AFQT Core Practice 7: Graphs, Work Rates and Cause and Effect

Answer: C

Correct answer: $0.79. Unit price = total cost divided by number of units:

or $0.79 per pen.

• A: This multiplies the price by 10 instead of dividing.
• B: This divides 10 by 7.90, which gives pens per dollar, not dollars per pen.
• C (correct): Divide the cost by the number of pens: 7.90 divided by 10 is 0.79.
• D: This moves the decimal point two places instead of one when dividing by 10.

Answer: C

Correct answer: 3 hours 30 minutes. Time = distance ÷ speed =

Convert the decimal part:

so the trip takes 3 hours 30 minutes.

• A: This reads the decimal 0.5 as 50 minutes instead of half an hour.
• B: This treats 0.5 hour as 5 minutes; half an hour is 30 minutes.
• C (correct): Time is 210 ÷ 60 = 3.5 hours, and 0.5 hour is 30 minutes.
• D: This adds an extra hour; 60 mph for 4.5 hours would cover 270 miles, not 210.

Answer: B

Correct answer: 133 miles. Distance equals rate times time:

The first 3 hours give 114 miles and the extra half hour adds

• A: This uses only 3 hours and drops the extra half hour of driving.
• B (correct): Multiplying 38 mph by 3.5 hours gives 133 miles.
• C: This rounds the time up to 4 hours before multiplying.
• D: This adds the speed and the time instead of multiplying them.

Answer: D

Correct answer: 68 inches. Convert to one unit:

then add the extra 8 inches:

• A: This treats a foot as 10 inches instead of 12.
• B: This adds the 5 and the 8 without converting feet to inches.
• C: This converts the 5 feet but forgets to add the extra 8 inches.
• D (correct): Each foot is 12 inches, so 5 x 12 + 8 = 60 + 8 = 68 inches.

Answer: A

Correct answer: About 5.1 days. Estimate first: the answer must be less than 9 days and more than half of 9, or 4.5 days.

Exactly:

per day, so the time is

• A (correct): The combined rate is 7/36 of the job per day, so the time is 36/7, which is about 5.1 days and lies between 4.5 and 9 days as it must.
• B: This is less than half of the faster carpenter's 9 days, which is impossible because the partner is slower.
• C: This averages the two times, but working together must be faster than either person alone.
• D: This adds the two times instead of adding the rates.

Answer: B

Correct answer: $16.00. Write 2.5 percent as a decimal by moving the point two places left: 0.025.

Fee:

Check: 1 percent of 640 is 6.40, and 2.5 times 6.40 is 16.

• A: This uses 0.25 for 2.5 percent, which is 25 percent of the payment.
• B (correct): 2.5 percent is 0.025, and 0.025 times 640 is 16.
• C: This uses 0.0025 for 2.5 percent, moving the decimal point one place too far.
• D: This is the payment plus the fee; the question asks for the fee only.

Answer: B

Correct answer: $1,900. To multiply by 25, multiply by 100 and divide by 4.

so the vests cost $1,900.

• A: This comes from a slip in the partial products: 70 × 25 = 1,750 and 6 × 25 = 150, not 100.
• B (correct): Multiply by 100 and divide by 4: 7,600 ÷ 4 = 1,900.
• C: This drops a zero; 76 vests at $25 must cost more than 40 × $25 = $1,000.
• D: This adds a zero; the product is less than 100 × $25 = $2,500.

Answer: A

Correct answer: 51 miles per hour. Distances:

for 255 miles.

Average speed:

per hour. The time spent at each speed acts as its weight.

• A (correct): The convoy covers 90 + 165 = 255 miles in 5 hours, and 255 divided by 5 is 51.
• B: 50 averages the two speeds, but more time was spent at 55 miles per hour.
• C: This gives the 3 hours to the 45-mile-per-hour leg, reversing the times.
• D: 255 is the total distance in miles; it still has to be divided by the 5 hours.

Answer: B

Correct answer: 2.45 grams. Convert to grams:

Divide by the number of rivets:

The two shifts of three places cancel each other.

