AFQT Core Practice 3: Percentages, Ratios and Polygons

Answer: C

Correct answer: 27. Multiplication and division are done in the order they appear, from left to right.

First

• A: This comes from multiplying 4 × 3 first and then dividing 36 by 12, which breaks the left-to-right rule.
• B: This divides 36 by 3 and ignores the 4, mixing up which numbers go with each operation.
• C (correct): Division and multiplication share a level, so work left to right: 36 ÷ 4 = 9, then 9 × 3 = 27.
• D: This adds the three numbers instead of dividing and multiplying.

Answer: C

Correct answer: 12:21. Equivalent ratios come from multiplying or dividing both terms by the same number.

so 12:21 matches 4:7.

• A: This reverses the order, which changes the comparison.
• B: This adds 4 to each term; equivalent ratios come from multiplying or dividing, not adding.
• C (correct): Multiplying both terms of 4:7 by 3 gives 12:21.
• D: This multiplies the first term by 3 but the second by 4, so it simplifies to 3:7.

Answer: B

Correct answer: 60 pallets. Whole equals part divided by percent:

pallets. Check: 30 percent of 60 is 18.

• A: This multiplies 18 by 0.30, finding 30 percent of 18 instead of the whole that 18 is 30 percent of.
• B (correct): 18 is 30 percent of the goal, and 18 divided by 0.30 is 60.
• C: This adds 30 to 18, treating the percent as a count of pallets.
• D: This divides 18 by 3 instead of by 0.30; the goal must be larger than the part already done.

Answer: A

Correct answer: 161 pounds. Turn the average into a total by multiplying by the count:

• A (correct): Average times count gives the total: 7 times 23 is 161 pounds.
• B: This adds the count and the average instead of multiplying them.
• C: This multiplies 23 by 8, using one crate too many.
• D: This comes from a multiplication slip: 7 times 20 is 140, but the 3 must also be multiplied by 7.

Answer: B

Correct answer: $60.00. After 15% off, the customer pays 85% of the original: 0.85 × original = 51. Divide:

Check:

• A: This adds 15% of the sale price; the discount was 15% of the original price, a different base.
• B (correct): The sale price is 85% of the original, so the original is 51 ÷ 0.85 = $60.
• C: This takes another 15% off the sale price instead of working back to the original.
• D: This adds $15 to the sale price, treating the 15% as $15.

Answer: C

Correct answer: 8 sections. Edging goes around the border, so find perimeter:

Sections:

Seven sections cover only 56 feet, so 8 sections are needed.

• A: This rounds 7.25 down, which leaves 2 feet of the border without edging.
• B: This uses the area, 198 square feet, but edging runs along the border, which is a perimeter.
• C (correct): The perimeter is 2(18 + 11) = 58 feet; 58 / 8 = 7.25, so 8 whole sections are needed.
• D: This uses only one length and one width, 29 feet, which is half the perimeter.

Answer: B

Correct answer: 2 hours. Work done by the first inspector:

so $\frac{2}{5}$ remains.

The second inspector's rate is $\frac{1}{5}$ per hour, so she needs

• A: This finishes the remaining 2/5 at the first inspector's slower rate of 1/10 per hour.
• B (correct): The first inspector finishes 6/10 = 3/5, leaving 2/5; at 1/5 per hour the second inspector needs 2 hours.
• C: This divides the 3/5 already finished by the second inspector's rate instead of the 2/5 that remains.
• D: This has both inspectors working together on the rest, but the first one was reassigned.

Answer: B

Correct answer: 1:15 p.m. Leg 1:

Leg 2:

= 1 hour 30 minutes.

Total: 2 h + 1 h 30 min + 25 min = 3 hours 55 minutes. From 9:20 a.m., that is 1:15 p.m.

• A: This counts only the driving time and leaves out the 25-minute lunch stop.
• B (correct): Driving takes 2 + 1.5 = 3.5 hours, plus 25 minutes, for 3 hours 55 minutes after 9:20 a.m.
• C: This reads 1.5 hours as 1 hour 50 minutes instead of 1 hour 30 minutes.
• D: This converts the 25-minute stop to 0.25 hour, which is only 15 minutes.

Answer: C

Correct answer: 54 gallons. Convert days to hours:

The rate is 3 gallons ÷ 4 hours = 0.75 gallon per hour.

