AFQT Core Practice 5: Decimals, Patterns and Suffixes

Answer: C

Correct answer: 900 flyers. Total = rate × time =

flyers. Minutes cancel, leaving flyers.

• A: This adds the rate and the time instead of multiplying.
• B: This divides the rate by the time; the total comes from multiplying.
• C (correct): Rate times time: 75 times 12 is 900.
• D: This adds an extra zero; 75 times 12 is 900.

Answer: D

Correct answer: 4 hours 30 minutes. Time equals distance divided by speed:

The 0.5 hour is

so the trip takes 4 hours 30 minutes.

• A: This reads the decimal 0.5 hour as 50 minutes instead of multiplying it by 60.
• B: This reads the decimal 0.5 hour as 5 minutes instead of 30 minutes.
• C: This multiplies 13.5 by 3 instead of dividing the distance by the speed.
• D (correct): 13.5 ÷ 3 = 4.5 hours, and half an hour is 30 minutes.

Answer: D

Correct answer: 3,516. A number is divisible by 4 when its last two digits form a multiple of 4.

Only 3,516 passes, because

Being even is not enough.

• A: It is even, but its last two digits, 38, are not a multiple of 4.
• B: It ends in 0, but its last two digits, 10, are not a multiple of 4.
• C: It is even, but its last two digits, 22, are not a multiple of 4.
• D (correct): Its last two digits, 16, form a multiple of 4.

Answer: B

Correct answer: 0.61. Pad every value to three places and compare with 0.600: 0.610, 0.599, 0.590, and 0.065. Only 0.610 is greater than 0.600, so 0.61 passes.

• A: 0.599 is just below 0.600, even though it has more digits.
• B (correct): Padding gives 0.610, which is greater than 0.600.
• C: Padded to 0.590, this is less than 0.600.
• D: This is about one tenth of 0.6; the 6 here is in the hundredths place.

Answer: D

Correct answer: $49. Divide the total pay by the hours: 1,176 ÷ 24. Since

which is 24 too many, the quotient is

Check with the inverse:

• A: 48 × 24 = 1,152, which is $24 short of the total paid.
• B: 59 × 24 = 1,416, which is more than the total; a digit slipped during the division.
• C: 47 × 24 = 1,128, which falls $48 short of the total paid.
• D (correct): 1,176 ÷ 24 = 49, and the check 49 × 24 = 1,176 confirms it.

Answer: C

Correct answer: 80 percent. To find what percent one number is of another, divide part by whole:

Multiply by 100 to get 80 percent.

• A: This divides the whole by the part, 35 / 28, which flips the comparison.
• B: This is the percent left unfinished, 7 / 35, not the percent finished.
• C (correct): Part divided by whole is 28 / 35 = 0.80, or 80 percent.
• D: This is the number of unfinished inspections, a count rather than a percent.

Answer: A

Correct answer: 45 bags. Set up bags over feet on both sides:

Look for a whole-number scale factor before cross-multiplying:

bags. Check:

• A (correct): Since 80 feet is 5 times 16 feet, the crew needs 9 × 5 = 45 bags.
• B: This adds 64 (the difference 80 - 16) to 9 instead of multiplying by a scale factor.
• C: This flips the ratio to feet per bag, computing about 80 × 16 ÷ 9.
• D: This is the scale factor 80 ÷ 16, not the number of bags.

Answer: B

Correct answer: 30. Divide the total by the dose size: $7.5÷0.25$. Move both decimal points two places right to make the divisor whole:

doses. Check:

• A: This shifts the divisor two places but the dividend only one place (75 divided by 25), which changes the answer.
• B (correct): Shifting both decimal points two places gives 750 divided by 25, which is 30.
• C: This shifts the dividend's decimal point too far, making the dividend 7,500 instead of 750.
• D: This multiplies 7.5 by 0.25 instead of dividing the total by the size of one dose.

Answer: B

Correct answer: 2 hours 24 minutes. Add the rates:

of the lot per hour.

Invert:

Convert the decimal: 0.4 x 60 = 24 minutes, so 2 hours 24 minutes.

