AFQT Core Practice 6: Rates, Distance and Words in Context

Answer: D

Correct answer: 12.68 grams. The hundredths digit is 8, and the digit just to its right is 4. Since 4 is less than 5, leave the 8 alone and drop the remaining digits: 12.68 grams.

• A: This comes from rounding in stages (12.6849 to 12.685 to 12.69); round once, looking only at the digit just right of the hundredths place.
• B: This rounds to the nearest tenth, not the nearest hundredth.
• C: This rounds to the nearest thousandth, keeping one place too many.
• D (correct): The digit right after the hundredths place is 4, so the 8 stays and the rest is dropped.

Answer: C

Correct answer: 883. Use compensation: 497 is 3 less than 500.

• A: This drops a carry in the tens column.
• B: This drops the carry into the hundreds column; the sum must be more than 500 + 300 = 800.
• C (correct): Add 500 instead of 497 to get 886, then take back the extra 3 to get 883.
• D: This adds the extra 3 back instead of subtracting it when using compensation.

Answer: D

Correct answer: 3 hours 30 minutes. Use

Convert the decimal part:

so the flight takes 3 hours 30 minutes.

• A: This reads 3.5 hours as 3 hours 50 minutes; the decimal part must be multiplied by 60.
• B: This reads the .5 as 5 minutes instead of half of 60 minutes.
• C: This divides the speed by the distance, which inverts the time formula.
• D (correct): 1,575 divided by 450 is 3.5 hours, and 0.5 hour is 30 minutes.

Answer: C

Correct answer: 2:3. Write tires first: 48:72. The greatest common factor of 48 and 72 is 24, so the ratio simplifies to 2:3.

• A: This is rims to tires, the reverse of the order named.
• B: This compares tires with the total of 120 items, a part-to-whole ratio.
• C (correct): Dividing both terms of 48:72 by their greatest common factor, 24, gives 2:3.
• D: This compares rims with the total of 120 items, not tires with rims.

Answer: A

Correct answer: 16 hours. Find the rate for one unit of work: 1.5 miles / 6 hours = 0.25 mile per hour.

Then time = work / rate =

• A (correct): The rate is 1.5 / 6 = 0.25 mile per hour, so 4 miles take 4 / 0.25 = 16 hours.
• B: This multiplies 4 miles by the rate of 0.25 mile per hour instead of dividing by it.
• C: This adds the extra 2.5 miles to the 6 hours as if each mile took 1 hour.
• D: This multiplies 4 by 6, treating the original job as 1 mile instead of 1.5 miles.

Answer: A

Correct answer: $24.75. Find the unit price first:

per pound. Then price the new amount:

• A (correct): The unit price is 14.85 ÷ 3 = $4.95 per pound, and 5 × 4.95 = $24.75.
• B: This multiplies the package price by 5 instead of the price per pound.
• C: This adds one more pound's price to the 3-pound package, which covers only 4 pounds.
• D: This is the cost of two 3-pound packages, which is 6 pounds.

Answer: C

Correct answer: 18 mph. Its speed is

mile per minute. An hour has 60 minutes, so the speed is

• A: This is the speed in miles per minute, not miles per hour.
• B: This multiplies 0.6 by 60 but forgets the trip took 2 minutes, not 1.
• C (correct): 0.3 mile per minute times 60 minutes gives 18 miles per hour.
• D: This multiplies by the 2 minutes instead of dividing by them.

Answer: A

Correct answer: 15 minutes. Combined rate:

pages per minute.

Time:

• A (correct): Together they print 68 pages per minute, and 1,020 divided by 68 is 15.
• B: This subtracts the rates; machines working on the same job add their rates.
• C: This uses the average rate of 34 pages per minute instead of the combined rate of 68.
• D: This uses only the faster copier and ignores the second machine's work.

Answer: A

Correct answer: $4.00. Total cost:

Total weight: 8 pounds.

Average price: $32 divided by 8 is $4.00 per pound.

• A (correct): The blend costs $18 + $14 = $32 for 8 pounds, which is $4.00 per pound.
• B: $5.00 averages the two prices without weighting; there is three times as much of the cheaper seed.
• C: This multiplies the 6 pounds by the $7 price, matching the amounts with the wrong prices.
• D: $32.00 is the total cost of the blend, not the cost per pound.

