18 sum of differences to 150 without dividing by the 6 pallets.
• B: 152.5 is the median, halfway between the two middle weights, not the mean.
• C (correct): The differences from 150 are −2, +3, +6, −1, +2, and +10, totaling +18; 18 divided by 6 is +3, so the mean is 153.
• D: 154 is halfway between the lightest and heaviest pallets, which ignores the four other weights.

Answer: B

Correct answer: $1,050. Rent:

Savings:

Total spending:

Remaining:

• A: This subtracts rent and savings but forgets the $1,260 of other bills.
• B (correct): Rent is $1,470 and savings are $420; 4,200 − 1,470 − 420 − 1,260 = $1,050.
• C: This subtracts only the $1,260 of bills and leaves out the rent and savings.
• D: This is the rent payment, 35% of $4,200, not the amount left over.

Answer: C

Correct answer: 8.4 days. Pick a job size both times divide evenly: the LCM of 14 and 21 is 42 units.

The crews clear

units per day, so 5 units per day together. Time:

• A: This is half of the faster crew's time, which would require both crews to work as fast as the faster one.
• B: This averages the two times; working together must be faster than either crew alone.
• C (correct): Calling the job 42 units, the crews clear 3 and 2 units per day, so 5 together, and 42 / 5 = 8.4 days.
• D: This adds the times instead of adding the rates.

Answer: D

Correct answer: 1 1/2. Convert to improper fractions, then multiply by the reciprocal of the divisor.

• A: This flips the first fraction instead of the divisor, giving 4/9 times 3/2.
• B: This multiplies 9/4 by 3/2 without flipping the divisor.
• C: This divides piece by piece (2 by 1 and 1/4 by 1/2), which does not work for mixed numbers.
• D (correct): As improper fractions this is 9/4 times 2/3, which is 18/12 or 1 1/2.

Answer: C

Correct answer: 35 days. Unknown rate = team rate - known rate:

The smaller dredge alone needs 35 days.

• A: This subtracts the times (14 - 10) instead of the rates.
• B: This adds the two times, which does not give the missing worker's time.
• C (correct): The smaller dredge's rate is 1/10 - 1/14 = 4/140 = 1/35 per day, so it needs 35 days.
• D: This adds the team rate and the larger dredge's rate instead of subtracting.

Answer: A

Correct answer: 48 pillows. The floor number does not connect to the question. Beds:

Pillows:

• A (correct): Beds: 6 x 4 = 24; pillows: 24 x 2 = 48.
• B: This is the number of beds, an in-between total, not the number of pillows.
• C: This also multiplies by 5, but the floor number is extra information.
• D: This adds 6, 4 and 2 instead of multiplying for equal groups.

Answer: D

Correct answer: 165 miles. By 8:00 a.m. the truck has gone 55 miles, leaving a 280-mile gap. The gap closes at

so they meet

after the car starts. The truck has then driven 3 hours, or

from the first town.

• A: This counts only the 2 hours after the car starts and forgets the truck's first hour.
• B: This is the car's distance from the second town, 85 × 2.
• C: This assumes they meet halfway between the towns, which ignores their different speeds and start times.
• D (correct): The truck drives 3 hours in all at 55 mph, which is 165 miles.

Answer: B

Correct answer: $23.56. Add first:

Divide:

The digit after the cents is 7, so round up to $23.56 each.

• A: This cuts off 23.557 after the cents instead of rounding; the next digit, 7, means round up.
• B (correct): The total is 164.90 dollars, and 164.90 divided by 7 is 23.557..., which rounds to 23.56.
• C: This splits only the bill and leaves out the tip.
• D: This places the decimal point one place too far left; 7 people sharing about $165 pay over $20 each.

Answer: A

Correct answer: $183.60. Apply the discounts one after the other. First:

Then take 10 percent off that sale price:

Adding the percents to 25 percent would wrongly give $180.

• A (correct): 240 times 0.85 is 204, and 204 times 0.90 is 183.60.
• B: This adds the discounts to get 25 percent off; the extra 10 percent comes off the lower sale price, so it saves less.
• C: This is the total amount saved, not the price the customer pays.
• D: This applies only the 15 percent discount and leaves out the extra 10 percent.

Answer: B

Correct answer: 82. Work with totals. All 40 recruits:

The platoon of 16:

The other 24 recruits total

so their average is

• A: This averages the averages, assuming 78 is halfway between 72 and the unknown, which ignores that the groups have different sizes.
• B (correct): The other recruits' total is 3,120 minus 1,152, or 1,968, and 1,968 divided by 24 is 82.
• C: 75 is halfway between 72 and 78; it does not use the group totals at all.
• D: This swaps the group sizes, multiplying 72 by 24 and dividing the remainder by 16.

Answer: B

Correct answer: 10. There are

parts, so one part is

recruits: 15 Army and 25 Navy.

For a 1:1 ratio the Army count must equal the Navy count of 25, so

more Army recruits must join.

• A: This subtracts the ratio terms, 5 - 3, treating them as actual counts.
• B (correct): The class has 15 Army and 25 Navy recruits, so 10 more Army recruits make 25:25.
• C: This is the current number of Army recruits, not how many must be added.
• D: This is half of the 40 recruits, which is not the number of Navy recruits to be matched.

Answer: A

Correct answer: beginner. The word "is" introduces a direct definition: someone new who is still learning. The choice that matches it is beginner.

• A (correct): The definition after "is" describes someone new and still learning, which is a beginner.
• B: This is the opposite; an expert has already mastered the activity.
• C: An instructor teaches the basics rather than still learning them.
• D: This guess comes from the look-alike word novel, but the definition says nothing about writing.

Answer: C

Correct answer: flexible. Elastic first describes material that stretches and returns to shape. Applied to a schedule, it means flexible or adaptable. Read the setting to pick that sense.

• A: Rubbery fits the physical sense of elastic material, but a schedule is not made of rubber.
• B: Rigid means unable to bend or change, the opposite of a schedule that shifts.
• C (correct): In everyday use, elastic means able to adjust, like a schedule that shifts around family needs.
• D: Overloaded means having too much to do, which the example does not suggest.

Answer: C

Correct answer: Kept out. Ex- means out, and the base clude means to shut. Visitors without a badge are shut out of the hangar, so excluded means kept out.

• A: Welcomed in is the include idea, where in- brings people into a place; ex- sends them out.
• B: Charged extra is a sur- idea of an added fee and has nothing to do with ex-.
• C (correct): Ex- means out and clude means shut, so visitors who are excluded are shut out, or kept out.
• D: Finished early matches conclude, which shares the base but uses con-, not ex-.

Answer: C

Correct answer: polite. Courteous means well-mannered and respectful toward others. Polite matches; rude is the opposite, and formal and cheerful describe different qualities.

• A: This is the opposite of courteous.
• B: A formal person follows strict rules of dress or ceremony, which is not the same as being kind and respectful.
• C (correct): Courteous means showing good manners and respect, which polite expresses.
• D: A cheerful person is in a good mood, which differs from having good manners.

Answer: B

Correct answer: speed up. The method tells the purpose: overnight air delivery is chosen to make the shipment arrive sooner. EXPEDITE means to speed up a process; the phrase choice states that meaning.

