Full ASVAB Practice Form 5: Genetics, Ignition and Gears

Answer: C

Correct answer: climate. Climate is the long-term average of weather in a region, usually based on 30 or more years of data. A 40-year average rainfall is a climate statistic, while a single storm or a rainy week would be weather.

• A: Weather is the short-term state of the atmosphere, such as this week's rain, not a decades-long average.
• B: A habitat is the place where a particular organism lives, not a measure of atmospheric conditions.
• C (correct): Climate is the long-term average pattern of weather, usually measured over 30 years or more.
• D: A niche is the role an organism plays in its community, which has nothing to do with rainfall records.

Answer: A

Correct answer: Jupiter. Jupiter and Saturn are gas giants, and Jupiter is the largest planet of all. Rings, distance from the Sun or being the biggest rocky planet do not decide overall size.

• A (correct): Jupiter, a gas giant, is the biggest planet in the solar system.
• B: Saturn is a large gas giant famous for its rings, but it is smaller than Jupiter.
• C: Neptune is the farthest planet, but being farthest does not make it the largest.
• D: Earth is the largest of the rocky inner planets, yet it is tiny next to the giant planets.

Answer: D

Correct answer: It is dissolved in water. State labels give the physical state: (s) solid, (l) liquid, (g) gas and (aq) aqueous. Aqueous means dissolved in water, so the silver nitrate is in solution.

• A: The label (aq) describes physical state, not acidity; silver nitrate is a salt, not an acid.
• B: A gas is labeled (g), not (aq).
• C: A pure liquid is labeled (l); (aq) means the substance is dissolved in water.
• D (correct): The label (aq) stands for aqueous, meaning the substance is in a water solution.

Answer: A

Correct answer: Amplitude. Volume, or loudness, is controlled by amplitude: how far the medium moves from its rest position. Since the note's pitch is unchanged, the frequency, and therefore the wavelength in the same air, stay the same.

• A (correct): Louder sound means the air is displaced farther from rest, which is a larger amplitude.
• B: Frequency sets pitch; the note stays the same, so frequency does not change.
• C: Wavelength depends on wave speed and frequency, and neither changes when the volume is raised.
• D: The speed of sound depends on the air, not on how loud the sound is.

Answer: A

Correct answer: The pituitary releases less TSH, so the thyroid makes less hormone. The hypothalamus and pituitary direct the thyroid through TSH. When thyroid hormone rises high enough, it signals them to slow down, TSH falls, and thyroid output drops. The response opposes the change, so it is negative feedback.

• A (correct): High thyroid hormone signals the hypothalamus and pituitary to slow down, cutting TSH and bringing the level back down.
• B: Pushing the level higher would amplify the change, which is positive feedback, not how this loop works.
• C: Insulin regulates blood glucose; it plays no role in thyroid hormone control.
• D: Epinephrine drives the fight-or-flight response and is not part of the thyroid control chain.

Answer: B

Correct answer: Using a few large lumps of marble with the same total mass. Rate depends on how often particles collide effectively. Temperature, concentration and stirring all raise the collision rate, while replacing small chips with large lumps reduces the exposed surface area, so the reaction slows.

• A: Higher temperature makes particles collide more often and with more energy, so the reaction speeds up.
• B (correct): Large lumps expose less surface area than many small chips, so fewer acid particles can collide with the solid at once.
• C: More acid particles per unit volume means more frequent collisions, which speeds the reaction up.
• D: Stirring brings fresh acid to the surface of the marble, which speeds most reactions in solution.

Answer: C

Correct answer: Toward the northwest. A hotspot stays roughly in place while the plate slides over it. Each island forms above the hotspot and is then carried away, so older islands end up farther along the plate's direction of travel. Since ages increase toward the northwest, the plate is moving northwest.

• A: Moving southeast would place the older islands to the southeast of the active one, the opposite of the pattern.
• B: An age progression across an island chain is evidence that the plate moves over the melt source.
• C (correct): Older islands are carried farther along the plate's direction of motion, so the plate moves northwest.
• D: The ages change along a southeast–northwest line, so the motion is not toward the northeast.

Answer: B

A hypothesis explains why, while a prediction states the specific result you expect to observe if the hypothesis is right. The if-then statement naming the setup and the expected outcome is the prediction.

• A: This proposes why something happens, so it is a hypothesis, not the specific expected result of a planned test.
• B (correct): This states the specific result expected in a planned test, in if-then form, which is what a prediction does.
• C: This is a testable question; it asks something but does not state what result is expected.
• D: This describes results that were already seen, so it is an observation, not a prediction.

Answer: C

Correct answer: 1/2, because he gets one of his mother's two X chromosomes. A son receives his Y from his father and one X from his mother. The carrier mother has one normal X and one X with the allele, so each son has a 1/2 chance of getting the allele, and with only one X he will be color-blind.

• A: A son gets his X from his mother, not his father, so the father's normal vision does not protect him.
• B: One-fourth is the chance that a child of either sex is an affected son, not the chance among sons only.
• C (correct): Each son receives one of the mother's two X chromosomes, and one of the two carries the allele; with only one X, he shows it.
• D: The mother passes her normal X just as often as the X with the allele, so not every son is affected.

Answer: C

Correct answer: Distillation. Distillation boils a liquid and condenses the vapor in a separate place, separating substances with different boiling points. The water leaves as steam and is recondensed, while the dissolved salt stays behind.

• A: A filter holds back undissolved solids by size, but dissolved salt passes right through it.
• B: Decanting pours a liquid off a settled solid, but dissolved salt never settles out.
• C (correct): Boiling the water and condensing the vapor elsewhere separates it from the salt, which has a far higher boiling point.
• D: Chromatography separates dyes by how far they travel along paper, not salt from water.

Answer: C

Correct answer: 20 °C. Energy = mass × specific heat × temperature change, so temperature change = energy ÷ (mass × specific heat).

For aluminum:

The water warms only about 4.3 °C because its specific heat is much higher.

• A: This uses water's specific heat; that is the water's rise, not the aluminum's.
• B: This divides the specific heat by the energy; the energy must be divided by mass times specific heat.
• C (correct): Temperature change = 18,000 ÷ (1 × 900) = 20 °C, much more than the water's rise because aluminum's specific heat is lower.
• D: This is a place-value slip, dividing 18,000 by 9,000 instead of by 900.

Answer: C

Correct answer: 8 times. Use

Doubling v multiplies $v^2$ by 4, and halving r doubles the result again, so the acceleration grows by 4 x 2 = 8 times.

• A: This doubles for the speed only and ignores both the squaring of speed and the smaller radius.
• B: This accounts for doubling the speed (squared gives 4) but ignores the halved radius, which doubles it again.
• C (correct): Doubling speed multiplies the acceleration by 4, and halving the radius multiplies it by 2, for 4 x 2 = 8.
• D: Constant speed on each curve does not make the two accelerations equal; the size depends on speed squared over radius.

Answer: C

Correct answer: 1/8. Work each gene separately, then multiply. Yy × yy gives 1/2 Yy (yellow), and Rr × Rr gives 1/4 rr (wrinkled).

• A: This is the yellow, wrinkled share from YyRr crossed with YyRr; the second parent here is yy, not Yy.
• B: This is the fraction that are yellow and round: 1/2 times 3/4.
• C (correct): Yy times yy gives 1/2 yellow, and Rr times Rr gives 1/4 wrinkled; 1/2 times 1/4 equals 1/8.
• D: This treats yellow as a 1/4 outcome as well, but Yy crossed with yy gives yellow half the time.

Answer: B

Correct answer: The cell likely has ribosomes that are too small to see with a light microscope. Reason only from what the microscope can actually show. A light microscope reveals nuclei and membranes, but ribosomes require an electron microscope. Since all cells have ribosomes, the safe conclusion is that they are present but too small to see.

• A: Ribosomes are one of the universal features of cells; not seeing them under a light microscope does not mean they are missing.
• B (correct): Every cell has ribosomes, and they are visible only with an electron microscope, so their absence in this view says nothing.
• C: A visible membrane-bound nucleus marks the cell as eukaryotic, which rules out a prokaryote.
• D: Ribosome parts are assembled in the nucleolus, but working ribosomes sit in the cytosol and on the rough ER.

Answer: B

Correct answer: 9/16. A Punnett square for Rr × Rr gives RR, Rr, Rr and rr, so 3 of 4 outcomes show round seeds.

Each offspring is independent, so multiply:

• A: This is the chance for one offspring; both offspring must be round, so the probabilities must be multiplied.
• B (correct): Each offspring has a 3/4 chance of round seeds, and independent events multiply: 3/4 × 3/4 = 9/16.
• C: This is the chance that both offspring are wrinkled, using 1/4 × 1/4.
• D: This treats round and wrinkled as equally likely, ignoring that three of four combinations show the dominant trait.