Answer: C

Correct answer: 11/16 inch. Use the common denominator 16:

• A: This adds the numerators and denominators straight across (8/24), which ignores the unlike part sizes.
• B: This multiplies the thicknesses; stacking items means adding them.
• C (correct): Renaming 3/8 as 6/16 and adding 5/16 gives 11/16 inch.
• D: This is the difference between the two thicknesses, not their total.

Answer: D

Correct answer: 1 hour 15 minutes. Turn the time head start into distance:

The friend gains

each hour, so she needs

which is 1 hour 15 minutes.

• A: This reads 1.25 hours as 1 hour 25 minutes instead of converting 0.25 hour to 15 minutes.
• B: This is the time measured from the first cyclist's start, not from the friend's start.
• C: This divides the 7.5-mile lead by the friend's full speed of 16 mph instead of by the 6 mph she gains.
• D (correct): A 7.5-mile lead closed at 6 mph takes 1.25 hours, or 1 hour 15 minutes.

Answer: C

Correct answer: 18. The ratio 5:3 has

parts, so each part is

people.

Adults:

Teenagers:

Difference:

which is also $(5-3)\times 9$.

• A: This is the number of adults, an in-between value rather than the difference asked for.
• B: This is the number of teenagers, not how many more adults there are.
• C (correct): The ratio has 8 parts, so each part is 72 / 8 = 9 people; adults are 45, teenagers are 27, and 45 - 27 = 18.
• D: This subtracts the ratio numbers, 5 - 3, without scaling them to the actual group size.

Answer: D

Correct answer: $254.88. Daily charge:

Extra miles:

so mileage is

Before tax:

With 8% tax:

• A: This is the charge before the 8% tax is added.
• B: This charges $0.25 for all 470 miles instead of only the 320 miles over 150.
• C: This taxes only the daily charge and leaves out the mileage charge.
• D (correct): Daily charge $156 plus mileage 320 × $0.25 = $80 gives $236, and $236 × 1.08 = $254.88.

Answer: D

Correct answer: 240 gallons. The added water raised the level from 30 percent to 65 percent, so 84 gallons is 35 percent of the capacity.

Whole equals part divided by percent:

Check: 35 percent of 240 is 84.

• A: This treats 84 gallons as 65 percent of the tank, but 84 gallons is only the added amount, not the final contents.
• B: This treats 84 gallons as 30 percent of the tank, which was the starting level, not the amount added.
• C: This multiplies 84 by 0.35 instead of dividing; the capacity must be larger than the 84 gallons added.
• D (correct): The 84 gallons filled 65 minus 30, or 35 percent, of the tank, and 84 divided by 0.35 is 240.

Answer: C

Correct answer: 500 miles. The first leg takes

If d is the second distance, its time is $d÷250$.

So

Check: 800 miles in 4 hours is 200 miles per hour.

• A: Equal distances put more time at the slower speed: 600 miles in 3.2 hours averages only 187.5 miles per hour.
• B: Flying 200 more miles gives 500 miles in 2.8 hours, about 178.6 miles per hour.
• C (correct): Then she flies 800 miles in 2 + 2 = 4 hours, and 800 divided by 4 is 200 miles per hour.
• D: Flying 400 more miles gives 700 miles in 3.6 hours, about 194.4 miles per hour, still short of 200.

Answer: D

Correct answer: move. Trans means across and fer means carry. To transfer is to move from one place to another, here to a new base in Germany.

• A: Retiring ends a career, but the sentence names a new base, which shows a move.
• B: Training could happen anywhere; the word is built from across plus carry.
• C: Return means going back, while transfer means moving across to a new place.
• D (correct): Trans means across and fer means carry, so to transfer is to carry or move from one place to another.

Answer: D

Correct answer: friendly. Greeting every guest by name with a smile shows a pleasant, warm manner. AMIABLE means friendly; hostile is an opposite and able and aimless are look-alikes.