• A: Paying extra could suggest insurance, but the stated method, overnight air, is about speed.
• B (correct): Speed up fits: choosing overnight air delivery makes the shipment arrive faster.
• C: Inspect is unrelated to the delivery method described.
• D: Explore is a look-alike that sounds a bit like expedition, but it does not fit sending a package.

Answer: C

Correct answer: record of events in time order. Chron means time. A chronicle records events in the order they happened, which is what a unit historian keeps.

• A: Maps relate to geo, earth; chron points to time.
• B: This borrows from chronic, which shares chron but describes a persistent condition.
• C (correct): Chron means time, and a historian's chronicle lists events in the order they happened.
• D: An inventory of supplies has no time order, which is the core of chron.

Answer: B

Correct answer: uncaring. The clerk ignores the guest's problem, which shows a lack of concern. Indifferent means not caring; impartial is a near-look-alike that means fair, so uncaring is the match.

• A: Impartial means fair to all sides; it is a professional virtue, while indifferent means not caring at all.
• B (correct): Indifferent means showing no interest or concern, as the clerk does by ignoring the complaint.
• C: Scrolling on a phone shows lack of interest, not a heavy workload.
• D: Hostile adds open unfriendliness or anger, which the sentence does not show.

Answer: D

Correct answer: free of errors. Accurate means correct, matching the facts. Free of errors keeps that meaning; honest concerns intent, full of details concerns amount of information, and lengthy concerns size.

• A: The length of an account says nothing about whether its facts are right.
• B: An honest witness can still be mistaken; honest describes intent, while accurate describes correctness.
• C: An account can be full of details and still contain errors; detail is not the same as correctness.
• D (correct): Accurate means correct and exact, which is what free of errors says.

Answer: D

Correct answer: Assemble. Con- means together, and the base vene means to come. A board that comes together at 9 a.m. assembles.

• A: Adjourn means to end a meeting, the opposite of gathering for one.
• B: Postpone moves an event later, a post- idea; the meeting is set for 9 a.m.
• C: Vote is something a board may do once gathered, not the act of coming together.
• D (correct): Con- means together, and vene means come, so to convene is to come together, or assemble.

Answer: A

Correct answer: clarifying. Explanatory sits between an article and a noun (the labels), so it is an adjective. Its base, explain, means to make clear, so the adjective means meant to clarify. Clarifying fits; explanation is only a related noun.

• A (correct): Clarifying means making something clear, which is what labels that tell visitors how tools were used do.
• B: Explanation is the noun from the same family; it cannot describe the labels in this sentence.
• C: Decorative labels would be there for looks, but these labels give information.
• D: Misleading means giving a false idea, the opposite of labels that inform visitors.

Answer: A

Correct answer: forced. Ask what the water did: it created pressure that made moving necessary. COMPEL means to force or require, so forced is the match; allowed is too weak.

• A (correct): Forced fits: the rising water left the family no real choice but to move the furniture.
• B: Allowed suggests permission, which is far weaker than the pressure rising water creates.
• C: The water did not assist the move; it caused the need for it.
• D: Completed shares the com- start, a spelling trap that ignores the meaning.

Answer: D

Correct answer: coil; moving air. In A, WIND is a verb with the object "hose" and "onto its reel," so it means coil. In B, "a cold wind swept" is the noun for moving air. Keep the order: coil, then moving air.

• A: Both meanings are correct, but in reverse order; A is the verb and B is the noun.
• B: Loosening is the opposite of winding a hose onto a reel.
• C: A is right, but in B wind is a noun after "a cold," naming moving air, not a twisting motion.
• D (correct): In A, wind rhymes with "find" and means to coil the hose; in B, it is the noun for moving air.

Answer: A

Correct answer: considered. Do not split pondered into pond plus -er plus -ed; a pond has nothing to do with the meaning. Treat ponder as a whole verb meaning to think about carefully. Keep the past tense: considered.

• A (correct): Ponder is a whole verb meaning to think over carefully, so considered fits the sentence and the past tense.
• B: This treats the word as pond plus a suffix, as if it involved water, which is a false split.
• C: Ignored means paid no attention to, the opposite of studying the map for minutes.
• D: Folding up the map is a physical action; the sentence describes careful thought.

Answer: D

Correct answer: able to express ideas clearly. In the family of words about talking, articulate is the positive member, talkative is neutral, and long-winded is negative. The clue so clearly that the whole platoon understood points to skill with words, not quantity of words.

• A: Talking a great deal is talkative; the sentence praises how clearly she spoke, not how much.
• B: Speaking at tiresome length is long-winded, the opposite of a clear explanation understood on the first try.
• C: Learning quickly is intelligence, which may help, but articulate is specifically about expressing ideas clearly in words.
• D (correct): Articulate describes someone who puts ideas into clear, well-chosen words, exactly what made the platoon understand at once.

Answer: A

Correct answer: concluded by reasoning. Deduce combines de, from, and duc, lead. The guard led his reasoning from the boot prints to a conclusion, so deduced means concluded by reasoning.

• A (correct): De means down or from and duc means lead, so the guard led his thinking from the clue to a conclusion.
• B: This is the meaning of reduced, a look-alike that also contains duc but has a different prefix.
• C: This reads duc, lead, too literally; nobody was being physically led anywhere.
• D: The guard reached a conclusion from evidence, not a refusal to accept it.

Answer: C

Correct answer: The plastic sheeting protected it from rain damage. This is a prevention passage: rain fell, but the sheeting kept it off the fresh concrete. The outcome is the absence of damage, shown by the smooth, undamaged surface on Tuesday. A choice saying the concrete was harmed contradicts the passage even though the risk is mentioned.

• A: The passage describes this only as a risk; on Tuesday the sidewalk was found smooth and undamaged.
• B: Nothing in the passage says the sidewalk was redone; it was undamaged.
• C (correct): Rain fell all night, yet the covered sidewalk came through undamaged, so the sheeting prevented harm.
• D: The passage says rain fell for most of the night, so it did not stop early.

Answer: A

Correct answer: The town bought a horse-drawn fire engine. Use the dates as time clues: horse-drawn engine 1908, store fire and vote 1921, paid department 1923, motor truck 1925. The earliest of the listed events is the 1908 purchase of the horse-drawn engine.

• A (correct): The passage dates this purchase to 1908, earlier than every other event listed here.
• B: This vote came after the 1921 store fire, well after the 1908 engine purchase.
• C: This fire happened in 1921, thirteen years after the town bought its horse-drawn engine.
• D: The truck arrived in 1925, making it the latest of these events, not the earliest.

Answer: B

Correct answer: Sarcastic and exasperated. Point to the words that carry feeling. Finally signals impatience, it took only three winters is ironic praise for a long delay, and at least until the next freeze adds doubt. Those exact words support a sarcastic, exasperated tone rather than a neutral or joyful one.

• A: The facts could be reported plainly, but words like finally, only and crater add a clear attitude, so the tone is not neutral.
• B (correct): Phrases like finally, it took only three winters and at least until the next freeze mock how long the repair took, which shows irritated sarcasm.
• C: The repair is good news, yet the author uses it to point out the long delay; reading only the surface event misses the irony.
• D: This is an intensity error; the author is mocking and annoyed, but there is no rage, threat or demand.

Answer: B

Correct answer: The online course's flexibility and speed outweigh the classroom's extra hands-on time. A concession word such as admittedly grants a point before the writer makes a stronger one. The director grants the classroom's hands-on edge, then stresses the online course's flexibility and six-week finish as the reason for the recommendation.