• A: This is the weight of one rivet in kilograms; it was never converted to grams.
• B (correct): 2.45 kg is 2,450 g, and 2,450 divided by 1,000 is 2.45 g.
• C: This converts kilograms to grams with only two shifts, using 100 instead of 1,000.
• D: This divides 2,450 by 100 instead of by 1,000.

Answer: C

Correct answer: 14 feet. Change the mixed number to an improper fraction and multiply by the conversion factor.

• A: Only the whole 4 yards were multiplied by 3; the 2/3 yard must be converted too.
• B: This divides by 3, but feet are smaller units, so the number of feet must be larger.
• C (correct): As an improper fraction the length is 14/3 yards, and 14/3 times 3 = 14 feet.
• D: This multiplies by 12, which converts feet to inches, not yards to feet.

Answer: C

Correct answer: 16 kilograms. Round to friendly values: 31.8 is about 32 and 0.49 is about 0.5. Then

kilograms. The exact weight, 15.582 kilograms, is close to this estimate.

• A: This has the decimal point one place too far left; half of about 32 is 16, not 1.6.
• B: This has the decimal point one place too far right; each meter weighs less than 1 kilogram, so the total must be less than 32.
• C (correct): Rounding to 32 meters and 0.5 kilogram per meter gives 32 times 0.5 = 16.
• D: This divides 32 by 0.5 instead of multiplying by 0.5.

Answer: B

Correct answer: $52. Gallons used:

since

is 32 too many.

Total cost:

Each share:

so each friend pays $52.

• A: $156 is the total fuel cost before it is split among the three friends.
• B (correct): 1,248 ÷ 32 = 39 gallons, 39 × $4 = $156, and $156 ÷ 3 = $52.
• C: This splits the 39 gallons three ways but never multiplies by the $4 price.
• D: This multiplies by 3 instead of dividing by 3 at the last step.

Answer: D

Correct answer: $26,000. The first $10,000 earns

The rest of the commission is

which is 5% of

Total sales:

• A: This divides the whole $1,100 by 5%, ignoring that the first $10,000 earns only 3%.
• B: This is only the portion of sales above $10,000; the first $10,000 must be added back.
• C: This divides the whole $1,100 by 3%, as if every dollar of sales earned the lower rate.
• D (correct): The first $10,000 earns $300, leaving $800 at 5%, which is $16,000 of extra sales; 10,000 + 16,000 = $26,000.

Answer: A

Correct answer: 480 square feet. Convert each plan length to real length first:

Then find the area:

• A (correct): The room is 2.5 × 8 = 20 ft by 3 × 8 = 24 ft, and 20 × 24 = 480 square feet.
• B: This finds the plan area, 7.5 square inches, and multiplies by 8 once; areas scale by 8 squared, or 64.
• C: This is the perimeter of the real room, 2 × (20 + 24) feet, not its area.
• D: This adds the two real side lengths, 20 + 24, instead of multiplying them.

Answer: D

Correct answer: 7 hours 20 minutes. Stage 1:

filled, so $\frac{2}{3}$ remains.

Stage 2 net rate:

per hour, so

= 5 hours 20 minutes.

Total: 2 hours + 5 hours 20 minutes = 7 hours 20 minutes.

• A: This is only the time after inlet B and the drain open; the first 2 hours must be added.
• B: This is the time to fill the whole cistern at the net rate of 1/8, ignoring the 1/3 already filled.
• C: This adds the drain's rate as if it were filling, instead of subtracting it.
• D (correct): Inlet A fills 1/3 in 2 hours; the net rate then is 1/8 per hour, so the remaining 2/3 takes 16/3 hours, giving 7 hours 20 minutes in all.

Answer: D

Correct answer: abundant. Plentiful is plenty (y to i) plus -ful, an adjective ending meaning full of. So plentiful means existing in large amounts, which is abundant.

• A: Scarce and rare mean in short supply, the opposite of having plenty.
• B: Plenty is the noun base; the target is an adjective.
• C: Empty means containing nothing, the opposite idea.
• D (correct): Plenty plus -ful means full of plenty, which is abundant.

