AFQT Core Practice 1: Word Problems, Roots and Context

Answer: C

Correct answer: 18 gallons. Fuel used:

Fuel left:

You can also find it directly:

• A: This is the amount used, not the amount left.
• B: This is only 1/5 of the tank; 2/5 of the tank is left.
• C (correct): The generator used 3/5 × 45 = 27 gallons, so 45 − 27 = 18 gallons remain.
• D: This subtracts 20 gallons instead of finding 3/5 of 45.

Answer: A

Correct answer: 51 miles. "A fraction of" means multiply. Divide by the denominator, then multiply by the numerator:

• A (correct): 85 divided by 5 is 17, and 17 times 3 is 51 miles.
• B: This is only 1/5 of the trip; it still needs to be multiplied by the numerator 3.
• C: This is 2/5 of the trip, the part still left to drive.
• D: This is 4/5 of the trip, from multiplying by 4 instead of 3.

Answer: C

Correct answer: 36. Work inside the parentheses first:

Then multiply:

• A: This ignores the parentheses and multiplies 3 × 8 before adding 4, counting the empty canteens only once.
• B: This adds all three numbers instead of multiplying the 3 by the sum.
• C (correct): Parentheses first: 8 + 4 = 12, then 3 × 12 = 36.
• D: This multiplies all three numbers, 3 × 8 × 4, instead of adding 8 and 4.

Answer: A

Correct answer: 375 miles. First find the rate:

Then distance =

• A (correct): The train's rate is 75 mph, and 75 × 5 = 375 miles.
• B: This sets up the proportion upside down, multiplying 225 by 3/5 instead of 5/3.
• C: This doubles 225 miles, as if 5 hours were twice as long as 3 hours.
• D: This adds one hour's distance of 75 miles to 225 instead of adding two hours' worth.

Answer: D

Correct answer: $1.87. Find each part:

The total is

Change:

• A: This counts only one box of screws: 25.00 - 7.35 - 7.89 = 9.76.
• B: This is the total cost of the items, not the change from $25.
• C: This makes a borrowing error when subtracting 23.13 from 25.00.
• D (correct): The purchase is 7.35 + 15.78 = 23.13 dollars, and 25.00 - 23.13 = 1.87.

Answer: D

Correct answer: 24 minutes. Time = distance ÷ speed =

Convert to minutes:

• A: This multiplies the distance by the speed instead of dividing.
• B: This reads 0.4 hour as 40 minutes instead of multiplying by 60.
• C: This divides the speed by the distance, turning the formula upside down.
• D (correct): 3 ÷ 7.5 = 0.4 hour, and 0.4 × 60 = 24 minutes.

Answer: D

Correct answer: 84.4. Multiply each score by its weight and add:

The weights total 100 percent, so no further division is needed.

• A: 87 is the simple average of the three scores, which ignores that quality counts for half the review.
• B: This puts the 50 percent weight on attendance and the 20 percent weight on quality, swapping them.
• C: This adds the three scores without applying the weights at all.
• D (correct): Weighting gives 19 + 39 + 26.4, which is 84.4.

Answer: A

Correct answer: 1:8. Convert to the same units first: 6 minutes =

The ratio is 45:360. The greatest common factor is 45, so it simplifies to 1:8.

• A (correct): 6 minutes is 360 seconds, and 45:360 simplifies to 1:8.
• B: This compares 45 with 6 without converting minutes to seconds.
• C: This reverses the order; the question asks for one hole to the whole job.
• D: This treats 6 minutes as 600 seconds, but a minute has 60 seconds, not 100.

Answer: D

Correct answer: 80 parcels. Rate times time gives each total: A ships

and B ships

"How many more" asks for a difference:

parcels.

• A: This compares only the hourly rates, ignoring that the warehouses work different numbers of hours.
• B: This adds the two totals, but "how many more" asks for a difference.
• C: This multiplies the rate difference of 45 by 8 hours, as if both worked the same time.
• D (correct): A ships 140 x 6 = 840 and B ships 95 x 8 = 760, so A ships 840 - 760 = 80 more.

Answer: A

Correct answer: 14.4 miles per hour. Times:

Average speed = total distance over total time:

per hour.