• A: Admittedly marks the hands-on advantage as a point the director concedes, not the main point; the director recommends the online course.
• B (correct): After conceding the hands-on advantage, the director recommends the online course for its flexible schedule and faster finish.
• C: The director says the classroom course gives more hands-on time, so they are not equal.
• D: This moves the hands-on advantage to the wrong side; it belongs to the classroom course.

Answer: B

Correct answer: About four weeks. Find the sentence about the length of the job: the remodel "would take about four weeks." Keep the word "about"; a choice that turns it into an exact number goes beyond the text, and the other time spans describe different parts of the project.

• A: Four weeks is 28 days, but the passage says "about," so "exactly" adds precision the contractor never gave.
• B (correct): This keeps the passage's own wording and its level of precision.
• C: Up to ten days is the possible wait for cabinets to arrive, not the length of the whole remodel.
• D: At least three days is how long the family may be without a sink, not the length of the project.

Answer: D

Correct answer: The trip plan the captain filed. Find the noun just before the pronoun and test it in the sentence: "he had filed a trip plan with the harbor office, and it gave rescuers his intended route." Only the trip plan can sensibly contain and give a route, so "it" refers to the trip plan. Earlier uses of "it" for the fishing boat do not decide this one; each pronoun points to its own nearby noun.

• A: The harbor office received the plan, but the office itself is not what listed the route; the nearest sensible noun is the plan.
• B: The response boat used the route information; it did not supply it, so it cannot be what gave rescuers the route.
• C: The fishing boat is referred to by "it" earlier in the passage, but in this clause a boat cannot give rescuers a route.
• D (correct): The captain filed a trip plan, and a written plan is the only noun in that clause that could list his intended route.

Answer: C

Correct answer: Letting guests request fresh linens only when needed lowered the hotel's costs. The passage lists results (fewer loads, a smaller water bill, less gas, less staff time) and then sums them up with "Overall": the new linen policy cut costs. The repeated concept is savings, so the choice that links the policy to lower costs covers every sentence.

• A: This is a true number from the passage, but it is only one of several results and does not state what they add up to.
• B: The passage says nothing about what guests prefer; this relies on an assumption the author never makes.
• C (correct): The last sentence pulls the facts together, and every detail, from fewer loads to lower water and gas use, is a form of savings.
• D: This stretches one hotel's experience into a claim about all hotels, which is too broad.

Answer: A

Correct answer: The idea that the beavers likely came from the creek upstream. An observation reports what was seen, an interpretation explains it, and a recommendation urges action. The stump count and the flooded trail were seen directly, and "should wrap" is advice. The statement about where the beavers probably came from explains the evidence, so it is the interpretation.

• A (correct): The ranger did not see the beavers arrive; "probably" marks this as an explanation of what was seen.
• B: Counting stumps is something the ranger directly saw, so it is an observation.
• C: "Should" urges an action, which makes this a recommendation.
• D: This reports a condition the ranger saw on patrol, so it is an observation.

Answer: C

Correct answer: the visible requests were a small part of a much larger hidden problem. Use the evidence that follows the phrase. Each logged request led to others that had never been entered, and the list grew from twelve to more than sixty. The feature of an iceberg the passage supports is that most of it is hidden below the surface, so the twelve requests were a small visible part of a much larger problem.

• A: This borrows the danger of icebergs to ships, but the passage stresses hidden size, not disaster.
• B: Nothing suggests the problems disappeared; the list grew larger, not smaller.
• C (correct): The twelve logged requests led to many that had never been entered, and the list grew past sixty, so most of the problem had been out of sight.
• D: Tip here means the top part that shows, not the top priority; the passage says nothing about which requests were most urgent.

Answer: C

Correct answer: The pond plan is estimated to cost less than the drain plan. Track who holds each view. The quoted claims belong to the engineer and the council member, while the cost estimates are reported by the article itself: $1.4 million for the pond is less than $2.1 million for the drain.

• A: This is the engineer's prediction in quotation marks, not something the article reports as fact.
• B: This is the council member's opinion, and the article does not confirm it.
• C (correct): The article reports county estimates of about $1.4 million for the pond and $2.1 million for the drain.
• D: The neighboring town's pond reduced flooding but did not end it, so this goes beyond the evidence.

Answer: A

Correct answer: 44 square meters.

The area is 44 square meters.

• A (correct): One-half of base 11 times perpendicular height 8 is 44.
• B: This leaves out the one-half in the formula.
• C: This adds the base and height instead of multiplying.
• D: This takes half of the sum 11 + 8 rather than half of the product.

Answer: C

Correct answer: 125 cu ft. Cubed means the base is used as a factor three times:

• A: This multiplies the base by the exponent, 5 times 3.
• B: This squares 5 instead of cubing it.
• C (correct): 5 x 5 = 25, and 25 x 5 = 125.
• D: This uses 5 as a factor four times, which is 5^4.

Answer: B

Correct answer: (3, 4). Test each pair in both equations. For (3, 4):

so both are true. A pair that works in only one equation is not a solution of the system.

• A: This adds to 7, but 3(4) − 3 = 9, not 5; it is the solution with the coordinates reversed.
• B (correct): It gives 9 − 4 = 5 and 3 + 4 = 7, so it satisfies both equations.
• C: This fits 3x − y = 5 but adds to only 3, so it fails x + y = 7.
• D: This adds to 7, but 3(5) − 2 = 13, so it fails 3x − y = 5.

Answer: A

Correct answer: 28π inches. Circumference is C = 2πr = 2π(14) = 28π inches.

• A (correct): Two times π times 14 is 28π inches.
• B: This is π times the radius; the formula needs 2πr, or π times the diameter.
• C: This is π times 14 squared, which is the area, not the distance around.
• D: This uses 4πr, doubling the circumference formula by mistake.

Answer: B

Correct answer: Matching arrowheads on the two lines. Parallel lines are marked with matching arrowheads. A small square means a right angle, and matching tick marks or arcs show equal segments or equal angles; appearance alone proves nothing.

• A: A small square marks a 90° angle, which shows perpendicular lines, not parallel ones.
• B (correct): Matching arrowheads are the standard mark for parallel lines.
• C: Tick marks show that segments are equal in length, not that lines are parallel.
• D: Figures may not be drawn to scale, so lines that look parallel are not proven parallel.

Answer: D

Correct answer: 24 - 2y. Distribute each factor:

Combine:

giving $24-2y$.

• A: This gives the last product as -12 instead of +12; -4 times -3 is positive.
• B: This adds 8y instead of subtracting it, ignoring the minus in front of the 4.
• C: This multiplies -4 by 2y but only subtracts 3 from 12, leaving out -4 times -3.
• D (correct): 6y + 12 - 8y + 12 combines to -2y + 24.

Answer: A

Correct answer: [−4, 7). The overlap of the two conditions is

List the left endpoint, then the right. Use a bracket for an included endpoint (≤ or ≥) and a parenthesis for an excluded one (< or >): [−4, 7).

• A (correct): −4 is included, so it gets a square bracket; 7 is not included, so it gets a parenthesis.
• B: This swaps the endpoint symbols: it leaves out −4 and includes 7.
• C: This leaves out −4, but the at-least sign means −4 is a solution.
• D: This includes 7, but the strict less-than sign means 7 is not a solution.