Answer: B

Correct answer: $7.00. Move the decimal point one place left to find 10 percent: $3.50. Double it for 20 percent:

• A: This is only 10 percent of the price; 20 percent is double that.
• B (correct): 10 percent of 35 is 3.50, and 20 percent is twice that, or 7.
• C: This uses 0.02 for 20 percent, moving the decimal point one place too far.
• D: This is the cost plus the tip; the question asks for the tip only.

Answer: B

Correct answer: 6 gallons. Write the percent as a decimal and multiply by the volume:

• A: This divides 40 by 15 instead of multiplying 40 by 0.15.
• B (correct): Pure amount equals concentration times volume: 0.15 times 40 is 6 gallons.
• C: This uses 1.5 instead of 0.15; the pure amount cannot exceed the 40 gallons in the tank.
• D: 34 gallons is the amount of the tank that is not fertilizer.

Answer: B

Correct answer: 203 books. The unknown is the starting count. The story is start minus lent equals left:

Add 47 to both sides:

Check:

• A: This subtracts 47 from 156, running the story backward because of the word "left."
• B (correct): Start minus lent equals left, so x - 47 = 156 and x = 156 + 47 = 203.
• C: This is an addition slip; 156 + 47 is 203, not 193.
• D: This is the number left after lending, not the starting number.

Answer: A

Correct answer: $480. Write 5% as 0.05 and multiply:

As a check, 10% is $960 and 5% is half of that.

• A (correct): Commission is 0.05 × 9,600 = $480.
• B: This uses 0.005 instead of 0.05 for 5%, making the answer ten times too small.
• C: This uses 0.5 instead of 0.05 for 5%, making the answer ten times too large.
• D: This is an arithmetic slip; 5% of 9,600 is half of 10% (960), which is 480.

Answer: A

Correct answer: 5,316. Test 3 with the digit sum and test 4 with the last two digits.

For 5,316:

a multiple of 3, and 16 is a multiple of 4, so it passes both tests.

• A (correct): Its digits add to 15, a multiple of 3, and its last two digits, 16, form a multiple of 4.
• B: Its digit sum, 15, passes the 3 test, but its last two digits, 18, are not a multiple of 4.
• C: Its last two digits, 24, pass the 4 test, but its digit sum, 16, is not a multiple of 3.
• D: Its digit sum is 10 and its last two digits are 30, so it fails both tests.

Answer: D

Correct answer: 30 minutes. The net growth rate is arrivals minus removals:

people per minute.

Time = amount / rate =

• A: This adds the two rates (95 per minute) even though loading removes people from the line.
• B: This uses only the arrival rate of 55 per minute and ignores the people being loaded.
• C: This divides 450 by the loading rate of 40, which does not measure how fast the line grows.
• D (correct): The line grows by 55 - 40 = 15 people per minute, and 450 / 15 = 30 minutes.

Answer: D

Correct answer: 50 mph. The trip out takes

so the return takes

Return speed =

• A: This is the average speed for the whole round trip, 300 ÷ 5.5, not the return speed.
• B: This divides one leg's 150 miles by the full round-trip time of 5.5 hours.
• C: This wrongly assumes the round-trip average is the simple mean of the two leg speeds.
• D (correct): The return leg takes 3 hours, and 150 ÷ 3 = 50 mph.

Answer: B

Correct answer: 4 kg. Multiply:

kilograms.

A shortcut is to swap the numbers: 16 percent of 25 equals 25 percent of 16, and one fourth of 16 is 4.

• A: This uses 1.6 for 16 percent; the result cannot be more than the 25 kg bag.
• B (correct): 16 percent of 25 equals 25 percent of 16, which is one fourth of 16, or 4.
• C: This uses 0.016 for 16 percent, moving the decimal point three places instead of two.
• D: This subtracts 16 from 25, treating the percent as a weight.

Answer: C

Correct answer: 15 minutes. Treat each leg separately. Out:

(45 minutes). Back:

(60 minutes). The return trip takes

longer.

• A: This reads the 0.25-hour difference as 25 minutes instead of 15 minutes.
• B: This is the total time for both legs, not the difference between them.
• C (correct): The trip out takes 45 minutes and the trip back takes 60 minutes, a difference of 15 minutes.
• D: This is the time for the trip out, not how much longer the return takes.

Answer: C

Correct answer: $0.10. Ream: 500 sheets is 5 hundreds, so

per 100 sheets.

Case: 2,500 sheets is 25 hundreds, so

per 100 sheets. The case is cheaper by

per 100 sheets.

• A: This compares sticker prices, but the case holds five times as much paper.
• B: This is the saving on all 2,500 sheets compared with five reams, not the saving per 100 sheets.
• C (correct): The ream costs $1.25 per 100 sheets and the case costs $1.15 per 100 sheets, a difference of $0.10.
• D: This is the case's price per 100 sheets, not how much less it costs.

Answer: C

Correct answer: 13/20. Fuel used is the start level minus the end level. With the common denominator 20:

• A: This subtracts the numerators and the denominators separately (8/6), and more than a full tank cannot have been used.
• B: This adds the two fractions instead of finding the difference.
• C (correct): With denominator 20 the change is 18/20 - 5/20 = 13/20.
• D: This multiplies the fractions; the amount used is the start level minus the end level.

Answer: D

Correct answer: 112.5 miles. Match the units. The rate is 27 miles ÷ 36 minutes = 0.75 mile per minute, and 2.5 hours =

Distance =

(Equivalently, 0.75 mile per minute is 45 mph, and

)

• A: This treats 2.5 hours as 250 minutes; half an hour is 30 minutes, so 2.5 hours is 150 minutes.
• B: This multiplies the per-minute rate by 2.5 without converting hours to minutes.
• C: This multiplies 27 miles by 2.5, as if 27 miles took a full hour instead of 36 minutes.
• D (correct): The rate is 27 ÷ 36 = 0.75 mile per minute, and 2.5 hours is 150 minutes, so 0.75 × 150 = 112.5 miles.

Answer: D

Correct answer: $1.20. Cost of 24 singles:

Savings:

Check: the pack works out to

dollar per bottle, saving 0.05 dollar on each of 24 bottles, and

• A: This is the savings on one bottle (0.79 - 0.74), not on all 24 bottles.
• B: This is the price of one bottle in the pack, 17.76 divided by 24, not the savings.
• C: This places the decimal point one place too far right; the savings must be less than the price of the pack.
• D (correct): 24 single bottles cost $18.96, and 18.96 - 17.76 = 1.20.

Answer: B

Correct answer: 4 hours. Together they paint

of the fence per hour. In 2 hours:

Remaining:

Painter A alone:

• A: This is how long Painter B alone would need for the remaining 4/9, but Painter B has left.
• B (correct): Together they finish 2 × 5/18 = 5/9, leaving 4/9; at 1/9 per hour, Painter A needs 4 more hours.
• C: This is the total time for the job (2 hours together plus 4 alone), not the extra time.
• D: This subtracts the 2 hours from Painter A's 9-hour time, ignoring the work Painter B did.

Answer: B

Correct answer: 13 1/3 square yards. Convert and multiply:

Then

• A: This multiplies the mixed numbers piece by piece (12 times 9 plus 1/2 times 3/5) instead of converting to improper fractions first.
• B (correct): The area is 25/2 times 48/5 = 120 square feet, and 120 divided by 9 is 13 1/3 square yards.
• C: This divides the 120 square feet by 3; 3 feet make a yard of length, but 9 square feet make a square yard.
• D: This multiplies by 9 instead of dividing; square yards are larger units, so the count must be smaller.

Answer: A

Correct answer: sturdy. The clue, surviving drops in the field, shows strength. ROBUST means strong and tough, so sturdy is the synonym; fragile is the opposite and robotic only looks similar.

• A (correct): Sturdy matches robust: strong and able to withstand rough use.
• B: Fragile is the opposite of a laptop that survives drops.
• C: Robotic is a look-alike that shares letters but means machine-like.
• D: Rugged laptops may cost more, but price is loosely related, not the meaning.

Answer: D

Correct answer: Enclosed. En- means to put into, and the base is case. To encase a wire is to put it inside a case or tube, which means to enclose it.

• A: Cut apart describes damaging the wire, while en- means putting it into something.
• B: Painted covers only the surface; the base case points to a container around the wire.
• C: Removed is the reverse of en-, which puts something in rather than taking it out.
• D (correct): En- means to put into, and a case is a covering, so encased wires are enclosed in tubing.

Answer: D

Correct answer: sends. Trans means across and mit means send. The weather station sends its readings across to the airfield, so transmits means sends.

• A: A station may record data, but the word is built from mit, send, and the readings travel to the airfield.
• B: This is the reverse direction; the station is sending the data, and the airfield is receiving it.
• C: Measuring would need the root meter; transmit is about passing the readings along.
• D (correct): Trans means across and mit means send, so the station sends its readings across to the airfield.

Answer: B

Correct answer: company. FIRM follows "a large construction," so it is a noun naming the employer. A firm is a business: "works for a large construction company."

