Your FREE Air Force Officer Qualifying Test (AFOQT) Practice Test 2026 – 630+ Q&A

Correct answer: Book

The answer is book. A petal is one part of a whole flower, and a page is likewise one part of a whole book. A library is a collection of books rather than the thing a page is part of, and a word and the text are what is printed on the page, so none of them is the whole that the page belongs to.

Correct answer: Scarce

The answer is scarce. Humid and arid are opposites, so the missing word must be the opposite of abundant, which is scarce. Lavish and rich describe having plenty, as abundant does, rather than the reverse, and steamy matches the humid half of the first pair, not the idea of quantity.

Correct answer: Weight

The answer is weight. A thermometer is the instrument that measures temperature, and a scale is the instrument that measures weight. Height and length are measured with a ruler or measuring tape, and volume with a measuring cup, so none is what a scale reads.

Correct answer: Deep

The answer is deep. Timid and bold are opposites, so the missing word must be the opposite of shallow, which is deep. Flat is close in meaning to shallow, while wide and long describe width or length rather than the reverse of shallow depth.

Correct answer: Pack

The answer is pack. A pride is the name for a group of lions, and a pack is the name for a group of wolves. A herd is the group name for cattle or deer, a lair is where a wolf shelters, and a howl is the sound a wolf makes, so none is the wolf's group name.

Correct answer: Sweep

The answer is sweep. Cutting is what scissors are used for, and sweeping is what a broom is used for. To scrub is the job of a brush or sponge, to rinse is the job of running water, and to shine is the job of a polishing cloth, so each names another cleaning action rather than the broom's.

Correct answer: Plant

The answer is plant. A spark grows into a flame, and a seed grows into a plant. A grain is a kind of seed rather than what a seed becomes, a shell is the hard outer covering of some seeds, and earth is where the seed is sown, so none is what the seed develops into.

Correct answer: Arrogant

The answer is arrogant. Generous and stingy are opposites, so the missing word must be the opposite of humble, which is arrogant. Modest means nearly the same as humble, and gracious and obedient are traits often found alongside humility rather than its reverse.

Correct answer: Podium

The answer is podium. The cockpit is the station a pilot works from, and the podium is the station a conductor leads from. A baton is the tool the conductor holds, a soloist is a featured performer the conductor accompanies, and a concert is the performance itself, so none is the conductor's station.

Correct answer: Descend

The answer is descend. Expand and contract are opposites, so the missing word must be the opposite of ascend, which is descend. Climb means nearly the same as ascend, and elevate and advance both describe moving upward or forward, so none of them means going down.

Correct answer: Symphony

The answer is symphony. An author creates a novel, and a composer creates a symphony. Lyrics are usually the work of a lyricist, an audience is who listens to the work, and a musician is the broader group a composer belongs to, so none is the work a composer creates.

Correct answer: Fatigue

The answer is fatigue. Friction produces heat, and exercise produces fatigue. A workout is simply another name for a session of exercise, an athlete is a person who exercises, and a barbell is equipment used for it, so none is the result that exercise brings about.

Correct answer: Car

The answer is car. A keyboard is the control part of a computer, and a steering wheel is the control part of a car. A horn is another part of the vehicle rather than the whole, a driver is the person who turns the wheel, and a garage is where the car is kept, so none is the machine the wheel belongs to.

Correct answer: Full

The answer is full. Weary and rested are opposites, so the missing word must be the opposite of famished, which is full. Hungry means nearly the same as famished, and faint and feeble describe how a famished person may feel rather than the reverse of being famished.

Correct answer: Play

The answer is play. A chapter is a major division of a book, and an act is a major division of a play. A scene is a smaller division within an act rather than the whole it belongs to, a role is the part one actor plays, and the cast is the group of actors who perform, so none is the whole work.

Correct answer: Distance

The answer is distance. A clock is the instrument that measures time, and an odometer is the instrument that measures distance. Speed is read from the speedometer, pressure from a pressure gauge, and altitude from an altimeter, so none is what an odometer records.