• A (correct): The trip is 72 miles in 3 + 2 = 5 hours, and 72 divided by 5 is 14.4.
• B: 15 is the simple average of the two speeds, but the boat spends more time at the slower speed.
• C: This divides only the one-way distance of 36 miles by the total time.
• D: This divides the total distance by the average of the two times instead of the total time.

Answer: B

Correct answer: $51.12. Tax raises the price, so multiply by 1 plus the rate:

The tax alone is

and 48 plus 3.12 is also $51.12.

• A: This is only the tax; the question asks for the total cost including the price of the boots.
• B (correct): Multiplying 48 by 1.065 gives 51.12, which includes both the price and the tax.
• C: This adds 6.5 dollars instead of 6.5 percent of the price.
• D: This uses 0.65 instead of 0.065 for 6.5 percent, a decimal slip of one place.

Answer: A

Correct answer: 7 hours 30 minutes. Inflow adds and outflow subtracts:

At two-fifteenths of a tank per hour, the fill takes

or 7 hours 30 minutes.

• A (correct): The net rate is 1/3 - 1/5 = 2/15 tank per hour, so filling takes 15/2 = 7.5 hours.
• B: This adds the two rates, treating the drain as if it also filled the tank.
• C: This subtracts the times, 5 - 3; for opposing pipes it is the rates that subtract.
• D: This averages the two times, which does not account for the drain working against the inlet.

Answer: D

Correct answer: 10.5 hours. Together the rate is

per hour, so in 3 hours they finish $\frac{1}{2}$ of the job.

The slower roofer does $\frac{1}{15}$ per hour, so the remaining half takes

Total:

• A: This is the time if both roofers stayed for the entire job; it ignores that the faster one left.
• B: This is only the time the slower roofer works alone after the other leaves; the first 3 hours must be added.
• C: This assumes the faster roofer stayed to finish the second half, but it was the slower roofer who finished.
• D (correct): Together they finish 1/2 in 3 hours; the slower roofer needs 7.5 more hours for the other half, so 3 + 7.5 = 10.5 hours.

Answer: B

Correct answer: Store B, by $2.88. At Store A,

per bottle, so 72 bottles cost $17.28. At Store B with the coupon,

per pack, or $0.20 per bottle, so 72 bottles cost $14.40. Store B is cheaper by

• A: This ignores the coupon; without it Store B costs $0.25 per bottle, but the coupon lowers it to $0.20.
• B (correct): Store A costs $0.24 per bottle and Store B costs 7.20 ÷ 36 = $0.20 per bottle, so 72 bottles save 72 × 0.04 = $2.88.
• C: This finds the savings for only 36 bottles; the shopper needs 72.
• D: This is the total coupon value on two packs, not the difference between the two stores' costs.

Answer: A

Correct answer: 5 gallons. Paint covers a surface, so find area. One side is

and both sides are

Gallons:

Since 4 gallons would fall short, the crew must buy 5 gallons.

• A (correct): Both sides cover 2 x 120 x 6 = 1,440 square feet; 1,440 / 350 is about 4.1, so 5 whole gallons are needed.
• B: This rounds 4.1 down, which leaves part of the fence unpainted.
• C: This paints only one side: 720 / 350 is about 2.1, rounded up to 3.
• D: This paints only one side and also rounds down.

Answer: B

Correct answer: leave. The situation gives the meaning: a fire is approaching, and officials want people safe at once. EVACUATE means leave.

• A: Residents are not told to stay and fight; the order is about getting out.
• B (correct): A fire heading toward homes leads officials to order people out of the area right away.
• C: Inspecting would keep people in danger, which does not fit an urgent order.
• D: Flooding the valley is not something residents could do and is not suggested.

Answer: B

Correct answer: easily led. Docile means calm and willing to be led, managed, or trained, as in a docile horse. First paraphrase it as easy to control, then reject choices that add a different idea, such as fear or laziness.

• A: A docile person may still work hard; the word is about going along with control, not about avoiding effort.
• B (correct): Docile describes a person or animal that accepts direction calmly and does what it is told.
• C: Fear can make someone obey, but docile names the willingness to be managed, not the emotion behind it.
• D: Stubborn is the opposite: it describes refusing to be led or managed.