• A: Hostile is the opposite of amiable.
• B: Able appears inside the word, but meaning skilled or capable makes it a spelling trap.
• C: Aimless shares the letters a, i and m but means without purpose.
• D (correct): Friendly is the meaning of amiable: pleasant and easy to get along with.

Answer: A

Correct answer: forbid. Prohibit means to forbid by rule or law. Forbid matches in meaning and strength; discourage is too mild, punish is a related consequence, and allow is the opposite.

• A (correct): Prohibit means to officially not allow something, which is what forbid means.
• B: This is the opposite of prohibit.
• C: Discouraging only tries to talk someone out of something, which is weaker than a ban.
• D: Punishment may follow breaking a rule, but it is not the same as forbidding.

Answer: C

Correct answer: shore. The partner words "river" and "muddy" select the land sense of BANK. The ground beside a river is its shore, and "the muddy river shore" passes the substitution check.

• A: A bank can be a financial company, but the partner word "river" rules out that familiar sense.
• B: Deposit is connected to the money sense of bank and does not describe a place by a river.
• C (correct): A river's bank is the land along its edge, so "river shore" fits the scene of flood debris.
• D: A bridge crosses a river, but bank names the ground at the water's edge, not a structure.

Answer: C

Correct answer: slow-moving. The ending -ish can mean like or typical of the base. A slug moves very slowly, so sluggish means slow-moving. The phrase "slow to collect their bags" confirms that sense.

• A: This takes slug as a literal animal and pictures its texture rather than its pace.
• B: Energetic means full of energy, the opposite of slow and heavy.
• C (correct): The ending -ish means like, so sluggish means like a slug, that is, slow-moving.
• D: Tired travelers may be grouchy, but sluggish describes slow, heavy movement, not a bad mood.

Answer: C

Correct answer: reduction in size. Cover -age to find shrink, to become smaller. The ending -age forms a noun naming a result or amount, as in breakage. So shrinkage is a reduction in size.

• A: Shrink is the verb base; the target is a noun naming the result.
• B: Stretching out makes material larger, the opposite of the change described.
• C (correct): The ending -age names a result or amount, so shrinkage is the amount a thing gets smaller.
• D: Hot water can fade colors, but shrinkage is about size, not color.

Answer: C

Correct answer: exhausting. Although signals that grueling stands against excellent pay, so it is negative, and the shifts wore people down. Grueling describes the cause of tiredness, so exhausting fits, while exhausted describes the workers' state.

• A: Exhausted names the state of the tired workers, but grueling describes the shifts that cause it; this swaps cause for effect.
• B: Boring means dull; the sentence stresses physical strain, not lack of interest.
• C (correct): Grueling describes a task so hard that it wears people out, matching long shifts in heat that wore down the crew.
• D: The contrast word although sets the shifts against the good pay, so grueling must be negative.

Answer: C

Correct answer: praised. The passengers kept thanking the driver for their safety, so the word must be positive. Cut the negative and neutral choices, and praised remains. COMMENDED means praised.

• A: This has the wrong tone; the passengers were grateful, not finding fault.
• B: Nothing mentions money; this adds a fact the sentence does not give.
• C (correct): Thanking someone repeatedly for keeping people safe is strongly positive, and praised has that same charge.
• D: Questioning is neutral or doubtful, which does not match repeated thanks.

Answer: C

Correct answer: ordinary. The contrast with exciting fieldwork tells you the desk job lacks excitement. MUNDANE means everyday or dull, so ordinary is the closest meaning.

• A: Demanding means hard, which is a different idea from being dull and routine.
• B: Nothing in the sentence says how long the job will last.
• C (correct): Ordinary fits: the desk job is plain and routine compared with exciting fieldwork.
• D: Danger is not suggested by a desk job and adds an unsupported story.

Answer: D

Correct answer: successful. Effective describes something that produces the intended result, and effectiveness is that quality. The falls dropped to zero, so the paint worked. Successful fits.

• A: Influenced is the usual meaning of affected, a different word that is often confused with effect.
• B: Temporary means short-lived; the sentence describes results, not how long the paint lasted.
• C: Noticeable means easy to see, but effective says the paint did its job, not merely that it was visible.
• D (correct): Effective means producing the intended result, and fewer falls is exactly the result the paint was meant to bring.