• A: This reads 2.4 hours as 2 hours 40 minutes; 0.4 hour is 0.4 x 60 = 24 minutes.
• B (correct): The combined rate is 5/12 of the lot per hour, so the time is 12/5 = 2.4 hours, and 0.4 hour is 24 minutes.
• C: This averages the two times; the team must beat the faster driver's 4 hours.
• D: This adds the times instead of adding the rates.

Answer: A

Correct answer: $1,219.00. Overtime rate:

Regular pay:

Overtime pay:

Gross pay:

• A (correct): Regular pay is 40 × 26.50 = $1,060 and overtime pay is 4 × 39.75 = $159, for a total of $1,219.
• B: This pays all 44 hours at the regular rate and ignores the overtime premium.
• C: This pays all 44 hours at the overtime rate of $39.75; only the 4 extra hours earn it.
• D: This pays the 4 extra hours at only half the regular rate ($13.25) instead of 1.5 times it.

Answer: A

Correct answer: 3/4 liter. The smallest common denominator for 3, 4 and 6 is 12.

• A (correct): With denominator 12 the amounts are 4/12 + 3/12 + 2/12 = 9/12, which simplifies to 3/4.
• B: This adds the numerators and the denominators, ignoring that the parts are different sizes.
• C: This multiplies the three amounts; combining liquids calls for addition.
• D: This adds only the first two amounts and leaves out the 1/6 liter.

Answer: B

Correct answer: 12:15 p.m. Moving apart, the distances add, so the gap grows at

Time:

= 3 hours 15 minutes. From 9:00 a.m., that is 12:15 p.m.

• A: This reads 3.25 hours as 3 hours 25 minutes; 0.25 hour is 15 minutes.
• B (correct): The gap grows at 55 + 65 = 120 mph, so 390 ÷ 120 = 3.25 hours, or 3 hours 15 minutes after 9:00 a.m.
• C: This uses only the faster truck's 65 mph, as if one truck covered the whole 390 miles.
• D: This divides by the average of the two speeds (60 mph) instead of their sum.

Answer: D

Correct answer: 81. Multiply each score by its weight and add:

The weights are counts, so divide by their sum,

• A: 80 is the simple average of the three scores, which ignores that the final counts three times.
• B: This gives the weight of 3 to homework and 1 to the final, reversing the weights.
• C: This divides the weighted total of 486 by 3 scores instead of by the sum of the weights, 6.
• D (correct): The weighted total is 80 + 148 + 258 = 486, and 486 divided by the total weight of 6 is 81.

Answer: B

Correct answer: 60. The number of bolts does not change and stays 4 parts in both ratios, so the parts are the same size. Nuts go from 3 parts to 5 parts, a change of 2 parts, which equals the 30 added nuts.

One part is

so bolts =

Check: 60:75 = 4:5.

• A: This is the original number of nuts, 3 × 15, not the bolts.
• B (correct): Bolts stay at 4 parts while nuts grow from 3 to 5 parts, so 2 parts = 30, one part = 15, and bolts = 60.
• C: This is the number of nuts after the 30 are added, 5 × 15.
• D: This multiplies 30 by 4, treating the 30 added nuts as one part instead of two.

Answer: C

Correct answer: $55.00. Multiply the change factors: the sale price is

times the cost.

Undo that by dividing:

so the ladder cost $55. Check: 55 times 1.5 is 82.50, and 20 percent off 82.50 is 66.

• A: This comes from combining 50 percent up and 20 percent down into a 30 percent increase and dividing by 1.30; successive percents cannot be added.
• B: This takes 20 percent off the $66 sale price, but the discount was figured on the marked price, so the change must be undone by dividing.
• C (correct): The sale price is 1.50 times 0.80, or 1.20 times the cost, and 66 divided by 1.20 is 55.
• D: This undoes only the 50 percent markup and ignores the 20 percent discount that came after it.

Answer: D

Correct answer: assigned station. The partners "sentry," "leave," and "next guard arrived" point to a place of duty. POST here means assigned station.

• A: Mail delivery is a common meaning of post, but a sentry cannot leave his mail delivery while on duty.
• B: A post can be an upright pole, yet the order is about where the sentry stands watch.
• C: Posting a message online is a different sense; a guard does not stand at a message.
• D (correct): A sentry's post is the spot he is assigned to guard, which matches "not to leave" until relieved.

