AFQT Core Practice 8: Percents, Money Math and Word Parts

Answer: A

Correct answer: 0.8. A fraction is a division:

Check:

and four of them make 0.8.

• A (correct): Dividing 4 by 5 gives 0.8.
• B: This just writes the digits 4 and 5 after a decimal point; it does not divide.
• C: This is 5 divided by 4, the fraction turned upside down.
• D: This puts the 8 in the hundredths place; 4/5 equals 8 tenths, not 8 hundredths.

Answer: A

Correct answer: 25%. Percent equals part divided by whole:

or 25 percent. Twelve is one fourth of 48.

• A (correct): 12 divided by 48 is 0.25, which is 25 percent.
• B: This divides 48 by 12 to get 4 and treats the result as a percent.
• C: This subtracts 12 from 48 instead of dividing the part by the whole.
• D: This uses the count of cracked eggs as the percent without dividing by the 48 eggs in the crate.

Answer: A

Correct answer: 48 mph. Add distances and times first:

Average speed =

• A (correct): Total distance 240 miles divided by total time 5 hours gives 48 mph.
• B: This averages the two speeds, 50 and 45 mph, instead of dividing total distance by total time.
• C: This adds the morning and afternoon speeds together.
• D: This divides the total distance by only the morning's 3 hours.

Answer: D

Correct answer: 1/6. A worker who needs h hours for a job completes $\frac{1}{h}$ of it each hour. Here h = 6, so she completes $\frac{1}{6}$ of the transcript per hour.

• A: This is the number of hours for the whole job, not the fraction finished per hour.
• B: This is the fraction still left after the first hour, not the fraction done each hour.
• C: This halves the correct rate for no reason, as if the job took 12 hours.
• D (correct): A job that takes 6 hours alone is done at a rate of 1 divided by 6, or 1/6 of the job per hour.

Answer: C

Correct answer: 15%. Find the change: 184 minus 160 is 24 loaves.

Divide by the original value:

which is a 15 percent increase.

• A: This divides the increase of 24 by the new value 184 instead of the original value 160.
• B: This treats the increase of 24 loaves as if it were already a percent without dividing by the original amount.
• C (correct): The increase is 24 loaves, and 24 divided by the original 160 is 0.15, or 15 percent.
• D: This is Tuesday's sales as a percent of Monday's; the increase is that minus 100 percent.

Answer: C

Correct answer: $90.72. Both percents use the $72 food bill as the base. Tax:

Tip:

Total:

• A: This figures the tip on the taxed amount; the stem says the tip is based on the food bill before tax.
• B: This adds the tip but leaves out the 8% sales tax.
• C (correct): Tax is 0.08 × 72 = $5.76 and the tip is 0.18 × 72 = $12.96; 72 + 5.76 + 12.96 = $90.72.
• D: This adds the tax but leaves out the 18% tip.

Answer: D

Correct answer: 40 miles. Convert the time: 40 minutes is

so the time is

Then

• A: This writes 1 hour 40 minutes as 1.4 hours; 40 minutes is two-thirds of an hour, not 0.4.
• B: This uses only the 40 minutes and leaves out the first full hour.
• C: This multiplies miles per hour by 100 minutes without converting minutes to hours.
• D (correct): 1 hour 40 minutes is 5/3 of an hour, and 24 times 5/3 is 40.

Answer: D

Correct answer: 8 fluid ounces. Convert first:

fluid ounces of gasoline.

The gasoline is 40 parts, so one part is

fluid ounces, and the oil is 1 part: 8 fluid ounces.

• A: This divides 320 by 41, treating the gasoline as the whole mixture instead of the 40-part share.
• B: This divides 2.5 by 40 without converting gallons to fluid ounces.
• C: This is the oil for only 1 gallon of gasoline, 128 ÷ 40.
• D (correct): 2.5 gallons is 320 fluid ounces, and 320 ÷ 40 = 8 fluid ounces of oil.

Answer: B

Correct answer: 76. Find each group's total:

Combined mean:

It lies closer to 72 because that group is larger.

• A: 77 is the simple average of 72 and 82, which treats the groups as if they were the same size.
• B (correct): The totals are 1,296 and 984, which add to 2,280, and 2,280 divided by 30 is 76.
• C: This gives the larger weight to the 82 group, mixing up which group has 18 sailors.
• D: 2,280 is the combined total of all the scores; it still has to be divided by 30.