Answer: C

Correct answer: meals. The fixed pairing "room and board" selects the sense of BOARD meaning food provided with lodging. Board here means meals.

• A: A board is a piece of lumber, but a job would not pay workers in planks.
• B: A board can be a governing group, which is not something a job offers as pay.
• C (correct): The collocation "room and board" means a place to sleep and daily meals.
• D: Boarding a bus or plane is a different sense; "room and board" does not mean travel.

Answer: B

Correct answer: smugly unconcerned. The past success leads the crew to stop guarding against risk, and the sentence treats that as a fault. Complacent means self-satisfied to the point of ignoring danger, so smugly unconcerned matches; confident has the wrong tone and experienced names the background, not the attitude.

• A: Confident is positive and implies justified self-belief; the sentence criticizes the crew for dropping a safety check.
• B (correct): Complacent describes being so pleased with past success that one stops watching for danger, which is why the crew skipped its checks.
• C: Ten years shows experience, but that is the background, not the attitude; experienced workers can still be careful.
• D: Nothing suggests tiredness; the crew stopped checking because it felt too safe, not too worn out.

Answer: A

Correct answer: Planning ahead. Fore- means before, and sight here means seeing or judging. Packing batteries for a delay that had not happened yet is judging needs ahead of time, which is planning ahead.

• A (correct): Fore- means before, so foresight is seeing and preparing for a need before it arrives, as the extra batteries show.
• B: Sharp eyesight takes the base sight literally and ignores fore-, the before idea.
• C: Looking back describes hindsight or retro-, the opposite direction in time.
• D: Good luck credits chance, but packing extra batteries was a deliberate choice made in advance.

Answer: A

Correct answer: shy. "Although" sets up a surprise: his confident orders were unexpected. That means in meetings he lacked confidence, which matches the clue that he rarely offered his views. DIFFIDENT means shy or lacking self-confidence.

• A (correct): The "although" surprise only works if he usually lacked confidence; quiet, hesitant behavior matches shy.
• B: This describes how he acted during the exercise, the surprising half of the sentence, not how he acted in meetings.
• C: This look-alike word means not caring, but the sentence shows hesitancy, not a lack of interest.
• D: Honesty is never mentioned, so this adds a fact the sentence does not support.

Answer: A

Correct answer: suggested. The speaker implies, and the listener infers. The foreman never said it outright but sent a signal, so implied means suggested. Concluded would describe the workers who read the signal.

• A (correct): To imply is to hint at something without stating it, as the foreman did by posting overtime instead of saying anything.
• B: Concluded is the meaning of inferred, which is what a listener does; the foreman is the one sending the hint.
• C: Announced means stated openly, but the sentence says he never said it.
• D: Denied means said it was not true, the opposite of signaling that the job was behind.

Answer: C

Correct answer: The airstrip for training pilots opened. Use the dates as anchors and ignore the order of the sentences: 1921 hospital, 1943 airstrip, 1958 clinic, 1975 museum. The second event is the airstrip, even though the museum is described first.

• A: At 1921, the hospital is the earliest date, so it came first, not second.
• B: The clinic dates to 1958, which makes it third in the order.
• C (correct): Ordered by year: hospital (1921), airstrip (1943), clinic (1958), museum (1975), so the airstrip is second.
• D: The museum is mentioned first, but 1975 is the latest year, so it happened last.

Answer: D

Correct answer: Anyone caught in a rip current should swim parallel to the shore. An observation describes what is; a recommendation says what should be done. The only sentence that tells readers how to act is the beach patrol's advice to swim parallel to the shore.

• A: This reports what lifeguards have seen, so it is an observation.
• B: This describes what a rip current is, which is an observation, not advice.
• C: This describes how swimmers usually behave, so it is an observation even though it explains a mistake.
• D (correct): The beach patrol "advises" this action, so it tells readers what should be done, which is a recommendation.

Answer: A

Correct answer: Each mower offers advantages that the other one lacks. Each mower wins on some features: the reel mower on noise, fuel and price, the gas mower on tall grass and speed. Because the flyer recommends neither, the best summary is a trade-off, not a winner.