Fuel used:

• A: This treats 3 days as 3 hours instead of converting days to hours.
• B: This sets up the rate upside down, as hours per gallon, computing 72 × 4 ÷ 3.
• C (correct): 3 days is 72 hours, and at 0.75 gallon per hour it burns 0.75 × 72 = 54 gallons.
• D: This is the fuel for only one day, 0.75 × 24.

Answer: D

Correct answer: 16%. Find the decrease: 1.25 minus 1.05 is 0.20 dollar.

Divide by the original price:

a 16 percent decrease.

• A: This divides the drop of 0.20 by the new price 1.05 instead of the original price 1.25.
• B: This treats the 20-cent drop as 20 percent without dividing by the original price.
• C: This is the new price as a percent of the old price, not the percent decrease.
• D (correct): The drop is 0.20, and 0.20 divided by the original 1.25 is 0.16, or 16 percent.

Answer: D

Correct answer: 1 hour 30 minutes. Outflow minus inflow gives the net rate:

per minute leaving.

which is 1 hour 30 minutes.

• A: This divides by the drain rate of 30 alone and ignores the water the hose keeps adding.
• B: This adds the hose rate to the drain rate, but the hose works against the drain.
• C: This divides by the hose rate of 6 gallons per minute instead of the net drain rate.
• D (correct): The net drain rate is 30 - 6 = 24 gallons per minute, and 2,160 divided by 24 is 90 minutes.

Answer: B

Correct answer: 4 hours 40 minutes. In 2 hours the painter does

of the job, leaving $\frac{2}{3}$.

Together:

job per hour, so the rest takes

or 2 hours 40 minutes.

Total: 2 hours + 2 hours 40 minutes = 4 hours 40 minutes.

• A: This is only the time the two work together; the painter's first 2 hours must be added.
• B (correct): After 2 hours one-third is done; the other two-thirds at a combined 1/4 job per hour takes 2 hours 40 minutes more.
• C: This adds 2 hours to the full 4-hour team time, ignoring the third of the job already done.
• D: This is the time if both worked together from the start, ignoring the helper's late arrival.

Answer: B

Correct answer: 45 vehicles. Non-trucks are $\frac{3}{5}$ of the total, and vans are $\frac{2}{3}$ of that:

Total:

vehicles (18 trucks, 9 jeeps, 18 vans).

• A: This treats the 18 vans as all of the non-truck 3/5, forgetting the jeeps.
• B (correct): Vans are 2/3 of the 3/5 that are not trucks, which is 2/5 of all vehicles, and 18 divided by 2/5 is 45.
• C: This counts only the jeeps and vans (9 + 18) and leaves out the trucks.
• D: This assumes vans are 1/3 of all vehicles, but they make up 2/5 of the total.

Answer: A

Correct answer: 3 hours 12 minutes. Time equals distance divided by speed for each leg:

Total: 3.2 hours.

Convert the decimal part:

so the trip takes 3 hours 12 minutes.

• A (correct): The legs take 1.5 hours and 1.7 hours, for 3.2 hours, and 0.2 hour is 12 minutes.
• B: This reads 3.2 hours as 3 hours 20 minutes; 0.2 of an hour is 0.2 times 60 = 12 minutes.
• C: This divides the total distance of 134.1 miles by 48 mph only, as if the whole trip were at the faster speed.
• D: This divides the total distance by 35 mph only, as if the whole trip were at the slower speed.

Answer: B

Correct answer: 6 miles. Let d be the one-way distance. The time out is d/6 and the time back is d/4, and together they make 2.5 hours:

With a common denominator this is

so d = 6 miles. Check: 1 hour out plus 1.5 hours back is 2.5 hours.

• A: This is the round-trip distance, not the distance from the beach to the island.
• B (correct): Six miles takes 1 hour out and 1.5 hours back, exactly 2.5 hours.
• C: This uses the simple mean speed of 5 mph for the whole trip, which overstates the true average.
• D: This assumes the faster speed of 6 mph for the whole trip and then halves the result.

Answer: B

Correct answer: confirm. Verify combines the root ver (true) with -ify (make or cause to be). To verify a fact is to show it is true, so the closest verb is confirm.