Answer: B

Correct answer: usual. Routine means regular, ordinary or done as standard practice, as in a routine check. Usual matches; boring is an association, quick is unrelated, and rare is the opposite.

• A: This is the opposite of something done regularly.
• B (correct): Routine means done as a regular or normal practice, which is what usual means.
• C: Routine tasks can feel dull, but that is an association, not the meaning.
• D: Speed has nothing to do with whether something is routine.

Answer: A

Correct answer: written account of a person's life. Bio means life and graph means write. A biography is a written account of a person's life, here the life of a medal recipient.

• A (correct): Bio means life and graph means write, so a biography is the written story of someone's life.
• B: Photos need the root photo, light; graph alone means writing, and bio adds life.
• C: This is biology; it shares bio but ends in -logy, study, rather than graph, write.
• D: Maps belong to geography; this word has bio, life, not geo, earth.

Answer: B

Correct answer: sour. Cover -ic to find acid. The ending -ic forms an adjective meaning relating to or like the base, so acidic means like acid, sharp or sour in taste.

• A: Acid is the noun base; the target is an adjective, so the base cannot replace it.
• B (correct): The ending -ic means relating to or having the quality of, so acidic means having the sharp taste of acid, which is sour.
• C: Sweet is the opposite taste of something acidic.
• D: Bitter is a different harsh taste, not the sharp tang of acid.

Answer: B

Correct answer: craftsperson. The commas set off an appositive that renames ARTISAN: a skilled worker who builds things by hand. Matching that built-in definition gives craftsperson.

• A: Selling is related to the trade but is not what the renaming phrase describes.
• B (correct): The phrase set off by commas renames the artisan as a skilled worker who makes things by hand, which is a craftsperson.
• C: An apprentice is a learner, but the phrase says the person is already skilled.
• D: A designer plans items; the phrase stresses building them by hand, not drawing them up.

Answer: D

Correct answer: eager to win. Compete means to try to win against others, and the -itive ending makes an adjective for someone who tends to do that. Turning runs into races shows the desire to win. Competent (capable) is a false friend.

• A: Capable is the meaning of competent, a look-alike that refers to skill, not the wish to beat others.
• B: Cooperative means working together, the opposite of racing against teammates.
• C: Being well trained is about ability; the sentence is about his attitude toward winning.
• D (correct): Competitive describes someone who wants to beat others, shown by turning every run into a race.

Answer: D

Correct answer: blockage. Ob means in the way and struct means build or arrange. An obstruction is something in the way that blocks passage, like a clog in a drain.

• A: This uses struct, build, too literally and ignores ob, in the way.
• B: A leak lets water out; the word means something that stops the flow.
• C: This is instruction, a look-alike word with a different prefix.
• D (correct): Ob means against or in the way and struct means build, so an obstruction is something placed in the way, which blocks a drain.

Answer: D

Correct answer: managed. The word's object is "the diner," a business, and "by the same family" names the people in charge. Run a business means manage it.

• A: Sprinting is the familiar sense of run, but a family cannot sprint a diner.
• B: Water can run, yet a diner is not a liquid.
• C: A road can run a distance, but the object here is a business.
• D (correct): To run a business is to operate it, and "managed by the same family" fits.

Answer: D

Correct answer: love of country. Patriot plus -ism names the attitude of a patriot, which is devotion to one's country. Choices that name a person, such as patriot, belong with -ist-type endings, not -ism.

• A: A patriot is a person; -ist and similar endings name people, but -ism names the idea or attitude.
• B: Nationality is the country a person belongs to, not a feeling about it.
• C: Bravery in combat is courage; a patriot may be brave, but the word names devotion to country.
• D (correct): The ending -ism names an attitude or belief, so patriotism is the attitude of a patriot: love of country.

Answer: C

Correct answer: moderate. Reasonable has a sense of fair or moderate, especially for prices and requests. The clue that it was close to what others charged rules out excessive. Logical belongs to rational, a different family member.