• A (correct): The reel mower is quieter, cheaper and fuel-free, while the gas mower handles tall grass and large yards better, a true trade-off.
• B: The flyer makes no recommendation, so naming an overall winner invents a judgment the passage avoids.
• C: Handling tall grass is only one criterion; the gas mower also costs more, is louder and needs upkeep.
• D: Noise is only one of several differences; price, fuel, upkeep and grass height also differ.

Answer: B

Correct answer: To raise doubts about whether the evidence supports the billboard's claim. Identify which direction the details push. Every point after the billboard's claim limits its evidence: a single year, an unusually high starting point and missing crime types. The closing sentence keeps an open mind about Ashford but calls the evidence thin, so the purpose is to question the claim.

• A: The author accepts the 30 percent drop as real but does not praise it; the details all push toward doubt, not celebration.
• B (correct): The author points out that the figure covers one year, follows an unusual high and leaves out other crimes, all of which question the claim's support.
• C: The author says Ashford may well be safe; the passage questions the billboard's evidence, not the city's actual safety.
• D: The billboard's location is a minor detail; the passage gives no risk or advice for drivers.

Answer: A

Correct answer: frank and honest. The words by contrast set Dr. Okafor against doctors who used vague phrases and changed the subject. The examples that follow, telling families exactly what tests showed and admitting what she did not know, point to open, direct speech. So candid means frank and honest.

• A (correct): Telling families exactly what the results showed and admitting what she did not know is open, honest behavior, the opposite of the vague doctors.
• B: Softening bad news is what the other doctors did; by contrast signals that Dr. Okafor did something different, not something gentler.
• C: Patients may have trusted her for many reasons, but the examples describe how she spoke, not her medical skill.
• D: This describes the other doctors' vague phrases; the contrast clue says candid means the opposite.

Answer: C

Correct answer: It explains several causes of a single effect. The passage names one effect, a narrower beach, and then gives three causes: stronger storms, the jetty and the removal of dredged sand. It never proposes or describes a fix, so it is cause-and-effect, not problem-and-solution.

• A: The shrinking beach is a problem, but the passage reports no response or fix, only the reasons it is happening.
• B: No term is defined or classified; the passage explains why something is happening.
• C (correct): The narrowing beach is the effect, and storms, the jetty and hauled-away sand are the causes the geologists list.
• D: The passage mentions twenty years only as background; its sentences are arranged as reasons, not as dated events.

Answer: B

Correct answer: Fewer ships struck the reef than in the ten years before. Sort the details: fog groundings are the cause, warning captains is the purpose, and the drop from seven ships to one is the outcome. The question asks for the result, so the answer is that fewer ships struck the reef. Saying none struck it goes beyond the passage.

• A: This is the cause that led the keepers to add the whistle, not what happened afterward.
• B (correct): The passage reports one ship striking the reef in the following ten years, compared with seven before, which is the outcome.
• C: This describes what the keepers intended the whistle to do, its purpose, rather than the result the passage reports.
• D: This overstates the outcome; the passage says one ship still struck the reef.

Answer: A

Correct answer: Some respondents found the weight room crowded early in the morning. Find the quantity word for each claim: "many" for the weight room and "a few" for the cardio machines. A correct inference stays on the passage's rung or steps down, so "some respondents" is safe, while "most" and "every hour" climb higher than the evidence allows.

• A (correct): "Many" respondents reported crowding, so "some" stays on the same rung of the quantity ladder or below it.
• B: This climbs from "many" to "most"; the passage never says the complaints came from a majority.
• C: Only "a few" mentioned the cardio machines, so "most" jumps several rungs up the ladder.
• D: The complaints are limited to 5 to 7 a.m.; the passage says nothing about crowding at other hours.

Answer: C

Correct answer: Captain Ortiz. Test each possible referent against the passage's logic. The person who felt vibration in the pedals during the last flight must have been flying, and the sentence's subject, Ortiz, is the pilot asking for another check. Delgado gave the inspection report, and Kim appears only later, so she means Captain Ortiz.