Answer: D

Correct answer: 2/5. Use 1/2 as a benchmark: 2/5 is below it because 2 is less than half of 5. Then compare with 1/3 by cross-multiplying:

so 2/5 is greater than 1/3.

• A: Cross-multiplying with 1/3 gives 9 versus 10, so 3/10 is less than 1/3.
• B: Its numerator 5 is more than half of 9, so 5/9 is greater than 1/2.
• C: With equal numerators, the larger denominator gives the smaller fraction, so 1/4 is less than 1/3.
• D (correct): Its numerator is less than half its denominator, so it is below 1/2, and cross-multiplying with 1/3 (6 versus 5) shows it is above 1/3.

Answer: B

Correct answer: 14 miles per hour. Speed is distance divided by time: $31.5÷2.25$. Move both points two places right:

per hour. Estimate:

which is close.

• A: This puts the decimal point one place too far left; 30 divided by 2 is about 15, not 1.5.
• B (correct): 31.5 divided by 2.25 is 3150 divided by 225, which is 14.
• C: This shifts the dividend's decimal point three places but the divisor's only two, which makes the quotient ten times too large.
• D: This multiplies distance by time; a rate is found by dividing distance by time.

Answer: C

Correct answer: 48. The sum of 9 and 6 is multiplied, so it goes in parentheses, and the quotient of 36 and 3 is a separate term: (9 + 6) × 4 − 36 ÷ 3.

Parentheses: 15. Then

Finally

• A: This leaves out the parentheses, so only the 6 is multiplied by 4: 9 + 24 − 12 = 21.
• B: This subtracts 36 from 60 and then divides by 3, but only 36 is to be divided by 3.
• C (correct): The sum needs parentheses: (9 + 6) × 4 − 36 ÷ 3 = 60 − 12 = 48.
• D: This subtracts 36 itself instead of the quotient of 36 and 3.

Answer: D

Correct answer: $1,120. Work backward. After groceries, 2/3 of the post-rent money is left:

after rent.

After rent, 3/4 of the paycheck is left:

Check: 1/4 of $1,120 is $280, leaving $840; 1/3 of $840 is $280, leaving $560.

• A: This subtracts 1/4 and 1/3 from the whole paycheck, but the 1/3 applies only to what was left after rent.
• B: This undoes only the grocery step and gives the amount left after rent.
• C: This undoes only the rent step and skips the grocery step.
• D (correct): After rent 3/4 is left, and after groceries 2/3 of that, so 1/2 of the paycheck is $560 and the paycheck is $1,120.

Answer: B

Correct answer: 37.5%. Cost per bike:

so total cost is

Revenue:

Profit:

• A: This leaves out the shipping cost, dividing $35 profit by the $75 purchase price.
• B (correct): Total cost per bike is 75 + 5 = $80 and profit per bike is 110 − 80 = $30; 30 ÷ 80 = 0.375 = 37.5%.
• C: This divides the $30 profit by the $110 selling price; the base here is the cost.
• D: This is the dollar profit per bike written as a percent, not profit divided by cost.

Answer: C

Correct answer: 80 tiles. Patio area:

Convert the tile side: 18 inches is 1.5 feet, so each tile covers

Tiles:

(Check by rows: 10 tiles along 15 feet and 8 along 12 feet give 80.)

• A: This divides the area by 1.5, the tile's side length, instead of by the tile's area.
• B: This divides 180 square feet by 18 without converting inches to feet or finding the tile's area.
• C (correct): Each tile is 1.5 ft by 1.5 ft = 2.25 square feet, and 180 / 2.25 = 80 tiles.
• D: This treats 18 inches as 1.8 feet, mixing up inches with tenths of a foot.

Answer: A

Correct answer: shielding. Protective is the adjective in the protect family, describing something that protects. Masks that guard the welder from sparks and light are shielding.

• A (correct): Protective describes something that guards from harm, and a welding mask shields the face and eyes.
• B: Protection is the noun for the safety itself; it cannot replace an adjective describing masks.
• C: Decorative means for looks, but welding masks are worn for safety.
• D: Dangerous is the opposite of something that keeps the wearer safe.

Answer: C

Correct answer: easily shaped. Malleable means able to be hammered, pressed, or bent into a new shape and keep it. Brittle is the opposite, and resilient means springing back, so easily shaped is the exact match.