Answer: A

Correct answer: danger. A hazard is something that could cause harm, such as a wet floor or a loose wire. Danger matches; accident is a possible result, warning is an associated sign, and safety is the opposite.

• A (correct): A hazard is a source of possible harm, which is what danger means.
• B: An accident is something that may result from a hazard, not the hazard itself.
• C: A warning tells people about a hazard; it is not the danger.
• D: Safety is the opposite of a hazard.

Answer: B

Correct answer: reinforce. The -en suffix turns the adjective strong into a verb meaning make strong. Adding braces makes the pier stronger, so reinforce is the synonym.

• A: Strength is the noun for power; it cannot follow will as an action word here.
• B (correct): Reinforce means to make stronger by adding support, exactly what steel braces do.
• C: Weaken is the opposite action, making something less strong.
• D: Lengthen means make longer; it shares the -en ending but not the meaning.

Answer: C

Correct answer: foretell. Pre means before and dict means say. To predict is to say ahead of time what will happen, which is what a forecast does.

• A: Remembering looks back, while pre points forward to what has not happened.
• B: Denying rejects a claim; forecasters are making one about the future.
• C (correct): Pre means before and dict means say, so to predict is to say what will happen before it does.
• D: Measuring would use meter; forecasters are saying what will come.

Answer: C

Correct answer: Exceeding. Sur- is a form of super- and means over or above. Collecting 12,000 cans when the record was 9,500 goes above that record, so surpassing means exceeding.

• A: Falling short of is the reverse; 12,000 is more than 9,500.
• B: Making sure of reads sur- as sure, the trap the lesson warns about.
• C (correct): Sur- means over or above, and pass means go, so surpassing means going above, or exceeding.
• D: Matching would mean an equal total, but 12,000 is greater than 9,500.

Answer: D

Correct answer: Unrelated. Ir- is the in- (not) prefix spelled to match the r in relevant. Not relevant means unrelated, which explains why the jury should ignore it.

• A: Incorrect means wrong; a true comment about the weather can still have nothing to do with the case.
• B: Repeated reads ir- as re- (again), a false split; ir- is the negative prefix before r.
• C: Disrespectful judges tone, but the judge's reason was that the comment did not bear on the case.
• D (correct): Ir- is the form of in- (not) before r, so irrelevant means not relevant, or unrelated.

Answer: D

Correct answer: strict. The second sentence restates the first in plain terms: permission is required for everything and small violations are punished. Rules like that are strict, so STRINGENT means strict.

• A: This is the opposite; lenient rules would not punish small violations with a week of extra duty.
• B: The rules are described clearly; nothing suggests anyone misunderstood them.
• C: Fairness is a judgment the sentence never makes; it only shows the rules were tight.
• D (correct): The second sentence restates the rules as tight and harshly enforced, which is what strict means.

Answer: D

Correct answer: reason given. Justification ends in -tion and follows a possessive, so it names a thing. Justify means to show an action is right, so a justification is the reason given. The flood warning is that reason.

• A: Defensible is the meaning of justifiable, an adjective; the sentence needs a noun naming the reason.
• B: Approval means official permission, but the sentence names a cause, not a sign-off.
• C: Punishment is unrelated to explaining why the hike was canceled.
• D (correct): A justification is the reason offered to show an action was right, here the flood warning.

Answer: C

Correct answer: unimportant. The example, folder color, is set against the safety budget, so the word must mean minor. TRIVIAL means of little importance, so unimportant is the match.

• A: Colorful picks up a detail from the example, not the meaning of the word.
• B: Urgent is the opposite; it describes the safety budget the speaker wants to focus on.
• C (correct): Unimportant fits: folder color is offered as an example of something minor compared with safety.
• D: Nothing suggests folder color is hard to understand; the contrast is about importance.

Answer: A

Correct answer: assign. Allocate means to distribute something for a particular person or purpose. Substitute assign: 'the supervisor will assign tasks to the crew' keeps the meaning; collect reverses it, and approve and finish are different steps.