Answer: D

Correct answer: {−1, 2, 5}. The domain is the set of inputs, the first numbers in the pairs: −1, 2, 5 and 2. A repeated value is listed once in a set, so the domain is {−1, 2, 5}. The repeated identical pair (2, 4) does not stop this from being a function.

• A: This is the range, the set of outputs, not the inputs.
• B: This mixes inputs and outputs together; the domain uses only the first coordinates.
• C: This drops the input 2 because its pair appears twice; a repeated pair still contributes its input once.
• D (correct): These are the distinct first coordinates of the pairs.

Answer: C

Correct answer: −3.2, −1.5, −0.4, 0.6. Negative numbers are less than positive ones, and among negatives the one farthest from zero is smallest. So

• A: This orders the negatives by size without signs; among negatives, a bigger absolute value is a smaller number.
• B: This is the order from greatest to least, the reverse of what is asked.
• C (correct): Moving left to right on the number line gives −3.2, then −1.5, then −0.4, then 0.6.
• D: This orders the numbers by absolute value, ignoring their signs.

Answer: D

Correct answer: 4,326. Check the last digit for 2 and the digit sum for 3. Only 4,326 is even with a digit sum (

) divisible by 3, and

• A: It is even, but its digit sum is 10, which is not a multiple of 3.
• B: Its digit sum of 12 passes the test for 3, but it ends in 1, so it is odd and fails the test for 2.
• C: It ends in 5, so it is odd, and its digit sum of 13 is not a multiple of 3.
• D (correct): It ends in 6, so it is even, and its digits add to 15, a multiple of 3, so it passes both tests.

Answer: D

Correct answer: 17. Write the integers as n, n + 1, n + 2 and n + 3. Their sum is

so 4n = 68 and n = 17.

Check:

• A: 18 is the second integer in the list.
• B: 18.5 is the average of the four integers, which lies between the two middle numbers, not an integer in the list.
• C: 20 is the largest of the four integers.
• D (correct): With n + (n + 1) + (n + 2) + (n + 3) = 4n + 6 = 74, n = 17, and 17 + 18 + 19 + 20 = 74.

Answer: D

Correct answer: 72 square inches. Perimeters scale by the side ratio, so

Areas scale by k squared.

• A: This multiplies the area by k = 3/2; areas scale by k squared, not k.
• B: This multiplies by k cubed (27/8), which is how volumes of similar solids scale, not areas.
• C: This adds the 12-inch difference in perimeters to the area; similar figures scale by multiplying, not adding.
• D (correct): The side ratio is 3/2, so the area is multiplied by 9/4: 32 times 9/4 = 72 square inches.

Answer: D

Correct answer:

Distribute:

The x terms already match, so the equation is an identity only when the constants also match:

Then both sides read 6x + 12, which is true for every x.

• A: With k = 4 the left side is 6x − 12, and 6x − 12 = 6x + 12 reduces to −12 = 12, a contradiction with no solution.
• B: This sets k equal to the constant instead of −3k; with k = −12 the equation becomes 6x + 36 = 6x + 12, which has no solution.
• C: This divides 12 by 6 instead of by −3; with k = 2 the equation reduces to −6 = 12, which has no solution.
• D (correct): Distributing gives 6x − 3k = 6x + 12, so −3k must equal 12, which makes k = −4 and both sides identical.

Answer: C

Correct answer: 170π square feet. The radius is half the diameter, 5 ft. Ends: 2 times 25 pi is 50 pi. Side: 2 pi times 5 times 12 is 120 pi.

• A: This counts only one circular end; a closed drum has a top and a bottom.
• B: This uses the diameter 10 as the radius in both parts of the formula.
• C (correct): Two ends of 25 pi each give 50 pi, the side gives 120 pi, for 170 pi.
• D: This is the curved side alone, leaving out both circular ends.

Answer: A

Correct answer:

·x + 9/2. Midpoint:

Slope of AB:

so the perpendicular slope is -3/2.

Substitute (1, 3):

• A (correct): The midpoint is (1, 3) and the perpendicular slope is -3/2; then 3 = -3/2 + b gives b = 9/2.
• B: This passes through the midpoint but uses the segment's own slope, 2/3, so it lies along AB instead of crossing it at a right angle.
• C: This flips the slope to 3/2 but forgets to make it negative, so the product of slopes is 1, not -1.
• D: This has the right slope but is drawn through endpoint A instead of the midpoint.

Answer: C

Correct answer: 180 W. Use

Here

• A: This divides voltage by current, which gives resistance in ohms, not power.
• B: This adds the voltage and current, which are different quantities.
• C (correct): Power is voltage times current: 120 times 1.5 is 180 W.
• D: This misplaces the decimal point when multiplying by 1.5.

Answer: B

Correct answer: Weber. Flux is

so its unit is teslas times square meters, which is named the weber (Wb). Keep tesla for field strength and weber for field through an area.

• A: The tesla measures flux density B, the field strength at a point, not the total field through an area.
• B (correct): Flux is field times area, and one weber equals one tesla multiplied by one square meter.
• C: The henry is the unit of inductance, a coil's opposition to changes in its current.
• D: Ampere-turns measure a coil's magnetizing strength, not the flux passing through a surface.

Answer: B

Correct answer: 5 mA. Convert 3 kΩ to 3,000 Ω and use

Shortcut: volts divided by kilohms gives milliamperes directly.

• A: This forgets the kilo prefix; 3 kΩ is 3,000 Ω, so the current is 1,000 times smaller.
• B (correct): Volts divided by kilohms gives milliamperes: 15/3 = 5 mA, which is 0.005 A.
• C: This multiplies voltage by resistance instead of dividing.
• D: This divides resistance by voltage, the formula upside down.

Answer: A

Correct answer: It lets current flow mainly in one direction and blocks it in the other. A diode is an asymmetric, one-way device: it conducts when its anode is more positive than its cathode and blocks current when the polarity is reversed.

• A (correct): A diode conducts well when forward biased and blocks current when reverse biased, making it a one-way device.
• B: Storing charge is the job of a capacitor or battery, not a diode.
• C: Amplifying a signal is the job of a transistor amplifier, not a diode.
• D: Changing AC voltage levels is the job of a transformer.

Answer: D

Correct answer: 6 Ω. For the same material and temperature, R is proportional to L/A. Multiply by the length factor and divide by the area factor.

• A: This multiplies by 3 and divides by 2, flipping the roles of length and area.
• B: This multiplies by both factors; a larger area lowers resistance, so it must divide.
• C: This divides by both factors; a longer wire raises resistance, so length must multiply.
• D (correct): Length doubles R and tripled area divides it by 3: 9 times 2 divided by 3 is 6 Ω.

Answer: D

Correct answer: Both stay lit at normal brightness. Lamps connected across the same two wires are in parallel. Each branch gets the full 12 V and has its own current, so when one filament opens only that branch stops; the other two keep shining normally.

• A: Every lamp going dark is what happens in a series string; these lamps are in parallel.
• B: Each parallel branch still sees the same 12 V, so the remaining lamps keep the same current and brightness.
• C: Parallel branches each get the full battery voltage; voltage is not divided among them.
• D (correct): In parallel, each lamp has its own path across the battery, so opening one branch leaves the others working.

Answer: A

Correct answer: 6 V. Use the divider rule:

The 3 kΩ resistor drops the other 18 V.