Correct answer: Reject

The answer is reject. Praise and criticize are opposites, so the missing word must be the opposite of accept, which is reject. To permit and to assent both mean to agree to something, and to obtain means to get it, so each sits on the same side as accept rather than turning it away.

Correct answer: Milk

The answer is milk. A bee produces honey, and a cow produces milk. A calf is a cow's young, a herd is the group a cow lives in, and hay is what a cow eats, so none is the product the cow makes.

Correct answer: Straighten

The answer is straighten. To wrinkle and to smooth are opposite actions, so the missing word must be the action opposite to tangle, which is straighten. Intertwine and snarl mean nearly the same as tangle, and to weave is to lace strands together on purpose rather than to undo them.

Correct answer: Bird

The answer is bird. A trout is one kind of fish, and a sparrow is one kind of bird. A wren is another small bird at the same level as the sparrow, a nest is the home a sparrow builds, and a beak is part of its body, so none is the broader category.

Correct answer: Cut

The answer is cut. A pen is used to write, and a knife is used to cut. To stir and to scoop are the jobs of a spoon, and to whisk is the job of a whisk, so each names what a different kitchen tool does rather than what a knife does.

Correct answer: Departure

The answer is departure. Victory and defeat are opposites, so the missing word must be the opposite of arrival, which is departure. An entrance means much the same as an arrival, a reception is the welcome given on arriving, and an itinerary is the plan for the journey, so none is the opposite event.

Correct answer: Building

The answer is building. A root anchors and supports a tree, and a foundation anchors and supports a building. A footing is one part of the foundation itself, flooring is the surface laid over a floor, and a basement is one level of the building, so none is the whole structure supported.

Correct answer: Rigid

The answer is rigid. Fertile and barren are opposites, so the missing word must be the opposite of flexible, which is rigid. Supple, pliable, and springy all describe something that bends easily, so each repeats the meaning of flexible rather than reversing it.

Correct answer: Medicine

The answer is medicine. A librarian looks after and hands out books, and a pharmacist looks after and hands out medicine. A pharmacy is the shop where the pharmacist works, a customer is the person served, and a hospital is one place a pharmacist may be employed, so none is the stock the pharmacist hands out.

Correct answer: Ruin

The answer is ruin. Overheating leads to a breakdown, and neglect leads to ruin. To shun is close in meaning to neglect itself rather than its result, and care and heed are the opposite of neglect, not what it causes.

Correct answer: Arm

The answer is arm. A hinge is the bending joint of a door, and an elbow is the bending joint of an arm. The leg is the limb whose bending joint is the knee, the hip is a different joint, and a rib is a bone of the chest, so none is the limb the elbow belongs to.

Correct answer: Kind

The answer is kind. Brave and cowardly are opposites, so the missing word must be the opposite of cruel, which is kind. Mean, cold, and vile all describe cruel or unfeeling behavior, so each repeats the meaning of cruel rather than reversing it.

Correct answer: Pencil

The answer is pencil. Ink is the marking material held inside a pen, and lead is the marking material held inside a pencil. A crayon is made of colored wax, a marker holds ink, and an eraser removes pencil marks, so none is the writing tool that holds lead.

Correct answer: Water

The answer is water. To ventilate is to supply a place with air, and to irrigate is to supply land with water. A field is the land that gets irrigated, a ditch is a channel that may carry the water, and wheat is a crop that benefits, so none is what is supplied.

Correct answer: Floor

The answer is floor. A summit is the top of a mountain and the base is its bottom, so the matching pair is the ceiling at the top of a room and the floor at its bottom. An attic is the space above the ceiling, a joist is a beam that holds the ceiling up, and a light is a fixture that often hangs from the ceiling, so none is the bottom of the room.

Correct answer: Wobbly

The answer is wobbly. Fluent and halting are opposites, so the missing word must be the opposite of steady, which is wobbly. Constant, balanced, and calm all mean much the same as steady, so each repeats its meaning rather than reversing it.

Correct answer: Conductor

The answer is conductor. A whistle is the tool a referee uses to direct play, and a baton is the tool a conductor uses to direct musicians. The orchestra is the group being directed, a rehearsal is a session where the baton is used, and a composer writes the music rather than directing it with a baton.