• A (correct): Allocate means to give out shares or portions to particular people, so assign fits giving out tasks.
• B: Approving tasks means giving permission for them, a separate decision from handing them out.
• C: Collecting gathers things in, which is roughly the opposite of handing them out.
• D: Completing tasks is what the crew does later; it is not what allocating means.

Answer: B

Correct answer: persistent. Paraphrase first: she kept going for days until she succeeded. Tenacious means persistently holding on in spite of obstacles, so persistent is the match.

• A: Pushy adds a negative sense of pressuring other people; the sentence shows her working on a problem, not pressuring anyone.
• B (correct): Tenacious means holding on and continuing despite difficulty, exactly what three evenings of testing shows.
• C: Impatience would make her more likely to give up; three evenings of wire-by-wire testing shows the opposite.
• D: Skill may help, but the context clue is how long she kept going, not how expert she was.

Answer: A

Correct answer: temporary. The clue, a night or two before moving on, shows a short stay. TRANSIENT means lasting only briefly; traveling covers only part of that idea and homeless adds a story the sentence does not tell.

• A (correct): Temporary fits: visitors who stay a night or two and move on are only there briefly.
• B: Nothing in the sentence describes the visitors' manners; transient is about how long they stay.
• C: Transient can describe people without homes, but the sentence is about campground visitors passing through.
• D: Permanent is the opposite of a stay of a night or two.

Answer: A

Correct answer: increased in value. APPRECIATED is measured by "20 percent," so it describes a change in worth, and "grew popular" tells the direction. Appreciate here means increase in value.

• A (correct): For property, appreciate means to rise in worth, which fits a 20 percent change as demand grew.
• B: Being thanked is the everyday sense of appreciate, but a house cannot be thanked by 20 percent.
• C: Appreciate can mean understand fully, but understanding cannot be measured as a percent of a house.
• D: Dropping in value is depreciation, the opposite; a popular neighborhood pushes prices up.

Answer: D

Correct answer: grew rapidly. The word is figurative: a rolling snowball picks up more snow and gets bigger faster. The result clause, until nearly everyone believed it, confirms the rumor grew rapidly; grew colder is the literal-image trap.

• A: This takes the snow image literally; a rumor has no temperature.
• B: Fading is the opposite of what happened, since the rumor ended up reaching nearly everyone.
• C: A rumor that nearly everyone believed was not kept secret.
• D (correct): Like a snowball rolling downhill and getting bigger, the rumor kept growing until nearly everyone believed it.

Answer: D

Correct answer: intensely eager. Every clue shows energy beyond what is required: every violation, every door, unrequested weekends. Zealous means fervently devoted and eager, so intensely eager fits; jealous is a sound-alike, and hostile imports an emotion the sentence never shows.

• A: Jealous only looks and sounds similar; it means resentful of what others have, which the sentence never suggests.
• B: Overly cautious means too careful to act boldly; the officer's behavior shows energetic devotion, not hesitation.
• C: Writing people up enforces rules; nothing shows he dislikes the crews, so hostile adds an emotion the text does not show.
• D (correct): Zealous describes great energy and devotion to a cause, shown by extra write-ups, signs, and unrequested weekend work.

Answer: A

Correct answer: May 15. The question asks for a starting date tied to online renewal. The sentence "You may renew online beginning May 15" answers it. The other dates belong to different events: expiration, the late-fee cutoff and sticker mailing.

• A (correct): The notice says the owner may renew online beginning May 15.
• B: June 30 is the date the current registration expires, not when online renewal opens.
• C: July 15 is the date after which a late fee applies.
• D: This is how long it takes for the new sticker to be mailed.

Answer: B

Correct answer: The mill's night shift led the gas station to stay open all night. Picture an arrow from cause to effect: night shift, then late-night customers, then the station staying open all night. The word because points from the new customers to the longer hours. Any choice that flips the arrow or invents a purpose does not match the passage.

• A: This reverses the arrow; the night shift came first and brought the customers that led to the longer hours.
• B (correct): The night shift brought late-night customers, and because of them the station began staying open all night.
• C: The passage gives no reason for the night shift, and helping the gas station is never named as a purpose.
• D: The 80 figure describes new mill workers, not anyone the gas station hired.