• A: Solid matches the adjective sense of firm, but here the word is a noun after "large construction."
• B (correct): A firm is a business, and "a large construction company" keeps the sentence's meaning.
• C: Steady is another adjective sense of firm and cannot name the place someone works for.
• D: A contract is an agreement a business signs, not the business itself that employs the engineer.

Answer: C

Correct answer: change. Modify means to alter something, usually in part. Change matches the core action; improve adds an outcome the word does not promise, replace goes too far, and approve is a different decision.

• A: Approving the design means accepting it, not altering it.
• B: Replacing swaps the design for a new one, which overstates a change to part of it.
• C (correct): Modify means to make some changes to something, so change is the closest match.
• D: Improving names a good result, but a modification may or may not make the design better.

Answer: B

Correct answer: Pay back. Re- here means back, and the base burse is related to purse, a holder of money. Soldiers who used their own money are paid back, so reimburse means pay back.

• A: Pay in advance describes pre-, not re-; the soldiers have already paid their bills.
• B (correct): Re- means back, and the soldiers spent their own money first, so the Army will pay them back.
• C: Charge again reads re- as again and reverses who pays; the soldiers are receiving money, not paying more.
• D: Tax heavily reverses the flow of money and has no link to the prefix re-.

Answer: D

Correct answer: slope. The modifier "steep" and the result "snow slides off" describe an angle. PITCH of a roof means its slope; tar is the near trap because it is also a roofing word.

• A: A pitch can be a throw in baseball, but a roof does not throw anything.
• B: Pitch can be a sticky tar used on roofs, but "steep" cannot describe tar.
• C: Pitch can mean how high or low a sound is, which does not fit a roof.
• D (correct): The pitch of a roof is its slant, and a steep slope lets snow slip off.

Answer: C

Correct answer: assemble. Compile means to collect material from different sources and put it together. Assemble fits 'into one binder'; write, review and mail are related office tasks with different meanings.

• A: Reading the reports closely and critically is a different task from collecting them together.
• B: Sending the reports is an action that might follow, not the act of gathering them.
• C (correct): Compile means to gather items from several sources into one collection, which assemble expresses.
• D: Compiling uses material others have already written; it does not mean writing out the text.

Answer: C

Correct answer: tedium. The ending -dom forms nouns naming a state, so boredom is the state of being bored. Keep the noun answers and test them in the sentence: tedium, the feeling of dull, repetitive time, is the match.

• A: Bored is an adjective describing a person; the target names a state, so it must be a noun.
• B: Excitement is a state of strong interest, the opposite of feeling dull.
• C (correct): Bore plus -dom names the state of being bored, which is tedium, a noun for dull sameness.
• D: Exhaustion is deep physical tiredness, which is stronger and different from feeling uninterested.

Answer: C

Correct answer: size or strength. Magn means great, as in magnify. The magnitude of an earthquake is how great it is, meaning its size or strength.

• A: Where the quake happened is a separate fact; magn refers to greatness.
• B: The cause explains why, but magnitude tells how big.
• C (correct): Magn means great, and magnitude tells how great something is, so an earthquake's magnitude is its size or strength.
• D: Duration would need a time root such as chron or temp.

Answer: C

Correct answer: reliance. Dependence is the -ence noun from depend, to rely on. The island relies on shipped fuel, which is why a delay hurt. Reliance fits. Direction matters: the dependable thing is relied on, while the dependent party does the relying.

• A: Dependability means being reliable for others; it describes a quality of the fuel supply, not the island's need for it.
• B: Independence means not needing outside help, the opposite of the situation described.
• C (correct): Reliance means needing or counting on something, which describes an island that needs shipped-in fuel.
• D: A shortage is the result of the delay; the word itself names the island's need, not the lack of fuel.

Answer: B

Correct answer: submissive. The key clue is never once objecting, even when the work was clearly theirs. Of the quiet-person words, meek is the one that means too willing to give in, so submissive matches; unassuming and reserved name different traits.

• A: She does a lot of work, but meek describes her failure to refuse, not her work ethic; this confuses the result with the trait.
• B (correct): Meek describes someone overly quiet and too willing to give in, like accepting unfair work without protest.
• C: Unassuming centers on modesty about one's own success; the sentence is about giving in to others, not about avoiding praise.
• D: Reserved means slow to share feelings, a neutral trait; meek adds the weakness of submitting when one should object.

Answer: C

Correct answer: momentous. Historic and historical share a base but split in meaning. Historic means significant in history, while historical simply means about the past. An event people still talk about is significant, so momentous fits.

• A: Ancient means very old, but the moon landing is recent history and the word stresses importance, not age.
• B: This is the sense of historical, a lookalike with an extra -al ending.
• C (correct): Historic means important or famous in history, which is momentous.
• D: An event can be well recorded without being important, so this misses the sense.

Answer: D

Correct answer: hasty and shallow. "Far from" negates CURSORY. The real diagnosis took two hours and covered every circuit, so CURSORY must name the opposite: done quickly without close attention, or hasty and shallow.

• A: This describes what the diagnosis actually was; "far from" means the word is the opposite of careful and thorough.
• B: Precision is a different idea; the clue contrasts the word with the time and care she spent, not with correctness.
• C: Cost is never mentioned, so this adds a fact the sentence does not support.
• D (correct): Removing "far from" shows the word names the opposite of her two-hour, check-everything effort: quick and not careful.

Answer: A

Correct answer: ended. Conclude has two senses: to finish and to reach a judgment. The subject is a briefing, and the clue about going to lunch shows it stopped, so concluded means ended here. Conclusive is a different, stronger family member.

• A (correct): Conclude can mean to finish, and a briefing that stops at noon before lunch has ended.
• B: Inferred matches the other sense of conclude, reaching a judgment from evidence, but a briefing does not reason about anything.
• C: This is the meaning of conclusive, an adjective for evidence that settles a question, not a verb for a meeting stopping.
• D: Began is the opposite of ended.

Answer: D

Correct answer: It defines the term that the rest of the passage explains. The first sentence explains what the term dew point means. The sentences after it give everyday cases (wet grass, a sweating glass) and a reason forecasters care, all building on that definition.

• A: The grass example comes in the second sentence; the first sentence states a general meaning, not a single case.
• B: No problem or fix appears in the first sentence; it simply explains a term.
• C: The passage does not list steps, and the first sentence opens the passage rather than closing a sequence.
• D (correct): The opening sentence tells what dew point means, and the later sentences give cases and uses that depend on that meaning.

Answer: B

Correct answer: mildly ill. The idiom is explained by the symptoms in the first sentence and the visit to sick call in the second. A sore throat and slight fever that clear up in a couple of days point to feeling slightly sick, so under the weather means mildly ill.

• A: This reads the words literally; no storm is mentioned, and her symptoms explain the phrase.
• B (correct): Her sore throat, runny nose and slight fever, plus the trip to sick call, show she was a little sick.
• C: This overstates the problem; she had cold symptoms, rested one day and was back on duty soon after.
• D: Nothing in the passage describes her feelings; the clues are physical symptoms and a visit to the medic.

Answer: D

Correct answer: A member with two years of service is not required to join the dog-handling unit. Sort the verbs: "must" states a requirement (the first-aid course), "can choose" states a choice left to the member (dog handling), and "may" states a possibility (night drills). Only the choice that keeps dog handling voluntary matches the sheet; the others turn can into must, may into will, or must into something a member may skip.

• A: This turns "can choose" into a requirement for everyone; the sheet offers the training only as a choice.
• B: The sheet says the team "may" hold them, depending on conditions; changing "may" to "will" upgrades a possibility into a certainty.
• C: The sheet says members "must" finish the course within six months; nothing allows anyone to skip it.
• D (correct): The sheet says members "can choose" to train with the unit, which describes a free choice, not a requirement.

Answer: C

Correct answer: It compares sales from two different months, when demand may naturally differ. A fair comparison uses the same time period for each subject. The memo sets a peak summer month at one shop against a cold-weather month at the other, so the gap in sales may reflect the season rather than the location.

• A: This accepts the comparison at face value and ignores that the figures come from different months.
• B: Flavors are not part of the comparison, and their absence does not explain the problem with mismatched months.
• C (correct): July and November are different seasons for ice cream, so the numbers are not lined up on the same period.
• D: The memo reports actual cone sales, not predictions, so this misidentifies the weakness.

Answer: A

Correct answer: Station North had a lower rate of failed inspections per vehicle than Station South. Keep each comparison in the right direction. If South had F failures and V vehicles, North had 2F failures and 4V vehicles.

So North's failure rate per vehicle was about half of South's, even though its total number of failures was higher.

• A (correct): North had 2 times the failures spread over 4 times the vehicles, so its failures per vehicle were about half of South's.
• B: Twice as many does not mean two more; this reads a ratio as a difference.
• C: This looks only at the raw count of failures and ignores that North has four times as many vehicles.
• D: This swaps the two motor pools; the passage says North has about four times as many vehicles.