Answer: B

Correct answer: Unfaithful. Dis- in this word means not, and loyal means faithful. Not faithful is unfaithful.

• A: Distant starts with the same letters but means far away; it has nothing to do with loyalty.
• B (correct): Dis- means not, so disloyal means not loyal, which is unfaithful.
• C: Deeply devoted is a synonym of loyal, ignoring the negative prefix.
• D: Lawful is a sound-alike trap from legal; loyal concerns faithfulness, not the law.

Answer: C

Correct answer: obvious. The muddy boots make the conclusion plain to see, and the related word evidence points the same way. EVIDENT means obvious; hidden is the opposite and eventual is a look-alike.

• A: Hidden is the opposite of evident.
• B: Eventual shares the ev- start but means happening later.
• C (correct): Obvious means easy to see or understand, which fits a conclusion drawn plainly from muddy boots.
• D: The fact may matter, but importance is a different idea from being easy to see.

Answer: B

Correct answer: carve or write. In means on or into and scrib means write. To inscribe names on a granite wall is to carve them into the stone.

• A: Reading names aloud uses the voice; scrib means write.
• B (correct): In means into or on and scrib means write, so to inscribe is to write or carve letters into a surface such as stone.
• C: Removing or erasing names is the opposite of putting them on the wall.
• D: This is the modern sense of subscribe, a different word with the same root.

Answer: B

Correct answer: clearly stated. The colon introduces a restatement: every step, person and time was spelled out. Instructions with nothing left to guess are clearly stated, so EXPLICIT means clearly stated.

• A: This is the opposite; vaguely worded instructions would leave out details.
• B (correct): Listing every step, person and time leaves nothing unsaid, so the instructions were clearly stated.
• C: The tone of the instructions is never described; the clue is their level of detail.
• D: Length is not the point; the colon explains that nothing was left unclear, not that the instructions ran long.

Answer: D

Correct answer: workable. Read the whole clause: as long as the foundation was reinforced shows the plan can succeed under a condition. FEASIBLE means possible or practical to do, so workable is the best match.

• A: Reinforcing a foundation may cost money, but the word describes whether the plan can work, not its price.
• B: The condition hints at a risk, but the architect is saying the plan can be done, not that it is unsafe.
• C: Nothing is built yet; the sentence describes a plan, so finished adds a fact that is not there.
• D (correct): Workable means able to be done successfully, which matches a plan that can go ahead once the foundation is reinforced.

Answer: D

Correct answer: resourceful. Inventive describes a person who produces original ideas, close to creative or resourceful. The clue about making a clamp from spare bits shows clever problem solving, and the tone is positive, so resourceful fits.

• A: Invention is the noun for the thing made; it cannot describe the mechanic.
• B: This borrows the sense of invent meaning to make up something false, but the sentence praises a practical fix.
• C: Forgetful has nothing to do with the clever repair in the sentence.
• D (correct): Resourceful means good at finding clever ways to solve problems, which fits a mechanic who built a clamp from scraps.

Answer: A

Correct answer: Offset. Counter- means against or in response, and act means to do something. The pilot pushes the rudder against the wind's force, so counteract means offset.

• A (correct): Counter- means against or in response, so to counteract the wind is to act against it and offset its push.
• B: Strengthen would help the crosswind push the plane further off, the opposite of the pilot's aim.
• C: Predict is about knowing in advance, a pre- idea; the pilot is pushing back against a force already acting.
• D: Report means to tell others, while the pilot is taking physical action against the wind.

Answer: A

Correct answer: serious. GRAVE comes after "were," so it is an adjective describing the injuries, and "needed immediate surgery" signals danger. Grave here means serious.

• A (correct): Grave as an adjective means very serious, which explains the need for immediate surgery.
• B: A grave is a burial place, a noun sense that cannot describe injuries.
• C: Minor is the opposite; minor injuries would not need immediate surgery.
• D: Visible describes whether something can be seen, not how dangerous it is.

Answer: C

Correct answer: supply. The phrase "ran low on" and the store setting call for goods on hand. STOCK here means supply.