• A: Logical is closer to rational; a price is not described as following a chain of logic.
• B: Excessive means too high, the opposite of a price in line with other shops.
• C (correct): Reasonable describes a price that is fair and not extreme, and matching other shops shows it was moderate.
• D: Explained comes from the noun reason, a cause or explanation, but the sentence describes the size of the price.

Answer: C

Correct answer: brief and clear. Concise means brief but complete and to the point. The contrast marker unlike sets the word against rambling, so the answer must involve shortness; complete is only half the meaning.

• A: The report does cover every key fact, but concise stresses brevity, which is what contrasts with rambling.
• B: Long and wordy describes the rambling first draft, the opposite of the final report.
• C (correct): Concise means saying a lot in few words, matching a half-page report that still covers every key fact.
• D: A report that covers every key fact is not careless; short does not mean sloppy.

Answer: B

Correct answer: Impartial. Use context first: he was chosen because neither company had hired him, so he has nothing to gain. Dis- (not) plus interested (having a stake) gives impartial; do not confuse it with uninterested, which means bored.

• A: Bored matches uninterested, a look-alike word; dis- here removes a personal stake, not attention.
• B (correct): Dis- means not, and interested here means having a stake; a referee with no stake in either side is impartial.
• C: Unpaid confuses a financial interest with a salary; the sentence is about having no tie to either side.
• D: Unqualified is a negative judgment about skill, but the sentence explains his neutrality, not his ability.

Answer: C

Correct answer: furious. "Not merely annoyed" signals a stronger degree of the same feeling, and the red face and shaking voice confirm intense anger. LIVID means furious here, not the color sense of the word.

• A: This is too weak; "not merely annoyed" says his feeling went beyond annoyance.
• B: Livid can describe a pale or bluish color, but his face was red, so that sense does not fit.
• C (correct): A red face, shaking voice and the phrase "not merely annoyed" show anger far stronger than annoyance.
• D: Worry is a different feeling; demanding answers with a shaking voice shows rage.

Answer: B

Correct answer: inborn. The contrast marker although sets never taking a lesson against having a sense of rhythm, so the skill was not learned. INNATE means present from birth, so inborn is the match; inner only shares letters.

• A: Trained is the opposite of what the sentence shows: she never took a lesson.
• B (correct): Inborn fits: the rhythm sense was natural, present without any lessons.
• C: An impressive skill may be rare, but the contrast clue is about where the skill came from, not how uncommon it is.
• D: Inner is a look-alike from the in- start; it means inside, not natural from birth.

Answer: A

Correct answer: scheming. All four choices touch on thinking, but the sentence condemns the broker for using friendship to profit. Calculating adds that negative edge of plotting for personal gain, so scheming is the only choice that matches both meaning and tone.

• A (correct): Calculating here means coldly planning for one's own advantage, which fits befriending people only to profit from them.
• B: Astute means shrewdly perceptive and is usually praise; it lacks the selfish motive the sentence clearly shows.
• C: This is the literal sense of calculate; the sentence is about motive and manipulation, not arithmetic.
• D: Intelligent is the broad, neutral word for mental ability and misses the negative judgment of exploiting others.

Answer: C

Correct answer: The storm window added outside the original. To resolve a reference word, look at the closest earlier noun that makes sense. The sentence before describes storm windows as a second layer of glass mounted outside the original, so This extra layer refers to the storm window.

• A: The single pane is the original glass, not something extra that was added.
• B: The frame is mentioned only as the place where drafts leak in, not as a layer.
• C (correct): The sentence just before defines a storm window as a second layer of glass, which This extra layer points back to.
• D: The air pocket is what the layer traps, so it cannot be the layer itself.

Answer: B

Correct answer: Bleeding trapped air from a radiator helps it fill with hot water and heat evenly. For a process passage, ask why the steps are being described. The opening names the problem (cool radiators from trapped air), the steps release the air, and the last sentence gives the result: radiators heat evenly. The main idea is the purpose of the whole process, not any single step.

• A: This is one step of the process, not the reason the whole process is described.
• B (correct): This states the purpose that unites the steps, which the final sentence makes clear, and it covers the problem described at the start.
• C: The passage never compares heating systems; this brings in outside ideas.
• D: The passage treats the trickle of water as a normal signal to close the valve, so this reverses its meaning.