Answer: C

Correct answer: To help farmers avoid applying fertilizer their fields do not need. The reason appears in the first sentence after "to help": farmers should avoid using more fertilizer than needed. "For instance" introduces an example, the corn grower, which illustrates the reason but is not the reason itself.

• A: This is an example of how the tests help, not the reason the office started offering them.
• B: The ten-day turnaround is a true detail about the service, but it does not explain why the tests were offered.
• C (correct): The passage states the tests were offered "to help farmers avoid using more fertilizer than their fields need."
• D: Fertilizer prices are never mentioned; this choice relies on outside assumptions rather than the passage.

Answer: A

Correct answer: Tankless water heaters save energy and space but cost more to buy and install. When a passage weighs two sides, the main idea is the balance itself. The first half lists energy and space savings, and after "On the other hand" the second half lists higher purchase and installation costs. The best summary keeps both.

• A (correct): This keeps both sides of the passage: the advantages before "On the other hand" and the costs after it.
• B: The passage weighs benefits against costs and never names a winner, so this picks a side and overstates.
• C: This reverses a detail; the passage says a standard tank, not a tankless unit, keeps water hot all day.
• D: This is one detail about installation costs and leaves out the advantages entirely.

Answer: A

Correct answer: Long idling is unnecessary for modern cars, which warm up best when driven gently. Check the direction of the claim. The passage argues against long warm-ups: modern engines need about thirty seconds and warm faster while driven gently. The correct choice keeps that direction, while one tempting distractor borrows the same words but flips the message.

• A (correct): This keeps the direction of the passage: the old habit is outdated, and gentle driving is the better way to warm up.
• B: This uses the passage's own topic but reverses its message; the passage says long warm-ups are unnecessary.
• C: This is background detail explaining where the habit came from, not the point the passage is making.
• D: The passage says idling wastes fuel and adds wear; claiming damage within minutes overstates it.

Answer: B

Correct answer: The author reaches a conclusion from evidence that includes the program's drawbacks. Check what evidence is presented and whether anything is left out. The author gives the $210,000 cost, the savings of about $260,000, and the drawbacks (a longer line and menu complaints), then concludes the program should stay with changes. A conclusion drawn from evidence that includes the downsides is careful reasoning, not one-sided bias.

• A: Having a conclusion is not bias; bias would mean hiding or distorting facts, and this author reports the program's cost and its problems.
• B (correct): The author reports costs, savings and two complaints, then concludes; presenting evidence on both sides before judging is reasoning, not bias.
• C: The $210,000 yearly cost is stated plainly, right next to the savings.
• D: The author does list the figures, but the final sentence says the program appears to pay for itself and that the plant would be wise to keep it, which is a clear judgment.

Answer: B

Correct answer: The months of aging and cracking that weakened the radiator hose. An immediate cause is the last event that directly produced the result; an underlying cause is the deeper condition that made it likely. Here the split hose losing coolant on the steep climb is the immediate cause, while the months of aging that weakened the hose are the underlying cause.

• A: The split was the final event that directly produced the overheating, so it is the immediate cause.
• B (correct): The slow deterioration is the long-standing condition that made a failure likely, which is what an underlying cause is.
• C: Pulling over was Jamal's response to the overheating, an effect rather than a cause.
• D: The passage never says the weather played a role; this brings in an outside explanation.

Answer: B

Correct answer: 360 degrees. Going once around any convex polygon, the exterior angles always total 360 degrees, no matter how many sides it has.

• A: This is the interior angle sum, (15 - 2) times 180; the question asks for exterior angles.
• B (correct): The exterior angles of every convex polygon add to 360 degrees, regardless of the number of sides.
• C: This multiplies 360 by 15 sides; 360 is already the total for all the exterior angles together.
• D: This is the sum of the interior and exterior angle at a single vertex, not the total around the polygon.

Answer: D

Correct answer: Obtuse. A triangle is obtuse if one angle is greater than 90°. Since 93° is more than 90°, the triangle is obtuse, even though its other two angles are acute.

• A: An acute triangle needs all three angles under 90°; 93° is not.
• B: A right triangle needs an angle of exactly 90°; 93° is close but larger.
• C: Equiangular means all three angles are equal (60° each), which is not the case here.
• D (correct): One angle, 93°, is greater than 90°, which makes the triangle obtuse.

Answer: C

Correct answer: 30 cubic feet. Volume of a rectangular box is V = lwh = 5 times 2 times 3 = 30 cubic feet.

• A: This adds the three dimensions instead of multiplying them.
• B: This is the surface area of the box, the covering, not the space inside.
• C (correct): Length times width times height: 5 times 2 times 3 is 30.
• D: This adds the three face areas once, which is half the surface area, not the volume.

Answer: A

Correct answer: 4,730. A number divisible by 2 ends in an even digit, and one divisible by 5 ends in 0 or 5. Only a last digit of 0 does both, so 4,730 is the answer.

• A (correct): It ends in 0, which passes the tests for 2, 5 and 10.
• B: It ends in 5, so it is divisible by 5 but is odd.
• C: It ends in 2, so it is even but not divisible by 5.
• D: It ends in 4, so it is even but not divisible by 5.

Answer: B

Correct answer:

In I = Prt, the letter r is multiplied by P and by t. Treat P and t like numbers and divide both sides by Pt:

For example, if I = 90, P = 1,500 and t = 2, then

or 3%.

• A: This is the reciprocal of the correct expression; it divides Pt by I instead of I by Pt.
• B (correct): Since r is multiplied by both P and t, dividing both sides by Pt isolates r.
• C: This subtracts Pt, but r is multiplied by Pt, so division is the inverse operation needed.
• D: This multiplies by Pt instead of dividing, which repeats the operation rather than undoing it.

Answer: B

Correct answer: 20π cm. The square's sides are inside the shape now, so they do not count. The outer edge is four semicircles of diameter 10, which equal two full circles: 2 times 10π = 20π cm.

• A: This also adds the square's four sides, but they are covered by the semicircles and are not on the outside.
• B (correct): Four semicircular arcs of diameter 10 make two full circumferences, 2 times 10π.
• C: This counts only two semicircles, one full circle; there is a semicircle on all four sides.
• D: This counts each attachment as a full circle instead of a half circle.

Answer: B

Correct answer: 6. Multiply every term of the second equation by 2:

Subtract it from the first equation:

so x = 6. Check:

gives y = 2, and

• A: This is the value of y, not x; the question asks for x.
• B (correct): Doubling x + 2y = 10 and subtracting it from 3x + 4y = 26 leaves x = 26 − 20 = 6.
• C: This comes from doubling only the variable terms and leaving the constant 10, so 26 − 10 = 16; every term must be multiplied.
• D: This is x + y = 6 + 2, the sum of the two values rather than x alone.

Answer: D

Correct answer: 0 ÷ (−6). Zero divided by a nonzero number is zero, so

Dividing by zero, as in −6 ÷ 0, is undefined rather than zero.

• A: Division by zero is undefined, so this has no value at all.
• B: This equals −12; subtracting 6 from −6 moves farther left.
• C: (−6)(0) = 0, but adding 1 gives 1.
• D (correct): Zero divided by any nonzero number is zero.

Answer: B

Correct answer: 30 units. Width:

Height:

Perimeter =

units.

• A: This is 9 times 6, the area, not the distance around.
• B (correct): The width is 3 - (-6) = 9 and the height is 4 - (-2) = 6, so the perimeter is 2(9 + 6) = 30.
• C: This finds the width as 3 - 6 = 3 by dropping the negative sign, then uses 2(3 + 6).
• D: This adds one width and one height but forgets that a rectangle has two of each.

Answer: A

Correct answer: A closed circle at −1 shaded left and an open circle at 4 shaded right. An or statement includes every number that satisfies at least one piece, so graph both rays.

gets a closed circle at −1 with shading left. x > 4 gets an open circle at 4 with shading right. The gap between −1 and 4 stays unshaded.

• A (correct): −1 is included (≤) and 4 is not (>), and an or statement keeps both outer pieces.
• B: This swaps the circles: −1 should be included and 4 should not.
• C: Shading between treats the statement as an and overlap; the or solution lies outside.
• D: These rays point toward each other and show the middle values, which satisfy neither condition.

Answer: D

Correct answer: 3.2 × 10⁴ kg. Multiply the front numbers and add the exponents:

giving $32\times 10^3$. Since 32 is 10 or more, rewrite it as $3.2\times 10^4$ kg.

• A: This changes 32 to 3.2 but forgets to raise the exponent by one.
• B: This adds the front numbers, 4 + 8, instead of multiplying them.
• C: This multiplies the exponents, 6 times -3, instead of adding them.
• D (correct): 32 x 10^3 is rewritten as 3.2 x 10^4 by moving the decimal and raising the exponent by one.