• A: Shares of ownership are a stock sense tied to the market, not to shovels a store sells.
• B: Livestock is a farm sense of stock and has nothing to do with snow shovels.
• C (correct): A store's stock is the goods it keeps on hand, so "ran low on its supply" fits.
• D: A store could raise its price, but you cannot "run low" on a price.

Answer: C

Correct answer: tactful. Do not let spelling decide: discreet (careful in what one says or reveals) is different from discrete (separate, distinct). The sentence's clue 'never discusses them in public' points to careful, tactful behavior.

• A: This is the meaning of the sound-alike word discrete, not discreet.
• B: Outspoken means quick to say what one thinks, which is the opposite of keeping quiet.
• C (correct): Discreet means careful about what one says or reveals, and tactful captures that careful, sensitive judgment.
• D: Someone forgetful might not repeat plans, but the word means failing to remember, not choosing to keep quiet.

Answer: D

Correct answer: person who stockpiles. Ask what the base is. Hoard is a verb meaning to collect and store up, so -er is the agent ending, naming the doer. The sentence calls the clerk a hoarder, so it means a person who stockpiles.

• A: This reads -er as a comparative on hoarse, a lookalike adjective meaning rough-voiced.
• B: This names the action, hoarding, not the person who does it.
• C: Some -er words name instruments or tools, but the sentence says the clerk was one, so it is a person.
• D (correct): Hoard is a verb meaning to store up, and the agent -er names the person who does it.

Answer: C

Correct answer: authority to act. Splitting mandate into man and date is a false split. A mandate is an official order or authority, and an election win gives a governor the authority to act on a promise.

• A: This is a false split on the letters man; the word has nothing to do with men.
• B: This is a false split on the letters date; no time limit is meant.
• C (correct): A mandate is an official order or grant of authority, and voters grant a governor the authority to carry out a program.
• D: Funding may follow, but the voters gave approval and power, not a bill.

Answer: D

Correct answer: careful discussion. Deliberation ends in -tion and follows "two days of," so it names a process. It comes from the verb deliberate, to think over and discuss before deciding. The board discussed for two days and then voted, so the answer is careful discussion.

• A: This choice borrows the adjective sense of deliberate, meaning on purpose, but the sentence needs a noun for a process of discussion.
• B: The vote came after the deliberation; this confuses the result with the process that led to it.
• C: Two days of weighing a choice is the opposite of a hasty decision.
• D (correct): Deliberation is the noun for thinking over and talking through a choice carefully, which is what the board did for two days before voting.

Answer: A

Correct answer: Repair cafes help people fix broken items, which cuts waste, saves money, and teaches skills. Build a one-sentence map: repair cafes help people fix their own broken things, with three benefits. The main idea must cover that full scope without going past it. Single examples are too narrow, and claims about most landfill items or fees are not in the text.

• A (correct): This covers the whole passage: what repair cafes do and all three benefits the organizers name.
• B: These are examples from the passage, so the statement is too narrow to be the main idea.
• C: The passage never measures how many discarded items could be fixed; this reaches beyond the text.
• D: No fee is mentioned, and the passage stresses saving families money, so this adds an unsupported detail.

Answer: B

Correct answer: Some sailors liked the omelet station. The evidence is that several sailors praised the omelet station. A safe inference stays on the same rung of the quantity ladder or steps down, so "some sailors liked it" is supported. "Most" and "no sailors" change the quantity, and "will keep the menu" predicts a decision the manager has not made.

• A: The passage says several sailors praised one part of the menu; "several" does not climb to "most."
• B (correct): Several sailors praised the station, and "some" stays at or below that level of quantity.
• C: The manager has not decided yet; the passage says she will read the cards first.
• D: Only a few sailors complained about speed, so jumping to "no sailors" turns a partial claim into a total one.

Answer: D

Correct answer: work at and run. Check the word class first: in to staff the booth, staff is a verb, so noun meanings such as a group of workers or a stick cannot fit. The next sentence lists what the firefighters will do there, hand out books and answer questions, so staff means work at and run the booth.