• A: This describes brittle, the opposite behavior: a brittle material cracks instead of changing shape.
• B: This describes resilient; a malleable material keeps its new shape rather than returning to the old one.
• C (correct): Malleable describes a material, such as copper or gold, that can be hammered or pressed into a new form without breaking.
• D: Shine is a different property altogether; malleable is about how a material responds to pressure, not how it looks.

Answer: D

Correct answer: reserved. "Unlike" places the sergeant opposite the talkative lieutenant, and he rarely said more than a few words. RETICENT means reserved or quiet.

• A: This describes the lieutenant on the other side of the "unlike" contrast, not the sergeant.
• B: Nothing in the sentence shows anger; it shows quietness.
• C: Honesty is not the contrast being drawn; the clue is about how much he speaks.
• D (correct): Rarely saying more than a few words, in contrast to a talkative person, describes someone reserved.

Answer: D

Correct answer: moist. Humid describes air that holds a lot of moisture. Moist matches; hot is a common association, windy is a different condition, and dry is the opposite.

• A: Humid weather is often hot, but humid describes moisture in the air, not temperature.
• B: Wind is a different weather condition from moisture.
• C: This is the opposite of humid.
• D (correct): Humid means containing a lot of moisture, especially in the air, which matches moist.

Answer: C

Correct answer: emotionally uninvolved. In this sentence detached describes a manner, not an object, so the literal sense of separated does not fit. She has feelings but keeps them out of view, which is emotionally uninvolved, not uncaring.

• A: Uncaring means not concerned at all; the sentence says she does feel worry but keeps it hidden.
• B: This is the literal sense of detached, as in a detached garage, which does not fit a description of someone's manner.
• C (correct): Detached means keeping one's feelings out of a situation, which matches calm speech that hides worry.
• D: Confusion would show uncertainty; the surgeon speaks calmly and clearly.

Answer: B

Correct answer: noticeable. The word describes the drop in noise, not a person. The -ible ending signals capacity: able to be perceived. So perceptible means noticeable, not observant (perceptive) and not as strong as enormous.

• A: Observant is the meaning of perceptive, which describes a person who notices things; a drop in noise cannot be observant.
• B (correct): Perceptible describes something that can be noticed, and a drop in noise that the driver can hear fits.
• C: Imaginary means not real, but nothing suggests the drop was only imagined.
• D: Enormous is much stronger than perceptible, which only says the change can be noticed.

Answer: D

Correct answer: probability. Undo the spelling change: likelihood is likely (y to i) plus -hood, a noun ending for a state. So it means the state of being likely, or probability. Watch that the base is likely, not like.

• A: Likeness means resemblance; it comes from like in the sense of similar, not likely.
• B: Likely is the adjective base; the target is a noun.
• C: Fondness takes like in the sense of enjoy, which is the wrong base meaning.
• D (correct): Likely plus -hood forms a noun meaning the state of being likely, which is probability.

Answer: D

Correct answer: lawsuit. The collocation "filed a suit against" plus "faulty work" points to a legal claim. SUIT here means a lawsuit.

• A: A suit of clothes is the familiar sense, but no one files clothing against a roofer.
• B: Suit can mean one of the four sets in a deck of cards, which has no place here.
• C: To suit can mean to fit or match, a verb sense; here suit is a noun after "filed a."
• D (correct): "Filed a suit against" is legal language, so suit means a lawsuit.

Answer: D

Correct answer: independence. The Greek parts are auto, self, and nomos, law or rule, so autonomy literally means self-rule, the same idea behind an autonomous region that governs itself. On the job it means freedom to make decisions without someone checking every step, which makes sense once a year of training has built trust. The look-alike trap is automated tools: automatic shares auto but describes machines running by themselves, not people. Supervision is the reverse of autonomy.

• A: A raise may come with experience, but auto, self, points to working on one's own, not to wages.
• B: This seizes on the auto letters from automatic but turns the word into a noun for machines.
• C: This is the opposite; autonomy means less oversight, not more.
• D (correct): Auto means self, and autonomy is self-government, so trained technicians with more autonomy are free to work on their own.

Answer: A

Correct answer: obvious. Blatant means glaringly obvious, done without any attempt to hide it. The clue is that the whole stadium saw it; violent describes the act, not how visible it was.