Correct answer: Wealth

The answer is wealth. Spending leads to debt, and saving leads to wealth. Thrift is another word for the habit of saving, a budget is a plan that helps a person save, and a loan is borrowed money that leads to debt, so none is the result that saving brings about.

Correct answer: Frog

The answer is frog. A bud develops into a blossom, and a tadpole develops into a frog. An egg is the stage before the tadpole, larva is the general name for the stage a tadpole already is, and a swamp is where tadpoles live, so none is the adult form.

Correct answer: Inaudible

The answer is inaudible. Legible and illegible are opposites, so the missing word must be the opposite of audible, which is inaudible. Perceptible and discernible describe something that can be noticed, as audible does, and visible concerns sight rather than hearing.

Correct answer: Mammal

The answer is mammal. A gill is the breathing organ of a fish, and a lung is the breathing organ of a mammal. Oxygen is the gas the lung takes in, a breath is the act of breathing, and the thorax is the part of the body that holds the lung, so none is the animal the organ belongs to.

Correct answer: Skill

The answer is skill. Study produces knowledge, and practice produces skill. A drill is one kind of practice rather than its result, a coach is the person who runs it, and a sport is what a person may practice for, so none is the ability gained.

Correct answer: Stars

The answer is stars. An archipelago is a group made up of islands, and a constellation is a group made up of stars. A comet is a single icy body, an orbit is the path such a body follows, and space is the setting a constellation is seen in, so none is the members that make up the group.

Correct answer: Strengthen

The answer is strengthen. Dilute and concentrate are opposites, so the missing word must be the opposite of weaken, which is strengthen. Debilitate, impoverish, and lessen all describe making something weaker, so each repeats the meaning of weaken rather than reversing it.

Correct answer: Garage

The answer is garage. A chef works in a kitchen, so the matching worker-and-workplace pair is a mechanic working in a garage. A vehicle is what the mechanic repairs, while a toolbox and a ratchet are equipment the mechanic uses, so none of them is the place where the work is done.

Correct answer: Tool

The answer is tool. A bone is one common kind of fossil, so the matching category-and-example pair is a tool as one common kind of artifact. A museum is where artifacts are displayed, culture is the way of life an artifact reflects, and a curator is the person who looks after a collection, so none of them is a kind of artifact.

Correct answer: Deflate

The answer is deflate. Exaggerate and understate are opposites, so the missing word must be the opposite of inflate, which is deflate. Increase means much the same as inflate, overfill means to inflate too far, and pump names the way air is usually forced in, so none of them is the reverse.

Correct answer: Length

The answer is length. A compass is used to find direction, so the analogy needs what a ruler is used to measure, which is length. An angle is what a protractor measures rather than a ruler, a pencil is what draws along the ruler's edge, and a margin is the blank border often ruled off on a page, so none of them is what a ruler measures.

Correct answer: Ladder

The answer is ladder. A spoke is one of the bars that make up a wheel, so the matching part-to-whole pair is a rung as one of the bars that make up a ladder. A step is another name for a rung rather than the whole, stairs are a different structure for climbing that has steps rather than rungs, and a roofer is a person who uses a ladder rather than the object the rung belongs to.

Correct answer: Fleeting

The answer is fleeting. Permanent and temporary are opposites, so the missing word must be the opposite of eternal, which is fleeting. Enduring and immortal both mean much the same as eternal, and ancient means very old, so none of the three is its reverse.

Correct answer: Downpour

The answer is downpour. A tremor is a mild form of an earthquake, so the matching mild-to-intense pair is a drizzle as a mild form of a downpour. Mist is even lighter than a drizzle, a sprinkle is about the same strength, and overcast describes a cloudy sky rather than heavier rain.

Correct answer: Sky

The answer is sky. A mariner travels across the sea, so the matching traveler-and-domain pair is an aviator traveling through the sky. A pilot is another word for an aviator, a plane is the vehicle, and a wing is part of that vehicle, so none of them is the space traveled through.