• A: This is the noun sense of staff; in the sentence staff follows to and takes the booth as its object, so it must be an action.
• B: This is another noun sense of staff and has nothing to do with a fair booth.
• C: The booth already exists near the main gate; the firefighters' listed tasks are talking with visitors, not construction.
• D (correct): Staff is used as a verb here: the firefighters will be at the booth handing out books and answering questions, which is running it.

Answer: C

Correct answer: Both are frozen precipitation, but hail builds up inside thunderstorm updrafts. Belonging to the same group is a similarity, not proof of identity. The passage puts both in the category of frozen precipitation and then gives hail the thunderstorm-updraft process and sleet the melt-and-refreeze process.

• A: Sharing a category does not make them identical; the passage stresses that they form in different ways.
• B: The passage describes two different formation processes, not one process at different times.
• C (correct): This keeps the shared category and correctly assigns the thunderstorm process to hail.
• D: The category is right, but the thunderstorm process belongs to hail, not sleet.

Answer: C

Correct answer: It defines a term and then sorts that term into types. The first sentence tells what a fault is, which is a definition. The second announces that faults are grouped by direction of movement, and the last three sentences describe each group. A definition followed by sorting into groups is definition and classification.

• A: Words like slides and pushed describe movement within each type, not a series of steps in forming a fault.
• B: No particular earthquake is described; the passage discusses faults in general.
• C (correct): Sentence 1 defines a fault, sentence 2 names the basis for grouping (direction of movement), and the rest describe each of the three types.
• D: Faults are compared only with one another; no other kind of rock formation is mentioned.

Answer: C

Correct answer: disapproving. Find the words that carry feeling: once again, without warning, simply vanished, stranded and the closing line rejecting the word routine. These show disapproval of the ferry authority, while a neutral notice would only report that the 6:15 a.m. boat was dropped.

• A: A neutral report would state the schedule change in plain words; this one adds judgment through words like stranded and the pointed final sentence.
• B: The author is critical but calm; there are no frantic, exaggerated words like disaster or doom.
• C (correct): Loaded phrases such as once again trimmed, without warning, simply vanished and stranded show that the author finds the change unfair.
• D: Nothing is praised; every judgment in the passage is negative toward the ferry authority.

Answer: A

Correct answer: Rumble strips can cut run-off-road crashes, though the benefit depends on road conditions. Watch the qualifying words. The passage says rumble strips "can reduce" crashes and that the benefit is smaller on narrow-shouldered roads. The best main idea keeps that same strength and limit; choices with "all" or a reversed effect go too far.

• A (correct): This keeps the passage's careful "can reduce" wording and its limit about narrow shoulders.
• B: The passage says rumble strips can reduce such crashes and help less on narrow shoulders; "prevent all" upgrades a possibility into a guarantee.
• C: This reverses the passage, which describes the noise as a helpful warning.
• D: This is a minor detail from the last sentence, not the point of the whole passage.

Answer: B

Correct answer: Two water jugs plus the first-aid kit. Each choice has two parts, and both must match. The sentence about the Wolf patrol lists 2 water jugs and the first-aid kit. The other choices mix in at least one item that belongs to a different patrol.

• A: The water jugs are right, but the cooking stove was brought by the Eagle patrol.
• B (correct): The passage assigns both of these items to the Wolf patrol.
• C: The first-aid kit is right, but the 4 tarps belong to the Fox patrol.
• D: The tents came from the Eagle patrol and the firewood from the Fox patrol.

Answer: D

Correct answer: The records show a link between audiobooks and fewer tickets, not a proven cause. The passage shows only that two things occurred together: audiobook listening and fewer tickets. Its last sentence lists factors the comparison ignored, which signals that the headline overclaims. The best-supported answer describes a link without claiming causation and keeps the measure (tickets) unchanged.

• A: This repeats the newsletter's headline; the passage points out that other factors were not checked, so no cause was proven.
• B: The comparison never measured experience or music, so this adds a claim the passage does not make.
• C: The records counted speeding tickets, not accidents; this changes what the figure measured.
• D (correct): The passage reports that the two went together but notes that age, experience, routes and timing were not examined.