Answer: A

Correct answer: 1. Subtract the second equation from the first, term by term:

Divide by 2:

(Solving fully gives x = 5.5 and y = 4.5, which agrees.)

• A (correct): Subtracting the equations gives 2x − 2y = 2, and dividing by 2 leaves x − y = 1.
• B: This is x + y, which comes from adding the equations (8x + 8y = 80) rather than subtracting them.
• C: This is the value of 2x − 2y; it still has to be divided by 2 to give x − y.
• D: This is the value of x alone; the question asks for the difference x − y.

Answer: C

Correct answer: 28. Substitute with parentheses: $2(-3{)}^2-(-3)(2)+(2{)}^2$. Square first:

Next,

and subtracting it adds 6. Last,

Total:

• A: This squares -3 as -9, giving -18 + 6 + 4.
• B: This treats -ab as -6 instead of +6, giving 18 - 6 + 4.
• C (correct): 2(9) - (-6) + 4 = 18 + 6 + 4 = 28.
• D: This doubles before squaring, using (2a)^2 = 36 instead of 2a^2 = 18.

Answer: A

Correct answer: 73°. Each of the three given angles has an equal vertical partner, so the three given angles fill half a turn:

6x = 144 and x = 24.

The angles are 44°, 63° and 73°, so the largest is 73°.

• A (correct): With x = 24 the angles are 44°, 63° and 73°, which total 180°.
• B: This sets the three angles equal to 360° (x = 54), forgetting that their vertical partners fill the other half of the turn.
• C: 24 is x, not an angle measure.
• D: 107° is the supplement of the largest angle, not the angle itself.

Answer: B

Correct answer: 2,700. A 25% loss leaves 75% each year, so multiply by 0.75 three times: 6,400 → 4,800 → 3,600 → 2,700. In formula form,

• A: This subtracts 25% of the original 6,400 (1,600) each year, treating the decay as a fixed amount rather than a fixed percent.
• B (correct): Multiplying by 0.75 for each of 3 years gives 6,400 × 0.421875 = 2,700.
• C: This is the population after 2 years; one more year of decay is needed.
• D: This is the population after only 1 year.

Answer: A

Correct answer: From the negative terminal, through the bulb, toward the positive terminal. Conventional current is defined as leaving the positive terminal, but the carriers in a metal wire are electrons, which are negative. They drift the opposite way: out of the negative terminal, through the bulb, and back toward the positive terminal.

• A (correct): Electrons are negative, so they drift opposite to conventional current, from negative toward positive through the load.
• B: This is the direction of conventional current, which is the opposite of the real electron drift in a metal.
• C: That describes household AC; a battery supplies DC, which does not reverse.
• D: Charge flows around one loop; nothing is used up inside the bulb, so carriers cannot simply meet and stop there.

Answer: C

Correct answer: Silver. Silver conducts best of the ordinary metals, with copper a close second. Copper is used for most wiring because it costs far less, aluminum is used where low weight matters, and gold plating is chosen for corrosion resistance.

• A: Copper is a very close second and is used for wiring because it is far cheaper, but it is not the best.
• B: Gold is used to plate connectors because it resists corrosion, not because it conducts best.
• C (correct): Silver has the lowest resistivity of the ordinary metals.
• D: Aluminum is chosen for overhead lines because it is light; its resistivity is about 1.6 times copper's.

Answer: D

Correct answer: Stay far away, keep others back, and call 911 and the utility. A downed line must be treated as energized even when it is quiet. Current can spread through wet ground, fences and puddles, so keep a wide distance, keep others away, and let emergency services and the utility make it safe.

• A: Approaching or touching the line exposes the person to hazardous voltage in the line and the ground around it.
• B: Lack of sparks or noise does not mean a line is dead; getting close is dangerous.
• C: Touching or approaching the line to check it is never a safe test.
• D (correct): A silent line may still be energized, and current can spread through wet ground near it.

Answer: C

Correct answer: The 1 kΩ resistor. Each branch has the battery voltage across it, and

Current is inversely related to resistance, so the 1 kΩ resistor carries the most.

• A: This assumes more resistance means more current, but the largest resistor carries the least.
• B: A middle value carries neither the most nor the least current.
• C (correct): All branches share the same voltage, so the smallest resistance passes the largest current.
• D: This is the second smallest value, so it carries the second largest current.

Answer: D

Correct answer: A regulator. Match the job to the device. Holding the output at a fixed voltage while the input or load changes is what a voltage regulator does.

• A: A rectifier changes AC into one-direction pulses; it does not hold a voltage steady.
• B: An amplifier makes a weak signal larger; it does not hold a supply at a set voltage.
• C: An inverter changes DC into AC, which is not this stage's job.
• D (correct): A regulator, such as a Zener circuit or regulator IC, holds the output at a set voltage despite changes in input or load.

Answer: D

Correct answer: 900 rpm. Rearrange

to solve for speed.

Check: 8 poles give 4 cycles per turn, and 900 rpm is 15 turns per second, so

• A: This uses 60 instead of 120 in the formula, counting each pole rather than each pole pair as one cycle.
• B: 3,600 rpm gives 60 Hz only for a two-pole machine; more poles let the shaft turn more slowly.
• C: 60 Hz divided by 4 pole pairs is 15 revolutions per second, not per minute; times 60 that is 900 rpm.
• D (correct): $n=120f/p=120\times 60/8=900$ rpm.

Answer: B

Correct answer: The pin connects to the positive supply rail. Supply rails are often shown by labels instead of long wires. VCC means the point is connected to the positive supply, so every point marked VCC is the same node as the positive rail.

• A: A named rail label shows a connection; it is not a mark for an unused pin.
• B (correct): A rail label such as VCC means the point joins the positive supply, even when no wire is drawn to the battery.
• C: Ground is shown with ground symbols; VCC names the positive supply.
• D: Signal lines carry information and are named for their signal; VCC is a power label.

Answer: A

Correct answer: OR. The output is 1 whenever at least one input is 1 and is 0 only when every input is 0. That is the definition of an OR gate.

• A (correct): An OR gate outputs 1 when any input is 1, so either open window, or both, sounds the alarm.
• B: An AND gate outputs 1 only when all inputs are 1, so it would need both windows open before sounding.
• C: A NOT gate has a single input and simply flips it; this alarm combines two inputs.
• D: A NOR gate outputs 1 only when all inputs are 0, so it would sound only when both windows are closed.

Answer: D

Correct answer: 0 Wb. Use

where $\theta$ is measured from the line perpendicular to the loop. Field lines parallel to the surface are at 90 degrees to that line, so

Wb. No field passes through the loop.

• A: This is the flux only when the field passes straight through the loop face; here it runs along the surface.
• B: Besides ignoring the angle, this gives the answer in teslas, the unit of field strength, not of flux.
• C: This divides the field by the area instead of multiplying, and it also ignores the loop's orientation.
• D (correct): The angle between the field and the line perpendicular to the loop is 90 degrees, and $\cos 90^{\circ }=0$.

Answer: D

Correct answer: $15.12. Convert to kilowatts: 300 W is 0.3 kW. Hours:

h, so energy is

kWh.

Cost:

• A: This is the cost of a single day; the 30 days were left out.
• B: This assumes the unit runs 24 hours a day instead of 12.
• C: This uses 300 W directly as if it were kilowatts, skipping the divide-by-1,000 step.
• D (correct): The month uses 0.3 kW times 360 h, or 108 kWh, and 108 times $0.14 is $15.12.

Answer: D

Correct answer: 500 Ω, more than P's 200 Ω. Read each line at the same voltage and use

converting milliamperes to amperes first.

On a current-versus-voltage graph the slope is 1/R, so the less steep line, Q, has the larger resistance.

• A: This swaps the two resistors; the line with less current at the same voltage has more resistance.
• B: This divides volts by milliamperes without converting to amperes, so both values are 1,000 times too small.
• C: This multiplies voltage by current instead of dividing voltage by current.
• D (correct): 6 V divided by 0.012 A is 500 Ω and 6 V divided by 0.03 A is 200 Ω, so Q, the less steep line, has more resistance.

Answer: C

Correct answer: 25 W. Peak-to-peak is twice the peak, so

For a sine,

• A: This uses the 30 V peak directly in $V^2/R$ instead of first converting to RMS.
• B: This puts the full 60 V peak-to-peak value into $V^2/R$, skipping both the halving and the RMS conversion.
• C (correct): The 60 V peak-to-peak gives a 30 V peak and about 21.2 V RMS, and $21.2^2/18\approx 25$ W.
• D: This divides by 2 one time too many after already converting the peak to an RMS value.

Answer: B

Correct answer: 13.5 W. After the change,

Lamp power:

down from 24 W before the resistor was added.

• A: This is the lamp power before the resistor was added; the added resistance lowers the current.
• B (correct): The new current is 12 over 8, or 1.5 A, and $1.5^2\times 6=13.5$ W.
• C: This is the total power of the loop, which includes the 2 Ω resistor.
• D: This is the power in the added 2 Ω resistor, not in the lamp.