• A (correct): The 1 kΩ resistor is one-fourth of the 4 kΩ total, so it takes one-fourth of 24 V.
• B: This is the drop across the 3 kΩ resistor, the larger share.
• C: This divides 24 V by 3, using the other resistor value instead of the total.
• D: This gives one series resistor the full source voltage, which only happens when it is alone.

Answer: C

Correct answer: A high-resistance connection at the outlet. Normal current and a working load rule out an open and a short, and 8 A on a 20 A circuit rules out overload. A poor contact adds resistance in a tiny spot, and

concentrates heat there without raising current enough to trip the breaker.

• A: A short would send a very large current and trip the breaker, and the heater would not work normally.
• B: An open would stop the current, so the heater would not run at all.
• C (correct): A loose or corroded contact heats at that spot while the circuit current stays normal, so the breaker does not trip.
• D: 8 A is well under the 20 A rating, so the circuit is not overloaded.

Answer: B

Correct answer: 2,160 J. Joules come from watts times seconds. Convert the time:

Then

• A: This multiplies by 8 without converting minutes to seconds.
• B (correct): Eight minutes is 480 s, and 4.5 W times 480 s gives 2,160 J.
• C: This treats the 8 minutes as 8 hours and then multiplies by 3,600.
• D: This uses only one minute, 60 s, instead of the full 8 minutes.

Answer: A

Correct answer: About −9 V. On a DC setting a multimeter reports the average voltage with its sign. Swapping the leads reverses the polarity being measured, so the battery reads about −9 V instead of +9 V. The battery is unharmed.

• A (correct): On the DC setting the meter reports a signed value, so reversed leads simply show the same size with a minus sign.
• B: The DC setting shows polarity, so swapping the leads changes the sign of the reading.
• C: A battery's steady DC does not average to zero; a near-zero DC reading happens with symmetric AC, not with reversed leads.
• D: This wrongly applies the 0.707 sine-wave factor to a steady DC battery reading.

Answer: D

Correct answer: 15 mA. In series the resistances add:

Then

The same 15 mA flows through both resistors.

• A: This uses only the 470 Ω resistor; in series both resistances oppose the same current.
• B: This uses only the 330 Ω resistor and ignores the other part in the loop.
• C: This slips a decimal: 12 divided by 800 is 0.015 A, which is 15 mA.
• D (correct): Series resistances add to 800 Ω, and 12 V divided by 800 Ω is 0.015 A, or 15 mA.

Answer: B

Correct answer: 220 W. First find the current:

Input power is

and winding heat is

With no friction, the rest becomes mechanical power:

W (the same as

).

• A: This is the total electrical input, $48\times 5$; part of it is lost as heat in the windings.
• B (correct): Current is (48 − 44)/0.8 = 5 A; input 240 W minus 20 W of winding heat leaves 220 W.
• C: This is the heat lost in the winding resistance, $5^2\times 0.8$, not the power converted to motion.
• D: This divides the square of the back emf by the winding resistance, but the back emf is not the voltage across the resistance.

Answer: D

Correct answer: 90 W. Reduce the parallel pair:

Total resistance is

The series resistor drops 20 V, leaving 30 V across the pair. Then

• A: This puts the full 50 V across the 10 Ω resistor, ignoring the drop in the series resistor.
• B: This is the power in the 15 Ω resistor, which has the same 30 V but more resistance.
• C: This is the power in the 4 Ω series resistor, which carries the full 5 A.
• D (correct): The parallel pair has 30 V across it, so the 10 Ω resistor dissipates 900 divided by 10, or 90 W.

Answer: D

Correct answer: 5 mA. In a series loop the resistor takes whatever voltage the LED does not: 12 V − 3 V = 9 V. Convert 1.8 kΩ to 1,800 Ω.

• A: This divides the full 12 V by the resistance, forgetting that the LED takes 3 V of the supply.
• B: This uses 1.8 Ω instead of 1,800 Ω, ignoring the k prefix and giving a current a thousand times too large.
• C: This uses the LED's 3 V drop instead of the 9 V left across the resistor.
• D (correct): The resistor gets 12 V − 3 V = 9 V, and 9 V ÷ 1,800 Ω = 0.005 A, which is 5 mA.

Answer: D

Correct answer: 1.25 × 10¹⁶. In one second the charge passing is

Each electron carries $1.6\times 10^{-19}$ C, so divide.

• A: This treats 2 mA as 2 A; the milli prefix makes the charge 1,000 times smaller.
• B: This multiplies the charge by e instead of dividing by it, giving a meaninglessly tiny number.
• C: This is the electron count for 0.5 C; it divides by 2 instead of using the 0.002 C that actually passes.
• D (correct): In 1 s, 0.002 C passes, and 0.002 divided by 1.6 times 10 to the negative 19 gives about 1.25 times 10 to the 16.

Answer: A

Correct answer: Camber. Camber is the tilt of the wheel's top inward or outward when seen from the front. Toe is seen from above and caster from the side, so only camber matches this description.

• A (correct): Camber is the inward or outward tilt of the top of the wheel seen from the front.
• B: Toe compares the front edges of a pair of wheels seen from above, pointing in or out.
• C: Caster is the forward or backward tilt of the steering axis seen from the side.
• D: Offset is the wheel's mounting-face position relative to its centerline, not an alignment tilt.

Answer: B

Correct answer: 3.6:1. Read ratios by their number: the larger the number, the greater the reduction and torque multiplication. That is why first gear, with the largest ratio (here 3.6:1), is called low gear.

• A: A ratio below 1 is an overdrive, the highest gear with the least torque.
• B (correct): The numerically largest ratio has the most reduction, so it is the lowest gear.
• C: A 1:1 ratio is direct drive, which gives no torque multiplication.
• D: This is a reduction, but a milder one than 3.6:1.

Answer: A

Correct answer: Shut down as the manual directs and let it cool before opening anything. Overheating with steam is a reason to stop. Park safely, shut down as the owner's manual directs, keep clear of the fan and belts, and never open a hot pressure cap; checks such as coolant level wait until the engine has cooled.

• A (correct): Waiting for the system to cool avoids scalding coolant and keeps hands away from fans that can start on their own.
• B: Opening a hot pressure cap can spray scalding coolant onto the driver.
• C: Sudden cold water on a hot engine can cause damage and puts the driver near steam and hot parts.
• D: Electric fans can start without warning, even with the key off, so hands must stay clear.

Answer: B

Correct answer: 0.5 V, meaning the post-to-clamp connection has resistance wasting voltage. A voltmeter shows

A clean clamp should lose almost nothing, so half a volt across one connection during cranking shows hidden resistance there, likely corrosion or a loose clamp.

• A: A voltmeter shows the difference between two points, not their sum, so no overcharge or regulator fault is shown.
• B (correct): The meter reads the difference between its probes, and a half-volt drop across one clamp under load points to a poor connection.
• C: A voltmeter across a connection does read the voltage lost there while current flows; that is the purpose of a voltage-drop test.
• D: The meter does not show the voltage of one point alone, and a large drop across a clamp is a fault sign.

Answer: B

Correct answer: It is rich for gasoline but lean for ethanol. Rich and lean are judged against the stoichiometric value for the fuel in use. A number below the reference has extra fuel (rich) and a number above it has extra air (lean). 12 is below 14.7 but above 9, so it is rich for gasoline and lean for ethanol.