• A: Delgado is the nearest earlier female name, but she reported the helicopter had passed inspection; the person who felt the pedals in flight is the pilot.
• B: Kim is not introduced until the third sentence and is never described as flying the helicopter.
• C (correct): She is the person who felt a vibration in the pedals during the last flight, which fits the pilot, Ortiz, who is also the subject of the sentence asking for the check.
• D: No flight instructor appears in the passage; this invents a referent.

Answer: B

The passage reports a pattern (fewer vandalism cases near gardens) and then explains why the cause cannot be pinned down. A correct main idea must keep that same careful strength, so it states the link without claiming that gardens, or block associations, caused the drop.

• A: This upgrades a link into a proven cause, repeating the residents' opinion while ignoring the department's stated doubt.
• B (correct): This keeps both halves of the passage: the pattern that was found and the department's warning that the cause is unclear.
• C: This swaps one unproven cause for another; the department said it could not tell which factor mattered.
• D: This is an accurate supporting detail, but it explains only the caution and leaves out the finding itself.

Answer: D

Correct answer: 4. Terms are the pieces joined by plus or minus signs. Here they are $4x^3$, $-2x$, $7y$ and $-1$, so there are 4 terms. A constant counts as a term.

• A: This counts only the terms with variables and skips the constant -1.
• B: This counts something extra, such as the exponent, as a separate term.
• C: This counts only the different letters, x and y, instead of the terms.
• D (correct): Plus and minus signs split it into four terms: 4x^3, -2x, 7y and -1.

Answer: B

Correct answer: 53°. The interior angles of a triangle add to 180°, so the third angle is

°.

• A: 127° is the sum of the two given angles, not the third angle.
• B (correct): 180 - 39 - 88 = 53°.
• C: This subtracts from 360°, but a triangle's angles total 180°.
• D: This is an arithmetic slip; 39 + 88 + 63 = 190, not 180.

Answer: A

Correct answer: Infinitely many. One equation in two unknowns allows endless pairs, such as (2, 10), (5, 7) and (15, −3). Its graph is a whole line of solutions; a second independent equation is needed to narrow the answer to one pair.

• A (correct): Every point on the line x + y = 12, such as (5, 7) or (0, 12), is a solution.
• B: One solution needs a second independent equation; alone, many pairs add to 12.
• C: A linear equation never has exactly two solutions; (1, 11), (6, 6) and (12, 0) already give three.
• D: Many pairs, such as (6, 6), make x + y = 12 true.

Answer: A

Correct answer: −8. Divide the absolute values,

The signs are different, so the quotient is negative: −8 feet per stage.

• A (correct): 48 ÷ 6 = 8, and a negative divided by a positive is negative.
• B: The size is right, but unlike signs give a negative quotient.
• C: This subtracts 6 from 48 instead of dividing.
• D: This adds the numbers instead of dividing them.

Answer: D

Correct answer: 16 m. Set up the trapezoid formula and solve for the missing base.

Multiply both sides by 2 and divide by 9:

so b = 16 m.

• A: This is the sum of both bases; the known 10 m base still has to be subtracted.
• B: This forgets the one half: 117 / 9 = 13 is taken as the base sum, and 13 - 10 = 3.
• C: This divides the area by the height as if the figure were a rectangle.
• D (correct): Doubling 117 and dividing by 9 gives 26 for the sum of the bases, and 26 - 10 = 16.

Answer: C

Correct answer:

Solve each part.

gives 3x ≤ 15, so x ≤ 5. An and statement keeps only the overlap:

• A: The endpoints are right, but the inclusion is swapped: −3 is excluded (>) and 5 is included (≤).
• B: This adds 1 to −5 instead of subtracting it, getting 2x > −4.
• C (correct): The first gives x > −3 and the second gives x ≤ 5; and means the overlap.
• D: This subtracts 4 from 11 instead of adding 4, getting 3x ≤ 7.

Answer: C

Correct answer: 77°. Angles outside the parallel lines on the same side of the transversal are same-side exterior angles, and for parallel lines they are supplementary. The other angle is

°.