Answer: D

Correct answer: 0.8 A. The parallel pair is

so the total is

and the source current is

The pair's voltage is 2 A times 12 Ω = 24 V, which appears across each branch.

Check: the 20 Ω branch carries 1.2 A, and

• A: 1.2 A is the current in the 20 Ω branch; the larger 30 Ω branch carries less.
• B: This splits the 2 A total equally, but parallel branches with unequal resistance carry unequal currents.
• C: 2 A is the total source current, which divides between the two branches.
• D (correct): The pair is 12 Ω, total 18 Ω, source current 2 A, pair voltage 24 V, and 24 V / 30 Ω = 0.8 A.

Answer: B

Correct answer: 1.25 A. Secondary voltage:

Load current:

so output power is

Input power is output divided by efficiency:

Primary current is

• A: This treats the transformer as ideal and ignores the 96 percent efficiency, so the input power is too small.
• B (correct): Secondary 24 V and 6 A give 144 W; input is 144/0.96 = 150 W, and 150/120 = 1.25 A.
• C: This multiplies the output by the efficiency instead of dividing; the input must be larger than the output.
• D: This uses the turns ratio the wrong way, multiplying the secondary current by 5 instead of dividing.

Answer: D

Correct answer: Recovery (overflow) tank. Coolant grows in volume as it heats. The cap releases the extra into the recovery tank, and when the engine cools, a vacuum valve in the cap pulls it back into the radiator so the system stays full.

• A: The heater core and its hoses pass coolant through to warm the cabin; they do not store expansion volume.
• B: The thermostat controls flow to the radiator by temperature; it does not hold extra coolant.
• C: The pump and its housing circulate coolant but have no space for expanded fluid.
• D (correct): The cap lets expanding coolant pass into this tank, and a vacuum valve draws it back as the system cools.

Answer: D

Correct answer: The hub. The hub is the vehicle's rotating mount, carried by a wheel bearing and fitted with studs or bolt holes. The wheel bolts to the hub, and the tire is mounted on the wheel.

• A: The rim is part of the wheel that holds the tire; it bolts to the hub rather than being the mount.
• B: The bead is the wire edge of the tire that seals on the rim.
• C: The valve stem is the fitting used to add or check air, not a mounting point.
• D (correct): The hub is the rotating mount, carried by a bearing, that the wheel bolts onto.

Answer: C

Correct answer: Compression. BDC alone could mean the end of intake or the end of power, so check the other clues. The charge is fresh and unburned, both valves are closed and the piston is starting upward, so intake has just finished and compression is beginning.

• A: Exhaust also starts at BDC with the piston rising, but the cylinder would hold burned gas and the exhaust valve would be opening.
• B: The power (expansion) stroke begins near TDC after ignition and drives the piston down, not up from BDC.
• C (correct): A full cylinder of fresh charge, both valves shut and the piston heading up from BDC is the start of compression.
• D: The intake (induction) stroke starts at TDC with the piston moving down; this one has just ended, since the cylinder is already full.

Answer: A

Correct answer: The charging system is not charging as expected, so the battery may be draining. The battery lamp is a charging-system lamp. With the engine running, it means the alternator system is not keeping up, perhaps from a slipping belt, a failed alternator or a wiring fault. Check the belt, then running voltage, then the alternator and its wiring before the battery runs down.

• A (correct): This lamp is really a charging-system warning; the car may be running on stored battery energy.
• B: The lamp does not measure battery health; the battery had enough energy to start the car, so immediate replacement is not indicated.
• C: The lamp warns of a charging problem; it is not a full-charge indicator.
• D: The lamp monitors charging, not the starter, and the engine started and runs normally.

Answer: D

Correct answer: A thinner rotor has less mass to absorb heat, so it overheats and fades sooner. Rotors and drums store the heat of each stop in their mass and then shed it to the air. Wear or machining removes metal and reduces that heat capacity, so a rotor below minimum thickness gets too hot faster and is more likely to fade or be damaged.

• A: Rotor thickness has nothing to do with fluid compressibility; air or vapor in the fluid causes a soft, spongy pedal.
• B: The red lamp responds to the parking brake, fluid level or hydraulic faults, not rotor thickness.
• C: Wheel-speed sensors read a toothed or magnetic ring, not the rotor faces, so rotor thickness does not affect them in any stop.
• D (correct): Rotors act as heat sinks; less metal means less heat capacity during a stop.

Answer: B

Correct answer: Test spark, fuel delivery and compression for cylinder 3. A diagnostic code points to a condition, not a specific failed part. A misfire can be caused by a worn plug or bad coil, a clogged injector, or low compression, so the technician tests spark, fuel and compression in that cylinder before replacing anything.

• A: Misfires can come from ignition, fuel or compression problems, so replacing the plug without testing may not fix the cause.
• B (correct): The code describes what happened, not why; checking each function for that cylinder finds the actual cause.
• C: The ECM detected and reported the misfire; reporting a fault does not mean the controller caused it.
• D: Clearing the code does not fix anything, and unburned fuel from an ongoing misfire can overheat the catalytic converter.

Answer: B

Correct answer: A sliding collar moved by a shift fork. In a constant-mesh gearbox all gear pairs stay meshed, and the gears on the output shaft spin freely on bearings. Moving the shift lever moves a fork, which slides a collar to lock the chosen gear to the shaft, so only that pair sets the ratio.

• A: Hydraulic bands select ratios in automatic planetary transmissions, not in a manual gearbox.
• B (correct): The shift lever moves a fork that slides a collar to lock the free-spinning gear to its shaft.
• C: In a constant-mesh gearbox the gear pairs are always in mesh; the collar does the locking.
• D: The clutch disc connects the engine to the input shaft; it does not select individual gears.

Answer: C

Correct answer: Fuel sprayed into the port washes over the back of the intake valve. In port injection, fuel enters the intake port just upstream of the intake valve, so it constantly washes the back of the valve. A direct injector sprays into the cylinder instead, so the intake valves lose that cleaning effect and carbon can build up.

• A: Port injection actually runs at moderate pressure; direct injection is the system that needs much higher pressure.
• B: Every four-stroke piston engine of this type has intake valves; in port injection the fuel is sprayed toward them.
• C (correct): In port injection the fuel hits the hot intake valve on its way into the cylinder, which helps keep the valve clean.
• D: The catalytic converter is in the exhaust system after the engine and has no effect on the intake valves.

Answer: C

Correct answer: The car is understeering, and the stability control may brake individual wheels and cut engine power. Understeer means the front tires reach their limit first and the car turns less than the driver steers. Electronic stability control compares steering angle with yaw rate; when they disagree, it brakes individual wheels and may reduce power, but it can never exceed the tires' grip.

• A: The car turning less than asked is understeer, and stability control acts through brakes and engine power, not by steering.
• B: Stability control cannot create grip beyond what the tires can give.
• C (correct): Turning less than steered means the front tires are slipping, and stability control responds with selective braking and power reduction.
• D: Rotating less than requested is understeer, a real event, so a sensor fault is not the best conclusion.

Answer: C

Correct answer: Normal condensation clearing as the exhaust warms. Thin white vapor on a cold morning is usually water condensing in a cold exhaust, and it stops once the system warms. Coolant entering combustion would give thick, sweet-smelling smoke that persists when hot and a dropping reservoir level, so the evidence here points to a normal condition.

• A: Coolant burning gives thick, sweet-smelling white smoke that persists when warm, along with falling coolant level, none of which is present here.
• B: Burning oil gives blue-gray smoke that does not clear up as the engine warms.
• C (correct): Thin vapor on a cold morning that fades with warm-up, with no odor and steady coolant, fits ordinary condensation.
• D: Excess fuel produces black smoke, not thin white vapor that clears with warm-up.

Answer: A

Correct answer: Tack welds. Tack welds are short welds placed at intervals along a joint to hold the parts in alignment and keep the gap even while the full weld is made. They help resist distortion as heat from welding causes the metal to expand. Tacks are usually blended into the final weld, so they must be clean and sound. Fillet and groove welds describe the shape of the joint being welded, and spot welds are made with resistance welding on overlapping sheet metal.

• A (correct): Tack welds are small temporary welds that hold parts in alignment before the final weld.
• B: A groove weld fills a prepared opening between members; it is a full joint weld.
• C: Spot welds are discrete resistance welds made with electrode pressure and current on overlapped sheets.
• D: A fillet weld fills the corner where surfaces meet at an angle; it is not defined by holding parts temporarily.

Answer: B

Correct answer: Remove it from the chuck. The chuck key is used only with the machine stopped. Remove it before applying power, because spindle rotation can eject a key left in the chuck.

• A: The key only tightens the chuck; left in place it becomes a projectile once the spindle turns.
• B (correct): A key left in the chuck can be flung out when the spindle rotates, so it must be removed first.
• C: Tightening a chuck must never be done with the spindle turning.
• D: Loose tools on the machine can fall or be caught; the key should be removed and kept clear.