• A: 12 is above ethanol's 9:1, so for ethanol it has extra air and is lean.
• B (correct): 12 is below 14.7, so it is rich for gasoline, and above 9, so it is lean for ethanol.
• C: This reverses both comparisons; a lower AFR than the reference means rich.
• D: Stoichiometric means matching the reference for that fuel; 12:1 matches neither 14.7 nor 9.

Answer: A

Correct answer: 90 degrees. Every cylinder fires once per 720 degree cycle, so evenly spaced firing puts the power strokes 720 divided by the number of cylinders apart. For eight cylinders that is 720 divided by 8, or 90 degrees.

• A (correct): Eight power strokes spread over a 720 degree cycle gives 720 divided by 8, or 90 degrees.
• B: This divides 360 degrees by 8, but a four-stroke cycle takes 720 degrees, not 360.
• C: That is the spacing for a four-cylinder engine, where four firings share 720 degrees.
• D: That is the spacing for a six-cylinder engine, 720 divided by 6.

Answer: D

Correct answer: The fluid absorbs moisture, which lowers its boiling point and promotes rust. Glycol-based fluids such as DOT 3, 4 and 5.1 slowly absorb moisture through seals, hoses and the reservoir vent. Water lowers the boiling point, so hot brakes can form vapor and give a soft pedal, and it also promotes internal rust. Replacing the fluid at set intervals removes that moisture.

• A: Healthy fluid stays nearly incompressible as it ages; the problem is absorbed water, not the fluid thickening or turning gas-like.
• B: Brake fluid is not burned or consumed during braking; a falling level points to pad wear or a leak.
• C: DOT 5 is a separate silicone-based chemistry; glycol fluid never converts into it with age.
• D (correct): Glycol fluid is hygroscopic; the water it collects makes it easier to boil and corrodes internal parts.

Answer: D

Correct answer: Test power, control and connections at the starter. A single click with bright lights and a charged battery is a no-crank that points beyond the battery to the starter circuit. Since the clutch was pressed and the terminals are good, measure power and control at the starter and check its cable connections before deciding the starter itself has failed.

• A: The battery is charged, the lights stay bright, and the terminals are good, so nothing points to the battery yet.
• B: The engine is not turning at all, so this is a no-crank; fuel matters only after the engine cranks.
• C: Erasing codes removes evidence and does nothing to explain a single click.
• D (correct): With a good battery and the clutch interlock satisfied, the next link is whether the starter receives power and its control signal while the key is turned.

Answer: C

Correct answer: 3,500 N. In a turn, load moves to the outside tires, so

• A: This uses the original 4,000 N load and ignores the added weight transfer.
• B: This subtracts the transfer, using 3,000 N; the outside tire gains load in a turn.
• C (correct): The tire load becomes 5,000 N, and 0.7 × 5,000 = 3,500 N.
• D: This divides the load by the friction coefficient instead of multiplying.

Answer: A

Correct answer: 2 kW. First find the heat:

Convert the time: 1.5 min × 60 = 90 s.

• A (correct): Q = 4.5 × 4.0 × 10 = 180 kJ, and 1.5 minutes is 90 s, so P = 180 ÷ 90 = 2 kJ/s = 2 kW.
• B: This divides 180 kJ by 1.5 without converting minutes to seconds.
• C: This is the total heat Q, not the rate; it was never divided by the time.
• D: This divides the time by the heat (90 ÷ 180), turning the formula upside down.

Answer: D

Correct answer: A die. A die is a hardened threaded ring with cutting edges on the inside. It is held in a diestock and turned onto the rod, cutting threads into the outside surface. A tap is the opposite: a threaded cutting tool turned into a drilled hole to make internal threads. A simple memory hook is that a nut needs a tap and a bolt needs a die. The end of the rod is usually chamfered first so the die starts square.

• A: A tap makes internal threads inside a prepared hole, not threads on the outside of a rod.
• B: A reamer refines the size and finish of an existing hole; it does not make threads.
• C: A countersink makes a conical recess at a hole opening.
• D (correct): A die cuts or forms external threads on rod or bolt stock.

Answer: B

Correct answer: Welding. The key verb is join. Welding joins metal along a seam, while oxy-fuel cutting and shearing separate material and reaming finishes a hole.

• A: Oxy-fuel cutting also uses heat, but its purpose is to separate metal, not to join it.
• B (correct): Welding joins parts by fusing them together with suitable heat, pressure, or both.
• C: Shearing cuts sheet apart with blades; it does not join pieces.
• D: Reaming finishes an existing hole; it does not join parts.

Answer: B

Correct answer: Drill a centered pilot hole, then turn the extractor counterclockwise with steady force. An extractor goes into a centered pilot hole drilled in the broken shank. Its reverse threads bite when turned counterclockwise, backing the bolt out; penetrating oil and steady, gentle force keep the brittle extractor from breaking.

• A: Turning clockwise would tighten the broken bolt, and heavy force risks snapping the brittle extractor.
• B (correct): The reverse-threaded extractor bites as it turns counterclockwise and backs the broken shank out.
• C: Extractors need a centered pilot hole, and hard blows can crack the brittle tool inside the bolt.
• D: A shank broken flush leaves nothing for pliers to grip, and pliers are not meant to turn fasteners.

Answer: B

Correct answer: 10.2 mm. Convert the length to millimeters, then use

• A: This is ten times too small, a decimal slip in the multiplication.
• B (correct): With 12 m = 12,000 mm, the growth is 0.000017 × 12,000 × 50 = 10.2 mm.
• C: This uses 12 for the length (meters) but labels the answer in millimeters; 0.0102 m is really 10.2 mm.
• D: This is ten times too large, a decimal slip when handling the $10^{-6}$ factor.

Answer: B

Correct answer: Clear glasses do not filter the intense light from the arc. First identify the exposure: arc welding produces intense optical radiation and hot spatter that can reach assistants and bystanders. Ordinary clear safety glasses stop impact but are not a welding filter, so the helper needs a filter lens of the right shade or a welding screen between the helper and the arc.

• A: Impact-rated eyewear is often worn under a welding helmet; the problem is that it lacks a filter for the arc light.
• B (correct): Arc welding gives off intense optical radiation, so nearby workers need a suitable filter shade or a welding screen, not just clear lenses.
• C: Splash goggles seal against liquids but do not filter arc radiation, so they would not solve the actual hazard.
• D: Reflected light and sparks still reach a bystander, so turning away is not a substitute for proper filter protection or screening.

Answer: D

Correct answer: Stop and switch to a square-drive bit that matches the recess width and reaches its base. A square recess is a Robertson drive and needs a square-profile bit of matching width that seats to the bottom. A tip that rocks or shows gaps is the wrong profile or size, so stop before the recess is damaged.

• A: Extra force on the wrong profile will damage the recess instead of fixing the fit.
• B: Hammering a mismatched bit deforms the recess and can break the bit.
• C: A slotted blade is made for a straight slot and would slip out of a square recess.
• D (correct): A square, or Robertson, recess needs a square-profile tip of the right size for full engagement.

Answer: D

Correct answer: 1.5875 mm. Pitch is the distance from one crest to the next. With 16 threads per inch, the pitch is 1/16 inch. Converting,

• A: This mistakes the threads-per-inch count for a pitch length in millimeters.
• B: This is the pitch in inches (1/16) with the unit changed to millimeters but no conversion made.
• C: This multiplies 25.4 by 16 instead of dividing, giving an impossible thread spacing.
• D (correct): One inch, 25.4 mm, divided among 16 threads gives 1.5875 mm between crests.