• A: This adjective reflects the root ver (true) but is not a verb.
• B (correct): The ending -ify means to make, so verify means to show to be true, which is to confirm.
• C: To doubt is to question whether something is true, the opposite direction.
• D: Revise means to change something, not to check that it is accurate.

Answer: B

Correct answer: good-humored. The phrase in other words introduces a restatement: always joking and laughing. That describes a good-humored, cheerful person.

• A: Strictness is not supported; the clue describes joking and laughing.
• B (correct): The restatement after in other words describes someone who jokes and laughs, which is good-humored.
• C: Joking involves talking, but jovial is about a cheerful mood, not how much someone likes to talk.
• D: Nothing in the sentence refers to age.

Answer: D

Correct answer: inform. After "will," BRIEF is a verb, and "the drivers on the route" shows information being passed. Brief here means inform.

• A: Short is the adjective meaning of brief, but "will brief the drivers" uses the word as a verb.
• B: Shortening the drivers makes no sense; the lieutenant is giving them route information.
• C: Dismissing the drivers would send them away, while "on the route" shows they are being told something.
• D (correct): To brief someone is to give them key facts, and "inform the drivers on the route" fits the mission setting.

Answer: C

Correct answer: easily cracked. Brittle means hard but likely to crack or shatter under a sharp blow. Flexible and malleable materials bend instead, so easily cracked is the match.

• A: Bendable describes a flexible material, which is close to the opposite of brittle.
• B: Rust is a kind of corrosion; it can make metal weak, but rusty does not mean brittle, and the bucket is plastic.
• C (correct): Brittle describes a hard material, such as thin glass or old plastic, that snaps or shatters instead of bending.
• D: Weight is a different property; a brittle object can be light or heavy.

Answer: C

Correct answer: make easier. Fac means make or do, and facilitate means to make something easier. A detailed map makes an unfamiliar road trip easier to complete.

• A: A map would speed a trip up, not hold it back.
• B: Funding a trip is a different idea; the root fac points to making the trip easier.
• C (correct): Fac means make or do, and to facilitate is to make a task easier, which is what a good map does for a trip.
• D: Planning uses the map, but facilitate describes helping the trip go smoothly.

Answer: B

Correct answer: hold back. Hinder means to create difficulties that slow or delay something. Hold back matches that degree; stop completely is too strong, assist is the opposite, and follow is unrelated.

• A: Stop completely overstates the word; hindering makes efforts harder or slower without necessarily ending them.
• B (correct): Hinder means to get in the way of something and slow it down, which hold back expresses.
• C: This is the opposite of hindering.
• D: Following comes after something; it does not mean getting in its way.

Answer: B

Correct answer: kept demanding firmly. Request verbs rise in force: suggest, urge, demand, insist. The clue even after the customer said no twice shows repeated pressure, which is what insist means.

• A: Suggest offers an idea gently and leaves the choice open, too weak for pushing on after two refusals.
• B (correct): Insist means to keep pressing a demand and refuse to accept no, as the salesman does after two refusals.
• C: Hinted means indirectly suggested; the salesman is pushing directly and repeatedly.
• D: Agreeing with her decision would mean accepting her no, the opposite of overriding it.

Answer: A

Correct answer: modification. Adaptation names one change made to fit a new need, while adaptability names the general ability to adjust. The crew altered the hitch for a bigger load, so the answer is modification.

• A (correct): An adaptation is one specific change made to suit new conditions, here a change to the hitch.
• B: Flexibility is the meaning of adaptability, the capacity to adjust, not one specific change.
• C: Acceptance means agreeing to take something as it is, while the crew actually changed the hitch.
• D: Removal means taking the hitch off, but the hitch was changed so it could tow.

Answer: B

Correct answer: living in water. The root aqu means water, the same root found in aquarium and aquifer. Aquatic insects are ones that live in water, which fits a sample taken from below a dam.

• A: Underground life would call for a different root; aqu points to water, not soil.
• B (correct): Aqu means water, as in aquarium, and insects collected below a dam live in the stream.
• C: This is nocturnal, which comes from noct, night, a root not found here.
• D: Many insects fly, but the root aqu tells where these insects live, which is water.

Answer: C

Correct answer: large number. The pattern "a host of" plus a plural noun works like "a lot of." HOST here means a large number.