Answer: D

Correct answer: Ten of the 12 vehicles passed the antifreeze test. Exception words limit a comparison. Except the two cargo vans means

vehicles passed the antifreeze test, and but not on the sedans means the snow-tire statement does not cover every vehicle.

• A: This ignores the exception; the two cargo vans did not pass.
• B: The sedans' problem was tires, not antifreeze; only the cargo vans needed coolant.
• C: The phrase but not on the sedans excludes them; they are still on all-season tires.
• D (correct): Every vehicle passed except the two cargo vans, and 12 - 2 = 10.

Answer: C

Correct answer: comforts and conveniences for visitors. Examples identify a category. Free internet, a water cooler, phone chargers and reading lamps are all things provided to make a wait more comfortable, so amenities means comforts or conveniences for the people using the building.

• A: The items listed are in the waiting room and none are used to treat patients.
• B: The examples are things, not people, so the category cannot be staff.
• C (correct): The examples, internet, water, chargers and lamps, are all features that make waiting easier and more pleasant.
• D: Nothing in the list is a rule; each item is something provided for patients to use.

Answer: C

Correct answer: Reyes set out warning flares on the shoulder. "By the time" sets a reference point (the tow truck's arrival), and "had already set out" places the flares before that point. The rest follows in order: arrival, towing to Lakeview, then the mechanic's discovery, so the flares came first among these choices.

• A: The truck's arrival is the reference point in the "by the time" clause; the flares were already out when it came.
• B: The mechanic worked on the car only after it was towed to Lakeview, near the end of the sequence.
• C (correct): "By the time the tow truck reached her, she had already set out" the flares, so placing the flares came before the truck's arrival and everything after it.
• D: Towing happened after the truck arrived, which was already after the flares were set out.

Answer: A

Correct answer: Fuel use fell 9 percent, which was short of the 15 percent goal. Separate the objective from the outcome and the outcome from the forecast. The goal was 15 percent, the actual result was 9 percent, and the tires are only a plan with an expected benefit. So fuel use fell, but not as far as the goal.

• A (correct): The passage gives the goal as 15 percent and the result after two years as 9 percent.
• B: The 15 percent figure is the objective; the actual outcome was only 9 percent.
• C: The tires are a plan that officials expect to help next year, so this treats a forecast as a result.
• D: Six percent is the gap between the goal and the result; the actual drop was 9 percent.

Answer: D

Correct answer: Admiring. Tone comes from word choice. The writer stresses Briggs's 27 years of service, lists his hands-on efforts, and closes with "tireless, generous leadership," which signals admiration. The "but" in the last sentence turns from Briggs's modesty to the writer's own praise.

• A: The writer finds no fault with Briggs; every detail about him is positive.
• B: The writer clearly cares about Briggs's work, choosing warm, approving words rather than flat ones.
• C: The writer never questions Briggs's role; instead the passage rejects his modest claim that the volunteers deserve all the credit.
• D (correct): Words such as tireless and generous, and the claim that the event would not happen without him, show strong approval and respect.

Answer: D

Correct answer: It is written in the second person, placing the reader inside the experience. Point of view can mean the narrator's grammatical position: first person uses I or we, second person uses you, and third person uses he, she or they. Every sentence here is built around you, which pulls the reader into the scene, and none of the sentences takes a side on the experience.

• A: First person would use I or we; this passage uses you, so the narrator is not telling his own story.
• B: Third person would use he, she or they; the passage addresses the reader directly as you.
• C: This confuses grammatical point of view with opinion; the passage contains no judgment or should statement about training.
• D (correct): The passage uses you throughout to put the reader in the recruit's shoes, and it reports events without arguing for anything.

Answer: A

Test each explanation against every detail. Steady lift-ticket sales and similar temperatures rule out fewer visitors and warmer weather. Two cafe changes came just before the drop, so the best answer names them as likely factors without claiming that one of them alone was the cause.