Answer: C

Correct answer: Hold the pieces in close contact while the glue cures. The adhesive forms the bond. Clamps simply hold the pieces aligned and in contact during the curing interval, after which they are removed.

• A: Clamps are removed after curing; the glue, not the clamps, forms the permanent bond.
• B: Ordinary clamps apply pressure only; they do not supply heat to speed curing.
• C (correct): Clamps keep the joint aligned and tight while the adhesive sets; the glue does the bonding.
• D: Clamping should hold the surfaces together, not force out the adhesive needed for the bond.

Answer: B

Correct answer: 9.525 mm diameter, about 1.058 mm pitch. The diameter is 3/8 inch:

The 24 is threads per inch, so the pitch is 1/24 inch: $25.4/24\approx 1.058$ mm.

• A: The diameter is right, but 24 is a count of threads per inch, not a pitch length.
• B (correct): 3/8 inch times 25.4 gives 9.525 mm, and 25.4 mm divided by 24 threads gives about 1.058 mm.
• C: This reads the 3/8 as 3.8 mm and treats the thread count as a length, two unit errors.
• D: These are the inch values (0.375 in and 1/24 in) labeled as millimeters without conversion.

Answer: B

Correct answer: 21 1/2 inches. Remaining length = stock - cut piece - kerf.

• A: This subtracts the cut piece but forgets the 1/8 inch turned into sawdust.
• B (correct): 36 - 14 3/8 = 21 5/8, and removing the 1/8-inch kerf leaves 21 4/8 = 21 1/2 inches.
• C: This subtracts the kerf twice, but only one cut was made.
• D: This adds the kerf instead of subtracting it; the saw removes material, so the remainder gets shorter.

Answer: A

Correct answer: The working fluid is air. Pneumatic and hydraulic symbols look much alike, but pneumatic triangles are drawn hollow to show air, while hydraulic triangles are filled to show liquid.

• A (correct): Hollow triangles mark pneumatic components; filled triangles mark hydraulic, liquid-filled ones.
• B: Oil, a liquid, is shown with filled triangles, not hollow ones.
• C: Triangles show the direction of energy flow by where they point, not by whether they are filled.
• D: A return to tank is shown by a line ending at the reservoir symbol, not by hollow triangles.

Answer: B

Correct answer: One fourth as much. Since

multiplying the speed by a factor multiplies the energy by that factor squared.

Halving the speed gives

of the original kinetic energy.

• A: This treats kinetic energy as proportional to speed, but speed is squared in the formula.
• B (correct): Kinetic energy depends on speed squared, and (1/2)² = 1/4.
• C: This cubes the speed factor; kinetic energy uses the square of speed, not the cube.
• D: Kinetic energy changes whenever speed changes; only the mass is unchanged.

Answer: C

Correct answer: Friction on its faces resists sliding. Friction lowers a wedge's efficiency, but it is also what keeps a wedge in place. Without friction on its faces, the door's squeeze would push a smooth wedge straight back out.

• A: A small rubber wedge is very light; its weight alone could not resist the door's push.
• B: Mechanical advantage multiplies an applied force; it does not create a force pulling the wedge in.
• C (correct): Friction between the wedge faces and the floor and door resists the squeeze that would push it back out.
• D: Air pressure acts on all sides of the wedge and gives no net force holding it in.

Answer: D

Correct answer: Instantaneous speed. Instantaneous speed is how fast an object is moving at a single moment. A speedometer reads exactly that. It shows no direction, so it is not a velocity, and it does not average over the trip.

• A: Average speed needs total distance and total time; the needle shows only the current moment.
• B: Average velocity uses displacement over elapsed time and includes direction, which a speedometer does not show.
• C: Acceleration is the rate of change of velocity; the speedometer shows the speed itself.
• D (correct): A speedometer shows how fast the truck is going at that moment, with no direction.

Answer: C

Correct answer: 0.20 m. In series every spring carries the full 60 N, so each stretches

Three of them give 0.20 m. Equivalently,

N/m and

• A: This adds the stiffnesses to 2,700 N/m, which is the rule for springs side by side, not end to end.
• B: This is the stretch of just one spring; in series each spring carries the full 60 N and the stretches add.
• C (correct): Three identical springs in series act like one 300 N/m spring, and 60 ÷ 300 = 0.20 m.
• D: This counts only two springs' worth of stretch; all three springs carry the load and each adds its own stretch.

Answer: B

Correct answer: 4 Hz. Frequency is proportional to $\sqrt{k/m}$. The mass became one quarter as large, so the frequency grows by

2 Hz × 2 = 4 Hz.

• A: This scales frequency directly with the mass ratio, forgetting the square root.
• B (correct): The mass dropped by a factor of 4, and frequency varies as the square root of k over m, so the frequency doubles to 4 Hz.
• C: A lighter mass vibrates faster, not slower; this reverses the effect of mass.
• D: This both reverses the direction and skips the square root.

Answer: A

Correct answer: 7.5 N. With

drag grows in direct proportion to speed. Find

N·s/m, then

• A (correct): Drag is proportional to speed here, and 0.5 is 2.5 times 0.2, so the drag is 2.5 × 3 N = 7.5 N.
• B: This treats the oil drag like dry sliding friction, which does not depend on speed.
• C: This scales drag with the square of speed, a pattern for fast air drag, not slow motion in thick fluid.
• D: This scales the drag down instead of up; a faster probe meets more fluid drag.

Answer: A

Correct answer: 2,000 Pa. Pressure is force divided by area:

Lying flat:

Standing would give

eight times as much, so lying flat is far safer on thin ice.

• A (correct): Dividing the 720 N weight by the 0.36 m² contact area gives 2,000 Pa.
• B: This is the pressure while standing, found with the 0.045 m² boot area.
• C: This multiplies the force by the area instead of dividing.
• D: This slips a decimal place, dividing 720 by 3.6 instead of 0.36.

Answer: C

Correct answer: 130 N. Put both arms in the same unit: 25 cm = 0.25 m. The IMA is

Ideal effort =

• A: This uses 25 for the load arm and 1.5 for the effort arm without converting, so the units do not match.
• B: This converts the wrong way, treating 1.5 m as 150 while using 0.25 m; both lengths must be in one unit.
• C (correct): With both arms in meters, the IMA is 6, and 780 ÷ 6 = 130 N.
• D: This multiplies the load by the IMA instead of dividing; a longer effort arm means less effort.

Answer: B

Correct answer: 31.5 kPa. Liquid pressure $\rho gh$ is proportional to density when the depth stays the same.

The density ratio is

so the new reading is

• A: This treats the pressure as depending only on depth; the liquid's density matters too.
• B (correct): At the same depth, liquid pressure scales with density: 25 kPa × 1.26 = 31.5 kPa.
• C: This divides by 1.26 instead of multiplying; a denser liquid gives more pressure.
• D: This adds about 100 kPa of atmosphere, but the gauge reads only the pressure above atmospheric.

Answer: A

Correct answer: 8 turns. Lead equals pitch times starts:

per turn.