• A: A host can be a person who welcomes guests, but software does not cause a party giver.
• B: A small set is close to the opposite; "a host of" stresses that there were many.
• C (correct): The phrase "a host of" means a great many, so "a large number of problems" fits.
• D: A host can be a networked computer, but here the word is followed by "of problems," which counts them.

Answer: B

Correct answer: weapons. "Including" introduces examples. What muskets, cannons and torpedoes share is that they are weapons, so ARMAMENT means weapons, not any single item on the list.

• A: Cannons are just one example from the list; the word covers all the examples.
• B (correct): Muskets, cannons and torpedoes are all weapons, so the word names the whole group.
• C: Uniforms are military items, but none of the examples listed is clothing.
• D: Torpedoes travel, but muskets and cannons are not vehicles, so this does not fit the group.

Answer: C

Correct answer: dependent. Direction matters. A reliable or dependable thing is relied on by others, while a reliant thing relies on something else. The station needs the panels, so reliant means dependent.

• A: Dependable means reliable, something others can count on; the station is the one doing the relying, and it shuts down in clouds.
• B: Self-sufficient means needing no outside help, the opposite of relying on sunlight.
• C (correct): Reliant means relying on something, and the station needs solar panels to keep working.
• D: Reluctant looks a little similar but means unwilling.

Answer: B

Correct answer: extravagant. The example clues, a band, imported flowers and a five-course dinner, all show large, generous spending. Wasteful and extravagant both mean spending a lot, but wasteful adds a negative tone the neutral sentence does not support, so extravagant is the better choice.

• A: Wasteful shares the idea of spending a lot, but it adds a critical judgment the sentence does not make.
• B (correct): Extravagant matches the meaning: rich, plentiful and costly, as the list of details shows.
• C: Three hundred guests is a lot of people, but the word describes the richness of the event, not its crowd.
• D: A large wedding may be formal, but formality is about manners and dress, not abundance.

Answer: D

Correct answer: Forerunner. Pre- means before, and the base cursor comes from a word for runner. The telegraph came decades before the telephone and led the way to it, so it was a forerunner.

• A: Replacement suggests something that comes after and takes over, the opposite time order.
• B: Successor means something that follows, which reverses the before sense of pre-.
• C: Rival implies the two competed at the same time, but the telegraph came decades earlier.
• D (correct): Pre- means before, and cursor comes from a word for runner, so a precursor is a forerunner.

Answer: C

Correct answer: disrespectful. Insolent means boldly rude, as when a recruit talks back to an instructor with open contempt. Eliminate the look-alikes indolent (lazy) and insolvent (bankrupt), then reject outspoken because frankness alone is not rude; disrespectful is the best match.

• A: Lazy is the meaning of indolent, a different word that shares the ending -olent.
• B: Bankrupt matches insolvent, a shape-alike word that differs by one letter.
• C (correct): Insolent describes speech or behavior that is boldly rude and lacking in respect, so disrespectful is the true synonym.
• D: A frank, outspoken person speaks plainly, but that can be polite; it misses the rudeness at the core of insolent.

Answer: C

Correct answer: Packing a go-bag ahead of time helps families evacuate quickly before a hurricane. First name the topic (go-bags for hurricanes), then state what the passage says about it: packing one ahead of time lets a family evacuate quickly. A choice that only names the topic is not a main idea, and a single supply item is only a detail.

• A: This names the topic but says nothing about it; it answers "about what?" but not "so what?"
• B: These are items from the list of supplies, details rather than the main point.
• C (correct): This is a full statement with a subject and a claim, and every sentence supports it.
• D: The passage advises preparing to evacuate, not moving permanently, so this adds an idea it never states.

Answer: A

Correct answer: Only the morning ferry stops at the fishing pier. The contrast signal whereas marks the difference: the morning ferry stops at the fishing pier and the afternoon ferry does not. Fare, car service and arrival time are all shared.

• A (correct): The word whereas sets up the contrast: the morning ferry stops at the pier, while the afternoon ferry goes directly.
• B: Both ferries charge the same $18 round-trip fare, so fare is a similarity.
• C: The passage says both boats carry cars, so this is a shared feature.
• D: This swaps the sides; it is the morning ferry that stops at the pier.