Answer: C

Correct answer: The lights were installed partly to reduce electricity costs. Words like made to and so that signal a purpose, which is what someone intends, not what has been measured. The passage gives two purposes and no reported result, since the bill comparison is still planned. Only the statement about the intended savings is supported.

• A: Lowering the bill is the stated goal, but no result is reported; the comparison of bills has not happened yet.
• B: The passage says nothing about tenant requests; the reasons given come from the manager.
• C (correct): The manager said the change was made to lower the electric bill, which is a stated purpose.
• D: The comparison is only planned for December, so no findings exist yet.

Answer: D

Correct answer: It admits a point in favor of online classes before the writer limits it. The phrase it is true that marks a concession. The writer grants that online tools can teach some things, then turns with still to limit that point and argue for keeping shop hours. The writer's own main claim comes in the last sentence.

• A: The main claim is in the last sentence, that hands-on shop hours should remain required.
• B: Admitting one strength of online lessons is not agreement; the writer goes on to argue against going fully online.
• C: No study or results are reported; the sentence is the writer's concession about what online tools can teach.
• D (correct): The words it is true that grant that online lessons teach some content well, and still then qualifies that point.

Answer: D

Correct answer: Campers at Pine Hollow will not find hot showers there. The word only marks an exclusive feature. Saying only Lakeshore has hot showers rules out showers at Pine Hollow and Bluff Top, so a camper at Pine Hollow will not find them.

• A: All three campgrounds have fire rings; Bluff Top's exclusive feature is its ridge view.
• B: Pine Hollow also allows RVs, so RV access is not exclusive to Lakeshore.
• C: Bluff Top is tents only; the RV sites are at Pine Hollow and Lakeshore.
• D (correct): Because only Lakeshore has hot showers, the other two campgrounds, including Pine Hollow, lack them.

Answer: A

Correct answer: trained heating and cooling technicians who service the company's units. Audience shows in what the writer assumes readers know and what the writer asks them to do. Technical terms are left undefined, readers are told to change how they charge systems and to finish a module before their next service call, so the text addresses the company's working technicians.

• A (correct): The passage leaves terms like superheat, subcooling and line set unexplained and refers to service calls, which signals readers already working in the trade.
• B: The passage gives no buying advice and assumes technical skills a typical homeowner would not have.
• C: Beginners would need terms such as superheat and subcooling explained; the writer assumes readers already know them.
• D: The passage gives work instructions, not a policy argument, and the switch to A2L is presented as already happening.

Answer: B

Correct answer: managed by using what was available. Read the phrase as a unit, not one word at a time. The truck was late, so the cooks used the canned beans, rice and powdered eggs already in the tent, and nobody went hungry. Made do with means managed by using what was available.

• A: This focuses on made as in made food, ignoring the whole phrase; the fresh supplies were exactly what had not arrived.
• B (correct): With the truck delayed, the cooks used the canned and dry food already on hand, and nobody went hungry.
• C: The passage says the meals came from the storage tent, so the cooks used that food rather than refusing it.
• D: Nobody went hungry, which means the cooks kept serving meals before Thursday instead of waiting.

Answer: D

Correct answer: Cracked paint likely let salt spray reach the bolts. Sort the log into three kinds of statements. What Lin found (rust streaks) is an observation, the sentence with "probably" offers an interpretation of why the rust appeared, and the sentence with "should" is a recommendation. The question asks for the interpretation.

• A: This is the observation, reported as what Lin found during the inspection.
• B: This is a recommendation, signaled by "should," urging action rather than explaining a cause.
• C: The log never makes this prediction; it adds an outcome the writer does not state.
• D (correct): The word "probably" marks this as an interpretation offered to explain the rust, not as something Lin directly observed.

Answer: A

Correct answer: The radiosonde measures wind speed as it rises. This is a negative question, so three choices are in the passage and the answer is the one that is not. The parachute, the swelling balloon, and the mail-back label are all stated. The passage names only temperature, humidity, and pressure as measurements, so the claim about wind speed is the one it does not make, even if it sounds true from outside knowledge.