Answer: C

Correct answer: Tongue-and-groove pliers. Tongue-and-groove pliers adjust to several jaw openings and grip large or irregular objects securely. Set the jaws so they engage fully and avoid over-squeezing the plastic.

• A: Their long, narrow jaws offer reach for small objects, not a wide, strong grip.
• B: These are made to cut wire, not to grip and turn a nut.
• C (correct): Their multiple jaw openings let them grip large or irregular round parts with useful handle leverage.
• D: Its toothed jaws bite into the material and can crush or scar a thin plastic nut.

Answer: B

Correct answer: Decline, because the two marking systems differ and the threads would not match. ISO property classes and SAE grades are separate rating systems, so similar numbers do not make them equivalent. The replacement must match the specified thread designation and the required strength, which an inch bolt cannot do in a metric hole.

• A: Strength ratings cannot be compared by the number alone, and the thread mismatch rules out the swap anyway.
• B (correct): Class 8.8 and Grade 8 come from different standards, and an inch thread will not mate with metric threads.
• C: Wrench size says nothing about thread pitch, diameter or strength class.
• D: A washer cannot correct a thread mismatch or a different strength rating.

Answer: C

Correct answer: Malleability. Look at the direction of the force. Squeezing by hammering or rolling tests malleability, while pulling into wire tests ductility. Hardness and brittleness describe different behavior entirely.

• A: Ductility is stretching under tension, such as drawing into wire; here the metal is squeezed, not pulled.
• B: Hardness is resistance to indentation or scratching, not the ability to be flattened without breaking.
• C (correct): Malleability is the ability to deform plastically under compression, such as hammering or rolling into sheet.
• D: A brittle material would crack with little deformation, the opposite of what happened.

Answer: C

Correct answer: 0.11 mm. Total indicated runout equals maximum minus minimum:

Subtracting a negative reading adds it.

• A: This subtracts 0.05 from 0.06 and ignores that the low reading is on the negative side of zero.
• B: This is only the high reading; runout must include the swing below zero as well.
• C (correct): Runout is the full needle swing: 0.06 minus (-0.05) equals 0.11 mm.
• D: This averages the two readings instead of taking the full difference between them.

Answer: D

Correct answer: 22.68 mm. Read the beam first: 22 mm. Then use the legend on the dial:

Add them:

• A: This assumes each division is 0.01 mm instead of reading the 0.02-mm legend on the dial.
• B: This treats each division as 0.001 mm, a tenfold slip from the more common 0.01 mm.
• C: This divides the 34 divisions by 2 as if each were 0.005 mm, instead of multiplying by 0.02 mm.
• D (correct): Each of the 34 divisions is worth 0.02 mm, adding 0.68 mm to the 22-mm beam reading.

Answer: D

Correct answer: Reject it or use it where it carries little load. A knot is the base of a branch; the grain bends around it and makes a weak spot. On the tension edge of a loaded member it is especially dangerous, so the piece should be rejected or placed where it carries little load.

• A: Knots bend the grain around them and create a real weak spot, so they are not just an appearance issue.
• B: Paint may seal the surface, but it does not restore the strength lost where the grain bends around the knot.
• C: Drilling leaves a hole in the tension edge, which removes even more material and weakens the joist further.
• D (correct): A large knot on a tension edge is a serious weak point, so the joist should be rejected or moved to a low-load spot.

Answer: C

Correct answer: Flatten one face on the jointer, then run that face down through the thickness planer. A thickness planer references the face that rides on its table, so it copies whatever shape that face has. First establish one flat face on the jointer; then that flat face rides on the planer table so the top face is cut parallel, giving consistent thickness.

• A: The planer's feed rollers can press the cup flat while it cuts, so the board springs back with the curve still in it.
• B: Each jointed face may be flat, but nothing makes the two faces parallel, so the thickness can still vary.
• C (correct): The jointer creates a flat reference face, and the planer then cuts the opposite face parallel to it for even thickness.
• D: Sanding refines a surface; it is not a reliable way to remove warp, and fine grit removes stock very slowly.

Answer: D

Correct answer: 0.02 mm. Minimum clearance occurs with the smallest hole and the largest shaft. Smallest hole = 20.00 mm; largest shaft =

Minimum diametral clearance =

• A: This compares nominal sizes only (20.00 − 19.95) and ignores the tolerances.
• B: This is the maximum clearance: largest hole 20.05 minus smallest shaft 19.92.
• C: This halves the minimum clearance, giving a radial value when the question asks for diametral clearance.
• D (correct): Worst case is the smallest hole (20.00 mm) with the largest shaft (19.98 mm), leaving 0.02 mm.

Answer: C

Correct answer: 400 J. Potential energy is weight times height, PE = mgh, and mg is the weight.

Since the weight is given as 250 N, PE =

Do not multiply by g a second time.

• A: This multiplies by g = 10 again, but 250 N is already a weight, not a mass.
• B: This divides the weight by the height instead of multiplying.
• C (correct): The weight is already in newtons, so PE = 250 × 1.6 = 400 J.
• D: This divides the weight by 10 as if converting it, which is not needed here.

Answer: A

Correct answer: It is at rest. On a position-time graph, slope equals velocity. A horizontal line has zero slope, so the velocity is zero and the forklift stays put 8 m from the origin.

• A (correct): The slope of a position-time graph is velocity, and a horizontal line has zero slope.
• B: The 8 m is a position, not a speed; a flat line means the position never changes.
• C: Steady acceleration makes a curved position-time graph, not a flat line.
• D: Moving toward the origin would make the line slope downward, not stay flat.

Answer: B

Correct answer: The filter. An air preparation unit is often called an FRL: the filter removes particles and liquid water, the regulator sets the working pressure, and the lubricator adds oil mist where tools need it.

• A: The regulator sets a steady downstream pressure; it does not clean the air.
• B (correct): The filter traps particles and separates out water before the air reaches tools and valves.
• C: The lubricator adds a fine oil mist for tools; it adds something rather than removing contaminants.
• D: A muffler quiets air leaving an exhaust port; it does not treat the supply air.

Answer: C

Correct answer: Two external spur gears meshing directly. When two gears mesh on the outside of each other, the teeth at the contact point move together, which spins the two gears in opposite directions. An open belt, a chain on sprockets and a pinion inside a ring gear all keep the same direction.

• A: With an open belt, both pulleys turn the same way.
• B: A chain drive, like an open belt, turns both sprockets in the same direction.
• C (correct): An external mesh always reverses direction, whatever the gear sizes.
• D: An internal mesh makes the pinion and the ring turn in the same direction.

Answer: B

Correct answer: About 520 N. On a slope the weight splits into a part along the ramp (W sin θ) and a part pressing into the ramp (W cos θ). With no other forces perpendicular to the surface, the normal force balances the part pressing in.

N = 600 × cos 30° ≈ 600 × 0.87 ≈ 520 N.

• A: This assumes the normal force always equals the weight, which is true only on level ground.
• B (correct): The normal force balances the weight component into the ramp, W cos θ ≈ 600 × 0.87.
• C: This is W sin θ, the part of the weight that tries to pull the crate down the ramp, not the part pressing into it.
• D: This divides the weight by cos 30° instead of multiplying; the normal force on a ramp is less than the weight.

Answer: B

Correct answer: About 37 degrees. An object on an incline starts to slip when

Here

The crate weight cancels out, so a heavier crate would slip at the same angle.

• A: This uses 1 divided by 0.75; the condition is tan θ equal to the coefficient itself, not its reciprocal.
• B (correct): Slipping starts when the tangent of the angle reaches the static coefficient, and tan 37° ≈ 0.75.
• C: Objects do not all slip at 45 degrees; that is the slip angle only when the coefficient is 1.0.
• D: At 30 degrees the tangent is only 0.58, which is less than 0.75, so static friction still holds the crate.

Answer: C

Correct answer: A low coefficient of thermal expansion. Thermal shock cracks a brittle material when one region heats or cools faster than another and the two try to change size by different amounts. A material with low expansion develops much less of this internal stress, so it resists cracking.

• A: Specific heat sets how much energy a temperature change takes; it does not limit the stress from uneven expansion.
• B: Thermal shock cracking happens far below melting; it comes from uneven expansion, not from softening.
• C (correct): With little expansion, hot and cool regions try to change size by only slightly different amounts, so internal stress stays small.
• D: Hardness resists scratches and dents; it does not reduce stress from uneven heating.

Answer: A

Correct answer: 80%. First find the AMA from measured forces, then compare it with the IMA from the segment count.

The sheave count does not matter; only the three supporting segments set the IMA.

• A (correct): AMA is 840/350 = 2.4 and IMA is the 3 supporting segments, so efficiency is 2.4/3 = 0.80, or 80 percent.
• B: This divides the AMA by 4, the number of sheaves; the IMA comes from supporting rope segments, not wheels.
• C: This divides the IMA by the AMA; efficiency is AMA over IMA and can never exceed 100 percent.
• D: This is the effort divided by the load, 350/840, which is the inverse of the AMA, not the efficiency.