Answer: A

Correct answer: Pilot Gomez. Connect two stated facts. One sentence says Gomez flew Aircraft 422, and another says Aircraft 422 had the rescue hoist. Linking them shows that Gomez flew the hoist-equipped helicopter, without adding anything new.

• A (correct): Gomez flew Aircraft 422, and the passage states that Aircraft 422 was fitted with the rescue hoist.
• B: Hayes flew Aircraft 418; the hoist is linked to Aircraft 422, not 418.
• C: The passage mentions a hoist on Aircraft 422 only, so it cannot be applied to both helicopters.
• D: Ames inspected both aircraft but is not described as a pilot or as flying either one.

Answer: D

Correct answer: explain how a dehumidifier removes moisture from room air. Finish the sentence "The author wrote this to (blank one) about (blank two)." The passage moves step by step (a fan first draws air, the vapor condenses, the droplets drip, the air finally returns) and never judges or recommends, so the action is to explain, and the topic is how a dehumidifier pulls water from the air.

• A: Nothing in the passage recommends buying anything; there is no should, must or judgment about value.
• B: The refrigerator and iced-tea comparisons only help explain the process; the passage never sets two products side by side to weigh their differences.
• C: No particular people or events appear, so the passage does not tell a story about anyone.
• D (correct): The passage walks through the steps in order (first, as, then, finally) and applies to any dehumidifier, so its job is to explain a process.

Answer: B

Correct answer: A single event is described, followed by several of its effects. The first sentence names one event, the late frost. Every sentence after it reports something that followed from that event: a smaller crop, fewer hired workers, higher cider prices and early stand closings. One cause leading to several effects is a cause-effect structure.

• A: The passage never says anyone tried to fix the damage; it only reports what the frost led to.
• B (correct): The frost is the one cause, and the small crop, fewer jobs, higher cider prices and early closings are the results that follow from it.
• C: This reverses the pattern: there is one cause (the frost) and many effects, not many causes and one effect.
• D: Past years are mentioned only in passing; the passage does not compare two seasons feature by feature.

Answer: B

Correct answer: It can clean water without anyone working a handle. Sort each feature to its side: pump filter = compact, works anywhere, needs hand pumping; gravity filter = drains on its own, bulkier, needs a place to hang. The only gravity advantage among the choices is that it filters water without anyone pumping.

• A: The passage says the pump filter is compact and the gravity filter is bulkier, so this swaps the features.
• B (correct): The passage says the gravity filter lets water drain through on its own, while the pump requires someone to work the handle.
• C: The passage says both types remove bacteria and protozoa, so this contradicts the text.
• D: This flexibility is described as a feature of the pump filter, not the gravity filter.

Answer: B

Correct answer: The wire screen goes on after the nest is marked with a stake. The passage gives order (mark, record and screen, hatchlings leave, then count shells) but never states how long any gap lasts. Choices that name an interval, such as several weeks or two months, go beyond the text. The supported choice states only order.

• A: The passage says the screen goes on after marking but gives no interval, so several weeks is invented.
• B (correct): The word after places the screening later than the marking, which is all the passage says about their timing.
• C: The passage says only that hatchlings eventually emerge; any specific time span comes from outside knowledge.
• D: The word then shows the nest is opened after the hatchlings leave, not before.

Answer: A

Correct answer: A buyer who saves money through a private sale should have the car inspected first to limit the risk. Watch the signal words. The first two sentences grant an advantage, "however" turns to the risk of no warranty, and "for that reason" leads to the writer's advice: have a mechanic inspect the car before paying. The main point is the one that keeps both the savings and the precaution.

• A (correct): The point after the turn word however, and the conclusion signaled by for that reason, is that the savings come with risk, so an inspection is advised.
• B: This is a supporting detail from before the turn, true but not the writer's main point.
• C: The writer accepts private sales and only advises an inspection; avoiding them entirely overstates the advice.
• D: The transmission failure is offered as a possible risk, not a claim that it usually happens.

Answer: C

Correct answer: far from proving the claim. Hardly acts like not, so hardly conclusive means the results did not settle the question. The surrounding evidence, a tiny group, a company-run trial, unequal ages and a call for a larger outside study, confirms the results are far from proving the claim. They do not prove the opposite either; they just leave it open.