• A (correct): The passage names two changes that happened just before sales fell and rules out a drop in visitors or warmer weather.
• B: Lift-ticket sales were about the same in both months, which works against this explanation.
• C: The passage says temperatures were similar in both months, so weather does not explain the change.
• D: The machine was also moved at the same time, so the passage cannot single out the price as the only cause.

Answer: A

Note what was studied (cooling vests), what was found (they helped and may delay heat exhaustion), and how sure the author sounds (qualified, with clear limits). The best main idea keeps all three: a real but limited benefit, used alongside shade, water, and breaks.

• A (correct): This matches the passage's careful verbs (helped many, may delay) and keeps the limits on time, humidity, and use with other precautions.
• B: The passage says the vests may delay heat exhaustion; this turns a possibility into a guarantee.
• C: The passage says the vests helped less in humidity, not that they failed; this reverses the overall positive but limited finding.
• D: This accurate fact is one limit among several and leaves out what the vests do and how they should be used.

Answer: C

Correct answer: 96 square inches. In a right triangle the two legs serve as base and height.

• A: This multiplies the legs but forgets the one half in the triangle formula.
• B: This uses the 20 inch longest side as if it were a leg; the legs are the base and the height.
• C (correct): The two legs are the base and height: half of 12 times 16 is 96.
• D: This adds the three sides, giving the perimeter in inches, not the area.

Answer: C

Correct answer: Point Q. When an angle is named with three letters, the middle letter is the vertex. In angle PQR the middle letter is Q, and the sides pass through P and R.

• A: P is a point on one side of the angle, not the vertex.
• B: R is a point on the other side of the angle, not the vertex.
• C (correct): The vertex is always the middle letter of a three-letter angle name.
• D: The vertex is where the two sides meet, which is Q, not a point between P and R.

Answer: D

Correct answer: -4. Rewrite in slope-intercept order:

The slope m is the coefficient of x, which is -4.

• A: This is the y-intercept, the constant term, not the slope.
• B: This drops the negative sign in front of 4x.
• C: This mixes the intercept with the sign of the x-term.
• D (correct): The coefficient of x, including its sign, is the slope; the line is y = -4x + 9.

Answer: D

Correct answer:

Undo division by 4 by multiplying both sides by 4. Since 4 is positive, the sign stays:

Check

is true.

• A: This reverses the sign, but multiplying by positive 4 does not change direction.
• B: This divides −3 by 4 instead of multiplying, which does not undo the division.
• C: This subtracts 4 from −3 instead of multiplying both sides by 4.
• D (correct): Multiplying both sides by positive 4 keeps the direction: x ≥ −12.

Answer: B

Correct answer: (20, -6). Read each axis separately: x = 4 times 5 = 20, and y = 3 times 2 = 6 units down, so

The point is (20, -6).

• A: This counts grid lines as single units without checking the axis scales.
• B (correct): Four x-lines at 5 units each give 20, and three y-lines down at 2 units each give -6.
• C: This uses the y-axis scale for x and the x-axis scale for y.
• D: This reads the scales correctly but forgets that below the origin means a negative y-value.

Answer: C

Correct answer: 45 feet. The sun's rays make similar triangles, so height and shadow are in the same ratio:

• A: This sets up the ratio upside down, multiplying 27 by 3/5.
• B: This adds the 2-foot difference between height and shadow instead of using a ratio.
• C (correct): Height is 5/3 of shadow length, and 27 × 5 / 3 = 45 feet.
• D: This multiplies 27 by 5 but forgets to divide by 3.

Answer: C

Correct answer: 4m²(3m² - 5m + 2). The largest number dividing 12, 20 and 8 is 4, and the lowest power of m in any term is $m^2$, so the GCF is $4m^2$. Divide each term: $3m^2$, $-5m$ and $2$. Check by distributing back.

• A: This is equivalent but not fully factored; 2m is a common factor, not the greatest one.
• B: This drops the last term; 8m^2 divided by 4m^2 is 2, not 0.
• C (correct): 4 is the largest number dividing 12, 20 and 8, and m^2 is the highest power of m in every term.
• D: Distributing back gives 8m, not 8m^2, so the last term is wrong.