Answer: D

Correct answer: At 240 rpm, on a shaft at a right angle to the crank shaft. Bevel gears connect shafts whose axes intersect, usually at a right angle. With equal tooth counts the ratio is

so the speed is unchanged. The pair only turns the drive around the corner.

• A: The speed is right, but bevel gears join shafts whose axes meet, typically at 90 degrees.
• B: Equal tooth counts do not change speed; halving would need a gear with twice as many teeth.
• C: Doubling the speed would need a driven gear with half as many teeth; these counts are equal.
• D (correct): Equal tooth counts give a 1:1 ratio, and bevel gears connect intersecting shafts.

Answer: A

Correct answer: Third class; it gives up force to gain speed and reach at the blade. Read the order of the three points from the pivot: top hand (fulcrum), lower hand (effort), blade (load). With the effort in the middle, this is a third-class lever.

Its effort arm is shorter than its load arm, so the ideal mechanical advantage is below 1: the landscaper pushes harder than the load but gains speed and reach at the blade.

• A (correct): The effort sits between the fulcrum and the load, so the effort arm is shorter and the lever trades force for motion.
• B: The fulcrum is at the top end, not between the effort and the load, so this is not a first-class arrangement.
• C: In a second-class lever the load is in the middle; here the effort hand is in the middle.
• D: The class is right, but a third-class lever always has an effort arm shorter than the load arm, so it reduces force.

Answer: D

Correct answer: 400 rpm. Each turn moves the belt one circumference,

The belt covers 6.28 m each second, which is about 6.67 turns per second.

• A: This leaves out the factor of 60, so it is the number of turns per second, not per minute.
• B: This leaves out $\pi$; each turn moves the belt one circumference, $\pi D$, not one diameter.
• C: This uses $2\pi \times 0.30$ for the circumference, treating the diameter as a radius.
• D (correct): Rearranging $v=\pi DN/60$ gives N = 60 times 6.28 divided by (3.14 times 0.30), about 400 rpm.

Answer: D

Correct answer: 0.08 m. Simplify from the inside out. The chain:

N/m. The chain and the single spring share the bar and the plate, so they are in parallel:

N/m.

• A: This adds all three stiffnesses as if every spring were in parallel; the 300 and 600 N/m springs are in series with each other.
• B: This treats all three springs as one series chain; the single spring shares the plate with the chain, so it is in parallel.
• C: This puts the 300 and 600 N/m springs in parallel and the 400 N/m spring in series, reversing the real arrangement.
• D (correct): The chain acts as a 200 N/m spring, which shares the plate with the 400 N/m spring, so the total stiffness is 600 N/m and 48 ÷ 600 = 0.08 m.

Answer: C

Correct answer: 75%. In fresh water the submerged fraction equals the density ratio, so the float's density is

/m³.

In the oil:

So 75% of the float is below the surface. A less dense liquid gives less lift per cubic meter, so the float sinks deeper.

• A: This multiplies 0.6 by 0.8; in a less dense liquid the float must sink deeper, not ride higher.
• B: This assumes the fraction stays the same, but the submerged fraction depends on the liquid's density.
• C (correct): The float's density is 600 kg/m³, and 600 ÷ 800 = 0.75, so 75% sits below the oil surface.
• D: This is the fraction that stays above the oil, not the fraction below it.

Answer: D

Correct answer: About 57 N. Split the pull: horizontal part = 100 × 0.87 ≈ 87 N, vertical part =

N upward. The upward part lifts some weight off the snow, so

N and kinetic friction =

Net horizontal force ≈

N forward.

• A: This sets the normal force equal to the full 200 N weight, giving 40 N of friction; the rope's upward part reduces the normal force.
• B: This uses the whole 100 N as if it were horizontal and also takes friction from the full weight; only the horizontal component pulls the sled forward.
• C: This is only the horizontal part of the pull; friction still acts backward and must be subtracted.
• D (correct): The horizontal pull of about 87 N minus the 30 N of friction, with friction based on the reduced normal force of 150 N.

Answer: B

Correct answer: About 70%. Slope component:

Normal force:

so friction is about 260 N and the push is about 860 N.

AMA =

The IMA is

/sin 30 degrees = 2.

• A: This bases friction on the full 1,200 N weight; on a slope the normal force is only $W\cos \theta$, about 1,039 N.
• B (correct): The push is 600 + 0.25 times 1,039 = about 860 N, so AMA is 1,200/860 = 1.40; IMA is 1/sin 30 degrees = 2, giving about 70 percent.
• C: This uses $W\sin \theta$ for the normal force; the force pressing into the surface is $W\cos \theta$.
• D: This divides IMA by AMA; efficiency is AMA over IMA and can never exceed 100 percent.

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 square.

• A (correct): This square 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: 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: A cut is in a different place, so the pieces do not match: one piece here covers about 62% of the shape, but the matching piece in the left box covers about 40%.

Answer: C

Check one letter at a time. Point P is at the center of the hexagon, and point Q is at the center 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 sharp corner, but point Q is at the center.
• B: The line ends in the wrong place: it meets the hexagon at the middle of a side, but point P is at the center and it meets the diamond at a sharp corner, but point Q is at the center.
• C (correct): The line joins the center of the hexagon to the center of the diamond, 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 diamond at the middle of a side, but point Q is at the center.

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 square.

• A: 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 82%.
• 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: This figure has 3 pieces, but the left box has 2. Every piece must be used once, and nothing may be added.
• D (correct): This square is made of exactly the 2 pieces in the left box, each only turned and slid into place.

Answer: A

Check one letter at a time. Point K is at a corner of the rectangle, and point L is at a sharp 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 (correct): The line joins a corner of the rectangle to a sharp corner of the diamond, the same spots as points K and L in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the rectangle at the middle of a short side, but point K is at a corner and it meets the diamond at a wide corner, but point L is at a sharp corner.
• C: The line ends in the wrong place: it meets the rectangle at the middle of a short side, but point K is at a corner.
• D: The line ends in the wrong place: it meets the diamond at the middle of a side, but point L is at a sharp corner.

Answer: A

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

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

Answer: B

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

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

• A (correct): This rectangle 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: A cut is in a different place, so the pieces do not match: one piece here covers about 48% of the shape, but the matching piece in the left box covers about 40%.
• D: This figure has 4 pieces, but the left box has 3. Every piece must be used once, and nothing may be added.

Answer: D

Check one letter at a time. Point E is at the middle of a long side of the rectangle, and point F is at the right-angle 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 rectangle at the center, but point E is at the middle of a long side.
• B: The line ends in the wrong place: it meets the right triangle at the sharpest corner, but point F is at the right-angle corner.
• C: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• D (correct): The line joins the middle of a long side of the rectangle to the right-angle corner 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.

Answer: B

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

• A: This figure is a right triangle. 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 52% of the shape, but the matching piece in the left box covers about 39%.
• D (correct): This triangle is made of exactly the 3 pieces in the left box, each only turned and slid into place.

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 26% of the shape, but the matching piece in the left box covers about 18%.
• B: This figure has 4 pieces, but the left box has 3. Every piece must be used once, and nothing may be added.
• C (correct): This rectangle is made of exactly the 3 pieces in the left box, each only turned and slid into place.
• D: This figure is a square. The pieces in the left box do not have these shapes, so they cannot fill this outline without gaps or overlaps.

Answer: A

Check one letter at a time. Point M is at the center of the square, and point N is at the middle of a short side 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 the center of the square to the middle of a short side of the parallelogram, the same spots as points M and N 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 square at a corner, but point M is at the center.
• C: One of the shapes here is a diamond, but the left box has a square. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the parallelogram at a sharp corner, but point N is at the middle of a short side.

Answer: D

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

• A: A cut is in a different place, so the pieces do not match: one piece here covers about 25% of the shape, but the matching piece in the left box covers about 33%.
• B: 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.
• C: A cut is in a different place, so the pieces do not match: one piece here covers about 25% of the shape, but the matching piece in the left box covers about 15%.
• D (correct): This rectangle is made of exactly the 4 pieces in the left box, each only turned and slid into place.

Answer: B

Check one letter at a time. Point J is at the middle of a side of the triangle, and point K 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: The line ends in the wrong place: it meets the parallelogram at a sharp corner, but point K is at the center.
• B (correct): The line joins the middle of a side of the triangle to the center of the parallelogram, 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 parallelogram at the middle of a short side, but point K is at the center.
• D: One of the shapes here is a rectangle, but the left box has a parallelogram. Joining parts never changes a shape.

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 half-circle. 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 4 pieces in the left box, each only turned and slid into place.
• C: A cut is in a different place, so the pieces do not match: one piece here covers about 33% of the shape, but the matching piece in the left box covers about 24%.
• D: 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 37%.