• A (correct): Blatant means done openly and plainly, so obvious that no one could miss it, just as the whole stadium saw the shove.
• B: A foul seen by everyone and impossible to ignore is the opposite of a minor one.
• C: The shove was rough, but blatant describes how openly it happened, not how much force was used.
• D: Nothing suggests the shove was unintended; blatant actually implies the act was done openly.

Answer: A

Correct answer: Shallow. Super- means above or on top, and the base comes from face or surface. Scratches that stay on the surface are shallow, which matches her quick return to work.

• A (correct): Super- means above or on top, so superficial scratches stay on the surface of the skin and are shallow.
• B: Severe contradicts the clue that she returned to work the next day.
• C: Extraordinary reads super- as superior or great, the wrong sense for scratches on the surface.
• D: Artificial shares the -ficial ending but means fake, which does not describe a real injury.

Answer: A

Correct answer: all-powerful. Split the word into omni, all, and potent, powerful, so omnipotent means all-powerful. The sentence confirms it: controlling storms and armies is a display of power, not of knowledge, which rules out the omniscient trap.

• A (correct): Omni means all and potent means powerful, and bending storms and armies to his will shows unlimited power.
• B: This is omniscient, which pairs omni with sci, know; the trap uses the shared omni root.
• C: This is omnipresent; it keeps omni but swaps in a different idea, being in all places.
• D: Riches are not the clue; the sentence stresses control over storms and armies, which is power.

Answer: C

Correct answer: Clumsy. Mal- means bad or poor and describes a quality, while adroit means skillful. Poorly skilled handling that worsens a customer's mood is clumsy.

• A: Skillful is the meaning of adroit alone; the mal- prefix flips it to poor quality.
• B: Mistaken points to a single wrong act, the job of mis-; mal- describes a poor quality in how something is done.
• C (correct): Mal- means bad or poor, and adroit means skillful, so maladroit means lacking skill, or clumsy.
• D: Sickly matches mal- words about health, but the sentence describes how a task was handled.

Answer: A

Correct answer: calm. Composed has several senses: written, made up of, and self-controlled. Only the self-controlled sense fits a person facing an emergency, and calmly confirms it. Always match the sense the sentence uses.

• A (correct): In this sentence composed describes a person keeping control of her emotions, which is what calm means.
• B: Composed can mean written, as in music, but that sense applies to works, not to a person reacting to an emergency.
• C: Composed of can mean made up of parts, but that sense does not fit a pilot's reaction.
• D: The pilot reads the checklist aloud, so silent is contradicted by the sentence.

Answer: A

Correct answer: spread out control. Work from the inside out: central, then -ize (to make central), then de- (reverse). Decentralize means to move control away from one center. The sentence confirms it: each company now decides for itself.

• A (correct): Central plus -ize means make central, and de- reverses it, so decentralize means spread control away from one center.
• B: This reads the -ize suffix but skips the prefix de-, which reverses the meaning.
• C: Central is the adjective base; the target follows "to" and must be a verb.
• D: Cancel means call off; the decisions still happen, just at company level.

Answer: A

Correct answer: To persuade base leaders to add a second shuttle bus. An explicit should statement is strong evidence of a persuasive purpose. The first sentences give facts about the single crowded shuttle, and the final sentence recommends a second one, so the facts serve the recommendation.

• A (correct): The last sentence states a recommendation with should, and the earlier facts about crowding and missed rides support it.
• B: The route is mentioned only briefly; the passage is built around a problem and a proposed fix.
• C: Walking is mentioned as a drawback of missing the bus, not as a set of directions.
• D: No second shuttle exists yet; the author is asking for one, so this treats a proposal as a decision.

Answer: D

Correct answer: watch closely. Figure out the idiom from what the person must do. Mason has to call out right away if the needle drops, so he must watch the gauge continuously. Keep an eye on means to watch closely.

• A: This decodes the words literally; nothing in the passage involves covering the gauge.
• B: Mason is told to report a drop, not to fix anything.
• C: A single glance would not let him catch the needle dropping at any moment; the job requires continuous watching.
• D (correct): Mason must call out as soon as the needle drops, which requires steady, careful watching of the gauge.

Answer: B

Correct answer: The Route 6 line it replaced. A comparative needs a reference point. The sentence about length follows directly from Route 14 replacing Route 6, and it explains that the new route skips the loop, so Route 14 is shorter than Route 6.