• A: This uses the sense of hard as difficult; in this phrase hardly means barely or not, so it removes the idea of proof.
• B: This weakens the criticism too much; the researcher wants a whole new study, which shows the doubts are serious.
• C (correct): Hardly works like a negative here, and the listed flaws, a small group, a company-run trial and an age difference, show the results settle very little.
• D: This swings to the opposite claim; weak evidence for the remedy is not evidence against it.

Answer: D

Correct answer: Darnell will not be kept from starting the course just because he has no tent. Because the notice says the list is complete, an item missing from it is not required, and Darnell has every listed item. However, the notice's silence about shelter tells you nothing about how trainees will sleep, so a choice claiming they will have no shelter treats absence of mention as evidence.

• A: The rule bars only trainees missing a listed item, and a tent is not listed.
• B: The list names five items and calls itself complete; the compass is not among them.
• C: The notice is silent about shelter; it may be provided, so silence does not prove there is none.
• D (correct): The notice calls its list complete, and a tent is not on it, so lacking one does not break the stated rule.

Answer: A

Correct answer: 4.5 hours. Let h be the hours worked:

Subtract 65 from both sides: 48h = 216. Divide by 48: h = 4.5 hours. Check:

• A (correct): The equation 65 + 48h = 281 gives 48h = 216, so h = 4.5.
• B: This divides the whole bill, $281, by $48 without first removing the $65 fee.
• C: This adds the $65 fee to the bill instead of subtracting it, then divides $346 by $48.
• D: This removes the fee correctly but divides $216 by the fee, $65, instead of the hourly rate.

Answer: A

Correct answer: 6. A cube root asks which number, used as a factor three times, gives 216. Try small numbers:

• A (correct): 6 x 6 x 6 = 216, so 6 is the cube root.
• B: This divides 216 by 3 instead of finding a number used as a factor three times.
• C: This is 6 squared, which is the result of using 6 as a factor only twice.
• D: 8 cubed is 512, far more than 216.

Answer: C

Correct answer: A rhombus. A parallelogram with four equal sides is a rhombus. Because its angles are not right angles, it cannot be a square, and with unequal angles it is not a rectangle either.

• A: A rectangle must have four right angles, and its neighboring sides need not be equal.
• B: A kite's equal sides come in two neighboring pairs, and a kite is generally not a parallelogram.
• C (correct): A rhombus is a parallelogram with all four sides equal; its angles need not be 90 degrees.
• D: Even books that let a trapezoid have two parallel pairs would not call it the most specific name; equal sides make this figure a rhombus.

Answer: D

Correct answer: It has infinitely many solutions. A true statement with no variables left means the two equations are really the same line. Every point on that line satisfies both, so the system has infinitely many solutions.

• A: No solution is signaled by a false statement such as 0 = 4, not by the true statement 0 = 0.
• B: The zeros come from the variables cancelling, not from the variables equaling zero.
• C: Exactly one solution appears when elimination leaves a single variable with one value, such as x = 4.
• D (correct): A true statement such as 0 = 0 means the equations describe the same line, so every point on it works.

Answer: B

Correct answer: 20π feet. Work backward from the area: r squared = 100π / π = 100, so r = 10 feet. The binding follows the edge, so find the circumference: C = 2π(10) = 20π feet.

• A: This is π times r; the circumference formula is 2πr, so the radius must be doubled.
• B (correct): The area gives r = 10, and the circumference is 2π times 10 = 20π feet.
• C: This halves the area; dividing by 2 does not turn an area into a circumference.
• D: This uses 20, the diameter, in place of the radius in 2πr.

Answer: D

Correct answer: x = 4. A fraction is undefined when its denominator is zero. Set

A zero in the numerator only makes the value 0.

• A: This makes the top zero, which gives a value of 0, not an undefined expression.
• B: This sets x equal to the constant 8 without dividing by the coefficient 2.
• C: This makes a sign slip; 2(-4) - 8 is -16, not 0.
• D (correct): The bottom 2x - 8 is zero when x = 4, and division by zero is undefined.