• A (correct): The passage lists only temperature, humidity, and air pressure; wind speed may come from background knowledge, but the passage never states it, so this is the unstated item.
• B: The passage says that after the burst a small parachute slows the package as it falls, so this is stated.
• C: This restates "the balloon swells as the surrounding air grows thinner," so it is supported.
• D: The mailing label lets a finder send it back to be repaired and flown again, which this choice paraphrases accurately.

Answer: B

Treat the license and checklist as necessary but not sufficient, since the passage says they do not guarantee a truck. Then apply the condition: off-post trips need written approval unless the trip is a scheduled range run. Her supply pickup is unscheduled, so the exception does not cover her and she still needs approval, but she is not banned from going.

• A: The passage says meeting the requirements does not guarantee a truck, since trucks go first come and some are held back.
• B (correct): The trip is off post and is not a scheduled range run, so the unless exception does not apply and written approval is still required.
• C: Same-day return is never mentioned; this invents a condition that the passage does not give.
• D: The unless clause only removes the approval step for range runs; other off-post trips are allowed with written approval.

Answer: B

Correct answer: 1/9. The slice's share equals its central angle over the full 360 degrees: 40/360, which simplifies to 1/9.

• A: This compares 40 to 180 degrees, which is only half a circle.
• B (correct): The fraction is 40/360, which reduces to 1/9.
• C: This puts the angle in the denominator; the fraction is angle over 360.
• D: This compares 40 to 90 degrees, which is only a quarter turn.

Answer: D

Correct answer: 104°. Supplementary angles add to 180°, so the other angle is

°.

• A: 14° is the complement (90 - 76), not the supplement.
• B: This subtracts from 360°, which applies to angles around a point, not to supplements.
• C: An angle equal to 76° would be a vertical partner; supplements must add to 180°.
• D (correct): 180 - 76 = 104°, so 76° and 104° are supplementary.

Answer: D

Correct answer: −3. Substitute with parentheses:

• A: This treats both parts as positive, 9 + 12, dropping the sign on 4(−3).
• B: This squares −3 as −9 by leaving out the parentheses, so −9 − 12 = −21.
• C: This drops the final sign; 9 − 12 is −3, not 3.
• D (correct): The square of −3 is 9, and 4 times −3 is −12, so the total is −3.

Answer: B

Correct answer:

On a number line, a number to the right is greater. Although 5 is greater than 2, −2 is to the right of −5, so

This is why multiplying by a negative reverses an inequality.

• A: −7 lies to the left of −3, so it is smaller, not greater.
• B (correct): −2 lies to the right of −5 on the number line, so it is the greater number.
• C: −1 lies to the right of −4, so −1 is greater, not less.
• D: 0 lies to the right of every negative number, so 0 is greater than −6.

Answer: B

Correct answer: 36π square feet. The outer radius is

Subtract the pool from the whole circle.

• A: This subtracts the radii first and squares the 2; the formula needs R squared minus r squared.
• B (correct): The outer radius is 10, so the ring is pi times 100 minus 64, or 36 pi.
• C: This is the whole outer circle; the pool in the middle must be subtracted.
• D: This adds 2 feet to each side of the radius, making R 12; the radius grows by only 2.

Answer: C

Correct answer: -8a⁹b⁶. An outside exponent applies to every factor:

Together that is $-8a^9{b}^6$.

• A: This drops the sign; an odd power of a negative number stays negative.
• B: This multiplies -2 by 3 instead of cubing it.
• C (correct): Cube each factor: (-2)^3 = -8, (a^3)^3 = a^9 and (b^2)^3 = b^6.
• D: This adds the outside exponent to each inside exponent instead of multiplying.

Answer: D

Correct answer: 33 inches. The first triangle's perimeter is

Perimeters scale by the same factor as sides, so

and the longest side becomes

• A: 11 is the longest side of the original triangle; it must be scaled by 3.
• B: This multiplies by $k^2=9$, but lengths scale by k; only areas scale by $k^2$.
• C: This adds the 50-unit perimeter difference to one side instead of using a ratio.
• D (correct): The scale factor is 75 / 25 = 3, so the longest side is 3 × 11 = 33.