• A: Route 20 is compared with Route 14 on speed during rush hour, not on length.
• B (correct): Route 14 replaced Route 6 and is shorter because it skips the loop that Route 6 made through the industrial park.
• C: Those lines are mentioned only in the officials' popularity claim, not in the length comparison.
• D: The loop explains why the route is shorter; it is not the route being measured against.

Answer: D

Correct answer: No, because burning is not allowed when the sign reads high. The rule gives permission on weekdays from 8 a.m. to 5 p.m. "unless" the sign reads high or extreme. Because the sign reads high, the exception controls the answer, and burning is not allowed regardless of the pile size or water supply.

• A: The time is within the normal window, but this ignores the "unless" condition, which overrides it.
• B: Pile size is a separate requirement; meeting it does not override the fire danger condition.
• C: Having water nearby is required for any burn, but it does not lift the ban when the danger is high.
• D (correct): The "unless" clause cancels the weekday permission whenever the sign shows high or extreme danger.

Answer: C

Correct answer: A problem is stated, and the causes behind it are explained. The first sentence states a problem, and every later sentence explains a reason for it. Because no one responds to the problem, this is cause-effect, not problem-solution; a passage becomes problem-solution only when it describes a fix.

• A: No repair plan or response appears; the engineers only explain what is causing the rot.
• B: The passage does not trace the pier's life over time; it explains why the posts are failing now.
• C (correct): The opening names the rotting posts, and the rest explains why: untreated wood, tidal wetting and drying, fungi and shipworms.
• D: Only one kind of wood is discussed, so there is no comparison.

Answer: A

Correct answer: It may need to be lowered within two years if the rust keeps spreading. The evidence span is the third sentence, which uses both a condition ("if the rust keeps spreading") and a possibility word ("might"). A correct answer must keep both, so the limit may need to be lowered within two years under that condition.

• A (correct): This keeps both the condition (if the rust keeps spreading) and the uncertainty (might) that the engineers expressed.
• B: The engineers said the county might have to lower it, and only if the rust keeps spreading; this turns a possibility into a certainty.
• C: The passage describes a possible future change; nothing says the limit has been lowered.
• D: The report says the bridge remains safe for cars and light trucks, so this contradicts the passage.

Answer: B

Correct answer: The rental kayaks stayed on the dock when the family arrived. The rule runs one way: an advisory means kayaks stay docked for the rest of the day. The advisory came at 11 a.m., so at 2 p.m. the kayaks were still on the dock. The rule does not say advisories are the only reason kayaks stay docked, so reversing it is not supported.

• A: The rule keeps kayaks docked for the rest of the day, and the passage never says the wind eased.
• B (correct): An advisory was issued at 11 a.m., and the rule keeps kayaks on the dock for the rest of that day, which includes 2 p.m.
• C: This reverses the rule; an advisory guarantees the kayaks stay docked, but they might stay docked for other reasons too.
• D: The rule mentions only rental kayaks, so this extends it beyond what the passage says.

Answer: A

Correct answer: hand out. Check the word class and the clues. Issue is a verb here, and the soldiers sign for each item and later return it, so the quartermaster is giving the gear out. Substitute: "the quartermaster will hand out cold-weather gear" keeps the meaning.

• A (correct): The quartermaster gives gear to each soldier, who then signs for it and must return it, so issue means to distribute or hand out.
• B: This is a familiar noun sense, but issue here is a verb with gear as its object; the replace-and-reread test makes the sentence nonsense.
• C: This is another noun sense of issue and has nothing to do with gear being given to soldiers.
• D: Soldiers sign for items and return them, which shows the gear is physically given out, not discussed.

Answer: A

Correct answer: Simulator practice helps new drivers but cannot replace supervised time on a real forklift. The passage praises the simulator (fewer damaged racks) and then turns with "though" to its limit, which is why supervised driving is still required. The choice that needs no outside facts and covers both halves is the main idea; the others reverse the point, add outside knowledge, or cover only one detail.

• A (correct): This covers both the benefit (fewer damaged racks) and the limit (the simulator cannot copy a shifting load, so supervised hours remain).
• B: This reverses the passage, which says every trainee must still complete twenty hours of supervised driving.
• C: This may be true in real life, but the passage never mentions pilots or truck drivers, so it relies on outside knowledge.
• D: This is an accurate result, but it ignores the trainers' warning and the supervised-driving requirement in the second half.