Answer: A

Correct answer: Enrollment rose after the new director was hired, but the passage does not say what caused the rise. Look for a stated cause. The passage gives sequence (a hiring, then higher enrollment), a contrast (although the fee rose) and an unlinked fact (new housing), but no because or as a result. It even notes that the report does not explain the change. The only supported statement keeps the order and leaves the cause open.

• A (correct): The passage gives the order of events and the numbers, while stating that the report does not explain the change, so no cause is established.
• B: The rise of 70 came after the hiring, but coming after is not the same as being caused by; no causal link is stated.
• C: Although signals contrast: more families joined in spite of the higher fee, not because of it.
• D: The developments are mentioned, but the passage never connects them to enrollment, so naming them as the cause adds unsupported reasoning.

Answer: C

Correct answer: 59 feet. Edging follows the boundary, so add all five sides:

• A: This leaves out one of the 9-foot sides; a pentagon has five sides to add.
• B: The sum is right, but perimeter is a length measured in feet, not square feet.
• C (correct): The perimeter is the sum of all five sides, 59 feet.
• D: This doubles the sum, a habit from the rectangle formula that does not apply when every side is listed.

Answer: B

Correct answer: 100π square centimeters. A sphere's surface area is four times the area of its largest circle.

• A: This is pi r squared, the area of one flat circle, not four times it.
• B (correct): 4 pi r squared with r of 5 gives 4 times 25 pi, or 100 pi.
• C: This is the volume formula, four thirds pi r cubed, which measures space inside, not the surface.
• D: This multiplies 4 pi by the radius without squaring it.

Answer: C

Correct answer: An open circle at 9 with shading to the left. A strict sign (< or >) uses an open circle because the boundary is not a solution. Values less than 9 lie to the left of 9, so shade left. Test 0: 0 < 9 is true, and 0 is on the left.

• A: A closed circle would include 9, which is used for at most, not for strictly less than.
• B: Shading right shows numbers greater than 9, which do not satisfy x < 9.
• C (correct): The strict sign excludes 9, so the circle is open, and smaller numbers lie to the left.
• D: This shows x ≥ 9: it includes 9 and points the wrong way.

Answer: C

Correct answer: 1/2. Divide any term by the one before it:

Each term is half the previous one, so

a ratio between 0 and 1 because the terms shrink.

• A: This divides the earlier term by the later one; the ratio is later ÷ earlier.
• B: This is the difference between the first two terms, which would describe an arithmetic sequence.
• C (correct): Each term divided by the previous term gives 1/2.
• D: This compares terms two places apart, such as 192 ÷ 768, instead of consecutive terms.

Answer: C

Correct answer: 26 feet. Let the width be w, so the length is 2w. The perimeter is

which gives w = 13 feet. The length is 2(13) = 26 feet. Check:

• A: This is the width; the question asks for the length, which is twice the width.
• B: This is half the perimeter, the sum of one length and one width.
• C (correct): With width w and length 2w, the perimeter is 2(2w) + 2w = 6w = 78, so w = 13 and the length is 26 feet.
• D: This divides 78 by 4 as if the run were a square with four equal sides.

Answer: A

Correct answer: 10π square cm. The fraction is

The full area is π(4)^2 = 16π square cm, so the sector is 5/8 of 16π = 10π square cm.

• A (correct): The fraction 5/8 of the 16π full area gives 10π square cm.
• B: This is 5/8 of the circumference, 8π, which is the arc length, not the sector's area.
• C: This is the area of the entire circle, not the 225-degree slice.
• D: This is the area of the remaining 135-degree slice, 3/8 of 16π.

Answer: A

Correct answer: 12. Test divisors from 1 up to about the square root of 72 (about 8.5): 1 × 72, 2 × 36, 3 × 24, 4 × 18, 6 × 12, 8 × 9.

Six pairs of different numbers give 12 factors.

• A (correct): The factor pairs are 1 × 72, 2 × 36, 3 × 24, 4 × 18, 6 × 12 and 8 × 9, giving 12 factors.
• B: 6 is the number of factor pairs; each pair holds two different factors.
• C: This misses a pair, such as 8 and 9, which are found just before stopping at the square root.
• D: This misses one factor, often 1 or 72 itself, which must both be counted.