Answer: D

Correct answer: −16. An odd power of −1 is −1, and an even power of −2 is positive:

The product is

• A: This makes (−1)⁷ positive; a negative base with an odd exponent stays negative.
• B: This multiplies −2 by 4 instead of raising −2 to the fourth power.
• C: This multiplies −2 by 4 and also loses the sign of (−1)⁷.
• D (correct): (−1)⁷ = −1 because the exponent is odd, (−2)⁴ = 16, and −1 × 16 = −16.

Answer: C

Correct answer: x = 4. Move the smaller x term: subtract 5x from both sides to get

Add 9 to get 6x = 24, then divide by 6: x = 4. Check:

• A: This comes from subtracting 9 from 15 instead of adding 9 to both sides, giving 6x = 6.
• B: This comes from adding 5x to both sides instead of subtracting it, giving 16x = 24.
• C (correct): Subtracting 5x and adding 9 gives 6x = 24, so x = 4.
• D: This is the right size but the wrong sign; 11(−4) − 9 = −53, while 5(−4) + 15 = −5.

Answer: A

Correct answer: 120 degrees. The angles of a quadrilateral total 360 degrees. So

and x = 30. The largest angle is 4x = 120 degrees.

• A (correct): With 12x = 360, x = 30, so the largest angle, 4x, is 120 degrees.
• B: This is the value of x, not the largest angle, 4x.
• C: This is 3x, one of the two middle-sized angles, not the largest.
• D: This sets the sum equal to 180, the triangle total, giving x = 15 and 4x = 60.

Answer: D

Correct answer: (4, 0). Substitute the isolated y:

Distribute:

so 8x = 32 and x = 4. Then

Check:

• A: This comes from writing 3(x − 4) as 3x − 4 without distributing to the 4; then 5(3) + 3(−1) = 12, not 20.
• B: This reverses the coordinates; with x = 0 the first equation gives y = −4.
• C: This comes from a sign slip, using +12 instead of −12; then 5(1) + 3(−3) = −4, not 20.
• D (correct): x = 4 and y = 0 satisfy both y = x − 4 and 5x + 3y = 20.

Answer: D

Correct answer: 7. Work inside out:

Setting

gives k = 7.

• A: This applies f first and g second: f(5) − 3 = 7 + k = 11 gives k = 4, which solves g(f(5)) = 11.
• B: This skips g and evaluates f(5) = 10 + k directly.
• C: This feeds g(5) = 2 into f but forgets to double it, so 2 + k = 11.
• D (correct): g(5) = 2 and f(2) = 4 + k, so k = 11 − 4 = 7.

Answer: A

Correct answer: 6. Handle each power: without parentheses

with parentheses

because the even power makes it positive; and

• A (correct): -3^2 = -9, (-2)^4 = 16 and 4^0 = 1, so -9 + 16 - 1 = 6.
• B: This reads -3^2 as (-3)^2 = 9, then computes 9 + 16 - 1.
• C: This treats 4^0 as 0 instead of 1, giving -9 + 16 - 0.
• D: This makes (-2)^4 negative; an even power of a negative number is positive.

Answer: C

Correct answer: 34π cm. A diameter is two radii, so

Then 3x = 24 and x = 8, so the radius is

• A: This is π times 17 squared, the area, not the circumference.
• B: This is π times the radius; the circumference is 2πr.
• C (correct): Setting the diameter equal to twice the radius gives x = 8, r = 17 and C = 34π cm.
• D: This uses 2π times the diameter, 34, which doubles the circumference.

Answer: D

Correct answer: 21 pieces. Equal pieces as long as possible call for the GCF. 96 = $2^5$ × 3 and 156 = $2^2$ × 3 × 13, so the GCF is $2^2$ × 3 = 12 inches.

Then

for

pieces.

• A: 12 is the length of each piece in inches, not the number of pieces.
• B: This uses 6-inch pieces; 6 is a common factor, but not the greatest one.
• C: This counts only the pieces cut from the 156-inch pipe and leaves out the 8 from the 96-inch pipe.
• D (correct): The longest equal length is the GCF, 12 inches, giving 8 + 13 = 21 pieces.