Answer: C

Correct answer: On some weekday mornings, a rider at a station near the train depot may find no bikes. Find each qualifier and make sure the answer keeps it: "usually," "in some cases" and "for now." Only the statement about some mornings at the depot stations preserves the passage's limits. The others turn "usually" into "always," "in some cases" into "every weekday" or a study into a promise.

• A: This drops "usually" and ignores the passage's point that some depot stations run empty.
• B: The office is only studying the idea, so "will soon expand" upgrades a possibility into a plan.
• C (correct): "In some cases" the depot stations run out by 8 a.m., so a rider there may sometimes find them empty.
• D: The passage says this happens only in some cases, so "every weekday" drops the qualifier.

Answer: A

Correct answer: −1. Replace x with 5:

• A (correct): Substituting 5 gives 9 − 10 = −1.
• B: This drops the negative sign; 9 − 10 is −1, not 1.
• C: This adds 2(5) to 9 instead of subtracting it.
• D: This subtracts first, (9 − 2) × 5, ignoring that multiplication comes before subtraction.

Answer: D

Correct answer: 31°. Complementary angles add to 90°, so angle

°.

• A: 121° is the supplement (180 - 59), not the complement.
• B: This is an arithmetic slip; 59 + 41 = 100, not 90.
• C: This subtracts from 360°, which is used for angles around a point.
• D (correct): 90 - 59 = 31°, so 59° and 31° are complementary.

Answer: A

Correct answer: (−4, 7). An ordered pair lists the x-value first and the y-value second, so

and y = 7 is written (−4, 7).

• A (correct): The x-value −4 comes first and the y-value 7 comes second.
• B: This puts y first; reversing the order names a different point.
• C: This moves the negative sign to the wrong coordinate.
• D: This swaps the numbers and keeps the negative in front, giving a different point.

Answer: D

Correct answer: −0.05. All four numbers are negative, so the greatest is the one closest to zero. Since 0.05 is the smallest absolute value, −0.05 is the greatest.

• A: It is to the left of −0.05 because it is farther from zero.
• B: Its larger absolute value makes it smaller, not larger, than −0.05.
• C: It is the farthest left of all, so it is the least of the four.
• D (correct): It is the closest to zero of the four negatives, so it lies farthest right on the number line.

Answer: A

Correct answer: 81 cubic feet. A cubic yard is a 3 ft by 3 ft by 3 ft block, which is 27 cubic feet. So 3 cubic yards is 3 times 27, or 81 cubic feet.

• A (correct): Each cubic yard is 27 cubic feet, and 3 times 27 is 81.
• B: This multiplies by 3, the linear factor; a cubic yard is 3 by 3 by 3 feet.
• C: This multiplies by 9, the square factor, which applies to area, not volume.
• D: This divides by 3 instead of multiplying; cubic feet are smaller, so the count must grow.

Answer: B

Correct answer: (4, 7). Use

one coordinate at a time:

Check: the average of (-6, 1) and (4, 7) is (-1, 4).

• A: This averages the start point and the midpoint, which finds a point a quarter of the way along the pipe.
• B (correct): Doubling the midpoint gives (-2, 8), and subtracting the start point gives (4, 7).
• C: This adds the start point to twice the midpoint instead of subtracting it.
• D: This gives the change from the start to the midpoint, not the far endpoint.

Answer: D

Correct answer: 20 - 5r. A minus sign before parentheses acts like multiplying by -1, so every sign inside flips: $12-5r+8$. Combine the constants:

The result is $20-5r$.

• A: This flips only the first sign and keeps -8, giving 12 - 5r - 8.
• B: This combines 12 and -5r as if they were like terms.
• C: This handles the 8 correctly but leaves +5r, so the r term was never flipped.
• D (correct): The minus sign flips both inside terms: 12 - 5r + 8 = 20 - 5r.

Answer: C

Correct answer: -63. Without parentheses the minus sign is not part of the base, so

With parentheses the base is negative, and an odd power keeps the sign:

• A: This reads -6^2 as (-6)^2 = 36, then adds -27.
• B: This gets -36 correctly but treats (-3)^3 as +27, as if an odd power of a negative were positive.
• C (correct): Only 6 is squared in -6^2, giving -36, and (-3)^3 = -27, so the sum is -63.
• D: This makes both powers positive, 36 + 27, ignoring both negative signs.