Answer: D

Correct answer:

Slope first:

Then substitute (2, 1) into

The line is

• A: This has the right slope but uses the y-value of (2, 1) as the intercept, though that point is not on the y-axis.
• B: This divides the change in x by the change in y, giving the reciprocal of the slope.
• C: This gives the slope the wrong sign; the y-values rise as x increases, so the slope is positive.
• D (correct): The slope is 8/4 = 2, and 1 = 2(2) + b gives b = -3; (6, 9) checks since 12 - 3 = 9.

Answer: D

Correct answer: 27. Each of the 9 vertices joins to

non-neighboring vertices, and each diagonal is counted from both ends.

• A: This forgets to divide by 2, counting each diagonal once from each end.
• B: This uses n(n - 1)/2, which also counts the 9 sides as if they were diagonals.
• C: This is the number of diagonals from a single vertex, not the total for the polygon.
• D (correct): Using n(n - 3)/2 with n = 9 gives 54 / 2 = 27.

Answer: A

Correct answer: 3. The known digits add to

The next multiple of 9 is 18, so

(The one after that, 27, would need k = 12, which is not a single digit.)

• A (correct): The digit sum becomes 3 + 7 + 3 + 5 = 18, a multiple of 9, and 3,735 ÷ 9 = 415.
• B: The digit sum would be 21, which is divisible by 3 but not by 9.
• C: The digit sum would be 15, which is divisible by 3 but not by 9.
• D: The digit sum would be 19, which is not divisible by 9.

Answer: C

Correct answer: 120 cubic inches. A pyramid holds one third of the matching prism. The base area is 6 times 6, or 36.

• A: This is the volume of a box with the same base and height; a pyramid holds only one third of it.
• B: This uses one half, as for a triangle's area, instead of the pyramid's one third.
• C (correct): Base area 36 times height 10 is 360, and one third of that is 120.
• D: This uses the side length 6 instead of the base area 36 before taking one third.

Answer: B

Correct answer: 73°. Angles around a point total 360°:

5x = 170 and x = 34. The angle asked for is

°.

• A: 34 is x; substitute it into 2x + 5 to get the angle.
• B (correct): 5x = 170 gives x = 34, and 2(34) + 5 = 73°.
• C: 102° is the (3x)° angle, not the one labeled (2x + 5)°.
• D: 68 is 2x; the + 5 was left off when finding the angle.

Answer: A

Correct answer: 17. Work inside out. First

Then feed 6 into g:

• A (correct): f(−2) = 4 + 2 = 6, and g(6) = 18 − 1 = 17.
• B: This applies g first and f second: g(−2) = −7 and f(−7) = 51, which is f(g(−2)).
• C: This squares −2 as −4, so f(−2) becomes −2 and g(−2) = −7; a negative squared is positive.
• D: This is only the inside value f(−2); it still has to be put into g.

Answer: A

Correct answer: 11 tickets. Total spending cannot exceed $250:

Combine:

so 18t ≤ 198 and t ≤ 11. Check:

which is allowed, while 12 tickets would cost $268.

• A (correct): 32 + 20 + 18t ≤ 250 gives 18t ≤ 198, so t ≤ 11; exactly 11 tickets uses the full $250.
• B: This treats the limit as strict; spending exactly $250 is allowed, so 11 tickets works.
• C: This forgets the $20 food money, giving 18t ≤ 218 and t ≤ 12.1.
• D: This ignores both the parking fee and the food money, dividing $250 by $18.

Answer: B

Correct answer: 47 m. The third side must be less than

and greater than

The largest whole number below 24 is 23, so the greatest perimeter is

• A: This lets the third side equal 24 m, but a side equal to the sum of the other two lies flat; the inequality is strict.
• B (correct): The third side can be at most 23 m, giving 9 + 15 + 23 = 47 m.
• C: 31 m is the smallest possible perimeter (third side 7 m), not the greatest.
• D: 23 m is the longest possible third side, not the perimeter.

Answer: B

Correct answer: −3. Parentheses:

Power:

Multiply and divide left to right:

Finally

• A: This squares −5 as −25, which makes the quotient −5 instead of 5.
• B (correct): (4 − 9)² = 25, −3 × 25 = −75, −75 ÷ (−15) = 5, and 5 + (−8) = −3.
• C: This gets 5 but takes (−2)³ as +8; an odd power of a negative stays negative.
• D: This gets −5 from the division and +8 from the cube, two sign errors.