• A (correct): The lead is 3 times 1.5 = 4.5 mm per turn, and 36/4.5 = 8 turns.
• B: This uses the pitch as the travel per turn; a triple-start screw moves three pitches each turn.
• C: This divides the distance by the number of starts only, ignoring the 1.5 mm pitch.
• D: This multiplies the distance by the pitch instead of dividing the distance by the lead.

Answer: D

Correct answer: 60°C. Both bars expand into the gap, so add their growth per degree:

m per °C.

Starting from 20°C, the ends touch at about 60°C.

• A: This is the temperature rise needed; it must be added to the starting 20°C to give the closing temperature.
• B: This counts only the aluminum bar's growth; the steel bar also expands into the gap.
• C: This counts only the steel bar's growth; the aluminum bar also expands into the gap.
• D (correct): Together the bars grow 70 × 10⁻⁶ m per degree, so closing 0.0028 m takes a 40 degree rise, from 20°C to 60°C.

Answer: A

Correct answer: 140 rpm counterclockwise. Work stage by stage, carrying speed across each shared shaft. Stage 1:

(counterclockwise). Stage 2:

(clockwise). Stage 3:

There are three external meshes, an odd number, so the output turns opposite to the input: 140 rpm counterclockwise. The overall ratio is

• A (correct): Multiplying the stage ratios gives 15:1, so 2,100 ÷ 15 = 140 rpm, and three external meshes reverse the direction.
• B: The speed is right, but three external meshes is an odd count, so the output turns opposite to the clockwise input.
• C: This adds the stage ratios (3 + 2.5 + 2 = 7.5) instead of multiplying them.
• D: This is the speed and direction of the middle shaft; the motion still passes through one more mesh.

Answer: C

Correct answer: 400 N. Add the moving-block weight:

Ideal effort is 1,500 divided by 5 segments, or 300 N.

The actual effort must always come out larger than the ideal effort.

• A: This applies the efficiency correctly but leaves out the 120 N lower block and hook, which rise with the load.
• B: This is the ideal effort; a real tackle that is only 75 percent efficient needs a larger pull than the ideal one.
• C (correct): Total lifted weight is 1,380 + 120 = 1,500 N; the ideal effort is 1,500/5 = 300 N, and dividing by 0.75 for losses gives 400 N.
• D: This multiplies the ideal effort by 0.75; friction makes the actual effort larger, so you must divide by the efficiency.

Answer: C

Correct answer: 825 N. Take torques about the left support so its unknown force drops out. The plank's weight acts at its center, 3 m from the left end; the worker is 6 m out.

This is more than the 700 N total load, so the left end must actually be held down with 125 N.

• A: This counts only the worker's torque (400 × 6 ÷ 4) and leaves out the plank's own 300 N weight at its center.
• B: This assumes the support carries the total load; with the worker on the overhang, the support near him carries more than the total.
• C (correct): Torques about the left support: (300 × 3 + 400 × 6) ÷ 4 = 825 N.
• D: This splits the 700 N total load evenly between the supports, which only works for a centered load between them.

Answer: C

Check one letter at a time. Point R is at the middle of the short side of the trapezoid, and point S 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 trapezoid at the middle of the long side, but point R is at the middle of the short side.
• B: The line ends in the wrong place: it meets the house shape at a corner where the roof meets a wall, but point S is at the middle of the bottom side.
• C (correct): The line joins the middle of the short side of the trapezoid to the middle of the bottom side of the house shape, the same spots as points R and S 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 trapezoid at a corner of the long side, but point R is at the middle of the short side and it meets the house shape at a bottom corner, but point S is at the middle of the bottom side.

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 diamond.

• A (correct): This diamond is made of exactly the 3 pieces in the left box, each only turned and slid into place.
• B: 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.
• 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 53% of the shape, but the matching piece in the left box covers about 37%.

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 parallelogram.

• A: This figure has 3 pieces, but the left box has 2. Every piece must be used once, and nothing may be added.
• 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 (correct): This parallelogram is made of exactly the 2 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 22% of the shape, but the matching piece in the left box covers about 44%.

Answer: C

Check one letter at a time. Point G is at the middle of the longer leg of the right triangle, and point H is at the middle of a side 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 diamond at a wide corner, but point H is at the middle of a side.
• B: The line ends in the wrong place: it meets the diamond at a sharp corner, but point H is at the middle of a side.
• C (correct): The line joins the middle of the longer leg of the right triangle to the middle of a side of the diamond, 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 right triangle at the sharpest corner, but point G is at the middle of the longer leg and it meets the diamond at a sharp corner, but point H is at the middle of a 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 hexagon.

• A: This figure has 4 pieces, but the left box has 3. Every piece must be used once, and nothing may be added.
• B (correct): This hexagon is made of exactly the 3 pieces in the left box, each only turned and slid into place.
• C: This figure is a pentagon. The pieces in the left box do not have these shapes, so they cannot fill this outline without gaps or overlaps.
• D: A cut is in a different place, so the pieces do not match: one piece here covers about 31% of the shape, but the matching piece in the left box covers about 19%.

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 3 pieces in the left box, each only turned and slid into place.
• 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 33% of the shape, but the matching piece in the left box covers about 26%.
• D: A cut is in a different place, so the pieces do not match: one piece here covers about 69% of the shape, but the matching piece in the left box covers about 56%.

Answer: A

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

Answer: C

Check one letter at a time. Point P is at the center of the rectangle, and point Q is at the middle of the longer leg 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 sharpest corner, but point Q is at the middle of the longer leg.
• B: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• C (correct): The line joins the center of the rectangle to the middle of the longer leg of the right triangle, the same spots as points P and Q 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 right triangle at the middle of the slanted side, but point Q is at the middle of the longer leg.

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 pentagon.

• 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 46%.
• B (correct): This pentagon 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 38% of the shape, but the matching piece in the left box covers about 30%.

Answer: A

Check one letter at a time. Point V is at a corner of the triangle, and point W is at the middle of the slanted side 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 a corner of the triangle to the middle of the slanted side 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.
• B: The line ends in the wrong place: it meets the triangle at the center, but point V is at a corner.
• C: The line ends in the wrong place: it meets the right triangle at the right-angle corner, but point W is at the middle of the slanted side.
• D: The line ends in the wrong place: it meets the triangle at the middle of a side, but point V is at a corner and it meets the right triangle at the middle of the shorter leg, but point W is at the middle of the slanted side.

Answer: D

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

Answer: C

Check one letter at a time. Point E is at a corner of the flat side of the half-circle, and point F is at the middle of the shorter leg 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 half-circle at the top of the curved side, but point E is at a corner of the flat side.
• B: The line ends in the wrong place: it meets the right triangle at the middle of the longer leg, but point F is at the middle of the shorter leg.
• C (correct): The line joins a corner of the flat side of the half-circle to the middle of the shorter leg of the right triangle, the same spots as points E and F 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 E is at a corner of the flat side and it meets the right triangle at the middle of the slanted side, but point F is at the middle of the shorter leg.

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 rectangle.

• 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 29%.
• B: 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.
• C (correct): This rectangle 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 12% of the shape, but the matching piece in the left box covers about 19%.

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 34% of the shape, but the matching piece in the left box covers about 52%.
• B: A cut is in a different place, so the pieces do not match: one piece here covers about 40% of the shape, but the matching piece in the left box covers about 52%.
• C: 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.
• D (correct): This pentagon is made of exactly the 4 pieces in the left box, each only turned and slid into place.

Answer: A

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