Answer: D

Correct answer: 24. Consecutive even integers differ by 2: n, n + 2, n + 4, n + 6. Their sum is

so 4n = 96 and n = 24. The integers are 24, 26, 28 and 30, which add to 108.

• A: This is the largest of the four integers (24, 26, 28, 30), not the smallest.
• B: This is the average, 108 ÷ 4, which falls between the middle two integers and is not even.
• C: This comes from spacing the integers by 1 instead of 2, giving 4n + 6 = 108.
• D (correct): With n, n + 2, n + 4 and n + 6, the sum is 4n + 12 = 108, so n = 24.

Answer: A

Correct answer: 72 m. The notched side becomes

m of edge. The other three sides are 20, 12 and 12 m. The perimeter is

A notch in the middle of a side adds its two 4 m depths to the original 64 m perimeter.

• A (correct): The original 64 m perimeter gains the two 4 m inner walls of the notch: 64 + 8 = 72 m.
• B: This uses the corner-notch shortcut, but a notch in the middle of a side adds two new edges, its depths.
• C: This adds only one 4 m depth; the notch has an inner wall on each side.
• D: This removes the 6 m opening but forgets that the notch's bottom edge and two depths replace it.

Answer: C

Correct answer: 81π square inches. Find the radius from the circumference: r = 18π / 2π = 9 inches. Then A = π(9)^2 = 81π square inches.

• A: This squares 18, which is the diameter, so the area comes out four times too large.
• B: This reuses the circumference value, a length, as if it were the area.
• C (correct): The circumference gives r = 9, and π times 9 squared is 81π.
• D: This uses 2πr squared, mixing the circumference formula into the area formula.

Answer: C

Correct answer: 72 square feet. The strip runs along both ends of each dimension, so the carpet is

by

covering 108 square feet. The room is 15 times 12 = 180 square feet, so the bare floor is

• A: This subtracts the 1.5-foot strip from each dimension only once (13.5 by 10.5), forgetting the strip on the opposite wall.
• B: This is the area of the carpet itself, not the bare floor around it.
• C (correct): Subtract 2 times 1.5 = 3 feet from each dimension, then take 180 - 108 = 72 square feet.
• D: This multiplies the room's perimeter, 54 feet, by 1.5 feet, which counts the four corner squares twice.

Answer: B

Correct answer: 12 + 12√3. The long leg (opposite 60°) is the short leg times $\sqrt{3}$, so the short leg is

The hypotenuse is twice the short leg, $8\sqrt{3}$.

Perimeter:

units.

• A: This treats 12 as the short leg (opposite 30°), but the given leg is opposite 60°.
• B (correct): The sides are 12, $4\sqrt{3}$ and $8\sqrt{3}$, which add to $12+12\sqrt{3}$.
• C: This treats 12 as the hypotenuse; the hypotenuse is opposite the 90° angle.
• D: This includes the hypotenuse but leaves out the short leg.

Answer: B

Correct answer: 9:12 a.m. Repeating schedules call for the LCM. 18 = 2 × $3^2$ and 24 = $2^3$ × 3, so the LCM is $2^3$ × $3^2$ = 72 minutes.

72 minutes is 1 hour 12 minutes, so the buses next leave together at 9:12 a.m.

• A: This adds 18 and 24 to get 42 minutes, but the buses do not line up after 42 minutes.
• B (correct): The LCM of 18 and 24 is 72 minutes, and 72 minutes after 8:00 is 9:12.
• C: This uses the product 18 × 24 = 432 minutes, a common multiple but not the least one.
• D: This uses the GCF, 6 minutes, which is the tool for equal groups, not repeating schedules.

Answer: A

Correct answer:

or x > 3. A greater-than absolute value means the expression is far from 0, so split it with or:

The first gives 3x > 9, so x > 3. The second gives

Check

|−13| = 13 > 11.

• A (correct): Splitting gives 3x + 2 > 11 or 3x + 2 < −11, so x > 3 or x < −13/3.
• B: This is the solution of |3x + 2| < 11; a greater-than absolute value splits into two outer pieces joined by or.
• C: This handles the negative piece wrongly: 3x + 2 < −11 gives 3x < −13, not 3x < −9.
• D: This assumes the answer is symmetric about 0, but the +2 shifts the center to −2/3.