Answer: A

Correct answer: x² - 5x - 14. Multiply every term by every term: first $x^2$, outer $2x$, inner $-7x$, last $-14$. Combine the middle terms:

The result is $x^2-5x-14$.

• A (correct): Products are x^2, 2x, -7x and -14; the middle terms combine to -5x.
• B: This multiplies only the first terms and the last terms, skipping the outer and inner products.
• C: This flips the sign of the middle term; 2x - 7x is -5x.
• D: This subtracts 2x instead of adding it when combining the middle terms.

Answer: D

Correct answer: Acute. Compare the squares with c as the longest side:

Since 225 is greater than 196, the triangle is acute.

• A: A right triangle needs the squares to be equal; 225 is not 196. (9-12-15 would be right.)
• B: Obtuse requires $a^2+b^2<c^2$, but here the sum is larger than $c^2$.
• C: 9 + 12 = 21 is greater than 14, so these lengths do form a triangle.
• D (correct): The squares of the two shorter sides total 225, more than $14^2=196$, so all angles are acute.

Answer: C

Correct answer: 44. Substitute with parentheses: $(-5{)}^2-3(-5)+4$. Square first:

Total:

• A: This squares -5 as -25 instead of 25, giving -25 + 15 + 4.
• B: This squares correctly but treats -3(-5) as -15, giving 25 - 15 + 4.
• C (correct): (-5)^2 = 25, -3(-5) = 15, and 25 + 15 + 4 = 44.
• D: This makes both sign mistakes, giving -25 - 15 + 4.

Answer: D

Correct answer: 144°. Neighboring angles at a crossing form a linear pair, so

Then 5x = 180 and x = 36, so the larger angle is 4(36) = 144°.

• A: 36° is the smaller angle; the question asks for the larger one.
• B: This uses 90° instead of 180° for the pair (5x = 90 gives x = 18, 4x = 72), but neighbors on a line are supplementary.
• C: Nothing says the lines are perpendicular; if the angles were 90° each, one could not be 4 times the other.
• D (correct): Neighboring angles total 180°, so 5x = 180, x = 36, and 4x = 144°.

Answer: B

Correct answer: Infinitely many. Rewrite the first equation:

Both equations have slope 2 and intercept -3, so they are the same line and every point on it is a solution.

• A: Lines cross once only when their slopes differ; here both slopes are 2.
• B (correct): Solving 6x - 3y = 9 for y gives y = 2x - 3, so the two equations describe the same line.
• C: Equal slopes alone are not enough for no solution; the intercepts must also differ, and here both are -3.
• D: Two straight lines can never meet in exactly two points.

Answer: C

Correct answer: −2 dollars. Add the gains and losses:

so the total is

The average is

per day.

• A: The size is right, but the losses outweigh the gains, so the average is negative.
• B: This is the total change for all five days, not the average per day.
• C (correct): The changes sum to −10, and −10 ÷ 5 = −2.
• D: This adds all the sizes as losses (26) and divides by 5, ignoring the two gains.

Answer: C

Correct answer: 3. Clear the decimals and fractions first. Multiply the first equation by 10:

Multiply the second by 6:

Multiply these by 2 and 5 respectively:

Adding gives 23x = 138, so x = 6, and then

gives y = 3.

• A: This is the value of x; the question asks for y.
• B: This is x + y, the sum of the two values rather than y alone.
• C (correct): With x = 6 and y = 3, both originals check: 2.4 + 1.5 = 3.9 and 3 − 1 = 2.
• D: This comes from a sign slip in 3(6) − 2y = 12; solving correctly gives −2y = −6, so y is positive 3.

Answer: D

Correct answer: 6√2. Pull out perfect-square factors:

All three are multiples of $\sqrt{2}$, so combine the numbers in front:

giving $6\sqrt{2}$.

• A: This adds and subtracts the numbers under the radicals, 50 + 18 - 8, which is not allowed.
• B: This simplifies correctly but adds the last term instead of subtracting it: 5 + 3 + 2.
• C: This combines the first two terms but leaves out the subtraction of root 8, which is 2 root 2.
• D (correct): Each radical simplifies to a multiple of root 2: 5, plus 3, minus 2, gives 6 root 2.