• A: Same-side exterior angles are supplementary, not equal; it is alternate exterior angles that are equal.
• B: This subtracts from 90°, but the pair must total 180°.
• C (correct): Same-side exterior angles add to 180°, so the other angle is 180 - 103 = 77°.
• D: This subtracts from 360°, which is the rule for angles around a point.

Answer: B

Correct answer: 80. The gaps 3, 5, 7, 9 rise by 2 each time, so the pattern is quadratic. Testing $n^2-1$:

The 9th term is

• A: This is only the next term, the 6th; the question asks for the 9th.
• B (correct): The rule is n² − 1, and 81 − 1 = 80.
• C: This is the 8th term, 8² − 1, one position short.
• D: This is the 10th term, 10² − 1, one position too far.

Answer: D

Correct answer: 60π square feet. Leave out the missing faces. The radius is 2 ft, and only the curved side is metal.

• A: This adds two circular ends, but a duct open at both ends has no ends.
• B: This adds one circular end that the open duct does not have.
• C: This uses the diameter 4 as the radius in 2 pi r h.
• D (correct): Only the curved side exists: 2 pi times 2 times 15 is 60 pi.

Answer: D

Correct answer: 11.4 ft. The side of a square is the square root of its area. Since

$\sqrt{130}$ is between 11 and 12, and closer to 11. Only 11.4 ft fits, and

• A: This is below 11, but 11 squared is only 121, which is already less than 130.
• B: This is above 12, but 12 squared is 144, which is already more than 130.
• C: This divides the area by 2 instead of taking the square root.
• D (correct): 130 lies between 121 and 144, so the side is between 11 and 12 ft, and 11.4 squared is about 130.

Answer: C

Correct answer: x = 7. Combine like terms on the left first:

Subtract 9: 3x = 21. Divide by 3: x = 7. Check:

• A: This comes from treating −x as +x, giving 5x + 9 = 30.
• B: This comes from adding 9 to 30 instead of subtracting it, giving 3x = 39.
• C (correct): Combining like terms gives 3x + 9 = 30, so 3x = 21 and x = 7.
• D: This ignores the constants 7 and 2 and solves 3x = 30.

Answer: A

Correct answer: y⁵. Multiply exponents for the power of a power:

Add exponents when multiplying:

Subtract when dividing:

• A (correct): Power of a power gives y^12, multiplying by y^-2 gives y^10, and dividing by y^5 leaves y^5.
• B: This treats the -2 exponent as +2, giving 12 + 2 - 5 = 9.
• C: This adds the bottom exponent instead of subtracting it: 12 - 2 + 5 = 15.
• D: This adds 3 and 4 for the power of a power, getting y^7, so 7 - 2 - 5 = 0 and y^0 = 1.

Answer: C

Correct answer: 44. For three equally spaced integers the sum is three times the middle one, so the middle is

Consecutive even integers are 2 apart, so they are 44, 46 and 48, and

The smallest is 44.

• A: 46 is the middle integer, not the smallest.
• B: This treats them as ordinary consecutive integers (45, 46, 47), but the question asks for even integers.
• C (correct): The middle integer is 138 ÷ 3 = 46, so the even integers are 44, 46 and 48.
• D: 48 is the largest of the three integers.

Answer: C

Correct answer: 54 square units. Two vertices share

giving a horizontal leg of

Two share

giving a vertical leg of

• A: This multiplies the legs but forgets the one half.
• B: This uses the 15 unit slanted side as the height; the height must be perpendicular to the base.
• C (correct): The horizontal leg is 9 and the vertical leg is 12, and half of 9 times 12 is 54.
• D: This takes half of 12 times 15, again using the slanted side instead of a leg.

Answer: C

Correct answer: 20π cm. The perpendicular from the center cuts the chord into two 8 cm halves. The radius to an end of the chord is the hypotenuse of a right triangle with legs 8 and 6.

The circumference is 2π(10) = 20π cm.

• A: This adds 8 and 6 to get a radius of 14; the radius is the hypotenuse, not the sum of the legs.
• B: This is the area, π times 10 squared, not the circumference.
• C (correct): Half the chord, 8, and the distance, 6, give a radius of 10, so C = 20π.
• D: This treats the chord as a diameter, but a chord 6 cm from the center does not pass through it.