Answer: B

Correct answer: 6y² - 2y + 1. Divide each term separately by $3y^2$:

The result is $6y^2-2y+1$.

• A: This treats 3y^2 divided by 3y^2 as 0, but anything nonzero divided by itself is 1.
• B (correct): Dividing each term by 3y^2 gives 6y^2, -2y and 1.
• C: This divides the last term by y^2 only and forgets to divide the 3 by 3.
• D: This adds the exponents, which is the rule for multiplying, not dividing.

Answer: A

Correct answer:

Since 52 is a multiple of −4, divide first instead of distributing:

Add 6:

Check:

• A (correct): Dividing both sides by −4 gives x − 6 = −13, so x = −7.
• B: This divides by 4 instead of −4, giving x − 6 = 13.
• C: After x − 6 = −13, this subtracts 6 instead of adding 6.
• D: This is the correct size with the wrong sign; −4(7 − 6) = −4, not 52.

Answer: C

Correct answer: 46. Here

and d = 1.5. Use

• A: This uses n = 30 steps instead of n − 1 = 29, overshooting by one difference of 1.5.
• B: This multiplies 30 by 1.5 and forgets to start from the first term.
• C (correct): Twenty-nine steps of 1.5 added to 2.5 give 46.
• D: This is only the total of the 29 steps; the first term 2.5 must be added.

Answer: A

Correct answer: −36. With parentheses the base is −3. An odd power stays negative:

An even power is positive:

Then

• A (correct): (−3)³ = −27 and (−3)² = 9, so −27 − 9 = −36.
• B: This takes (−3)² as −9; a negative base with an even exponent is positive.
• C: This takes (−3)³ as +27, giving 27 − 9; an odd power of a negative number stays negative.
• D: This multiplies the base by the exponent, (−3)(3) − (−3)(2) = −9 + 6, instead of raising to a power.

Answer: D

Correct answer: −3. Solve the second equation for y:

For the two equations to describe the same line, their slopes (both 2) and their intercepts must match, so

• A: This drops the sign when dividing 6 by −2; the intercept is −3, and c = 3 would give parallel lines.
• B: This divides only the x-term by −2 and leaves the constant as 6 with a sign change; every term must be divided.
• C: This is the slope of both lines, not the intercept c that must also match.
• D (correct): Rewriting 4x − 2y = 6 gives y = 2x − 3, so c = −3 makes the lines identical.

Answer: C

Correct answer: 26 square yards. Floor area minus the island: 21 times 12 = 252 square feet, and

Since 1 square yard = 9 square feet,

• A: This divides by 3 instead of 9; a square yard is 3 feet by 3 feet, or 9 square feet.
• B: This converts the full 252 square feet but forgets to remove the island.
• C (correct): Subtract the 18-square-foot island from 252 square feet, then divide 234 by 9.
• D: This is the tiled area in square feet; it was never converted to square yards.

Answer: A

Correct answer: Friday. Days of the week repeat every 7 days, so only the remainder matters.

with remainder 2 (

).

Two days after Wednesday is Friday.

• A (correct): 100 = 7 × 14 + 2, so after 14 full weeks there are 2 extra days, and Wednesday plus 2 days is Friday.
• B: This would be right only if 100 were a multiple of 7, but 100 ÷ 7 leaves a remainder of 2.
• C: This moves ahead only 1 day; the remainder of 100 ÷ 7 is 2.
• D: This moves ahead 3 days, as if the remainder were 3 instead of 2.

Answer: A

Correct answer: (4, 3). Add the two equations so y cancels: 3x = 12, so x = 4. Substitute into

so y = 3.

Check in the first equation:

The lines meet at (4, 3).

• A (correct): Adding the equations gives 3x = 12, so x = 4, and then 4 - y = 1 gives y = 3.
• B: This has the correct numbers in swapped order; (3, 4) fails both equations.
• C: This finds x = 4 but then solves x - y = 1 as y = x + 1; the correct step is y = x - 1.
• D: This point lies on 2x + y = 11 but not on x - y = 1, since 2 - 7 is -5.