Correct answer: Welder

The answer is welder. Stitching is the joining work done by a tailor, so the matching task-and-worker pair is welding as the joining work done by a welder. A torch is the tool, goggles are protective gear, and girders are steel beams a welder often joins, so none of them is the worker.

Correct answer: Liberate

The answer is liberate. Confine and release are opposites, so the missing word must be the opposite of capture, which is to liberate, or set free. Seize and apprehend both mean much the same as capture, and overpower describes subduing someone, which usually comes with a capture rather than reversing it.

Correct answer: Location

The answer is location. A calendar is used to find a date, so the analogy needs what a map is used to find, which is a location. A compass is a separate tool for direction, a navigator is the person who reads the map, and geography is the wider subject maps belong to, so none of them is what a map is used to find.

Correct answer: Wakefulness

The answer is wakefulness. A lullaby brings on sleep, so this cause-and-effect pair is matched by an alarm bringing on wakefulness. Restfulness is the calm state a lullaby encourages and an alarm ends, snooze is the setting that delays it, and a firefighter is who a fire alarm calls, so none of them is the state the alarm produces.

Correct answer: Hidden

The answer is hidden. Transparent and opaque are opposites, so the missing word must be the opposite of visible, which is hidden. Obvious and evident both mean much the same as visible, and optical describes sight itself, so none of them is the reverse.

Correct answer: Athlete

The answer is athlete. A teacher instructs a student, so the matching instructor-and-learner pair is a coach instructing an athlete. A clipboard is something a coach carries, an umpire enforces the rules rather than learning a skill, and a passenger is who rides a coach in its sense of a bus.

Correct answer: Opera

The answer is opera. A prologue is the opening section of a story, so the matching opening-and-whole pair is an overture as the opening section of an opera. A finale is the closing section rather than the whole, an aria is a single song within the work, and an encore is an extra piece played after it ends.

Correct answer: Flood

The answer is flood. Fuel feeds a fire and makes it grow, so the matching cause-and-effect pair is heavy rain feeding a flood. Hail is another kind of falling weather, thunder often comes with a storm, and a drought is what happens when rain is missing, so none of them is what rain causes.

Correct answer: Verbose

The answer is verbose. Brief and lengthy are opposites, so the missing word must be the opposite of concise, which is verbose, or wordy. Terse and laconic both mean much the same as concise, and precise only looks like it, since it means exact rather than long-winded.

Correct answer: Glass

The answer is glass. A mason works with stone, so the matching worker-and-material pair is a glazier working with glass. A window is the finished product a glazier fits, pottery is coated with a glaze that only sounds like the glazier's trade, and varnish is a finish for wood rather than the glazier's material.

Correct answer: 130 miles per hour

130 miles per hour is correct. One hour and 30 minutes is 1.5 hours, and speed is distance divided by time: 195 / 1.5 = 130. Writing the time as 1.3 hours gives 195 / 1.3 = 150 miles per hour; counting only the 1 hour gives 195 miles per hour; and multiplying instead of dividing gives 195 x 1.5 = 292.5 miles per hour.

Correct answer: 18 miles

18 miles is correct. Forty-five minutes is 45/60 = 0.75 hour, and distance is rate times time: 24 x 0.75 = 18. Writing 45 minutes as 0.45 hour gives 24 x 0.45 = 10.8 miles; dividing instead of multiplying gives 24 / 0.75 = 32 miles; and reducing 45/60 to 2/3 instead of 3/4 gives 24 x 2/3 = 16 miles.

Correct answer: 18 hours

18 hours is correct. A knot is one nautical mile per hour, so the distance and the speed are already in matching units: 540 / 30 = 18. Converting only the speed to statute miles per hour (30 x 1.15 = 34.5) gives 540 / 34.5, or about 15.7 hours; dropping the zero from the speed and dividing 540 by 3 gives 180 hours; and treating a knot as a nautical mile per minute turns the answer into 18 minutes, or 0.3 hours.

Correct answer: 50 miles

50 miles is correct. Twelve minutes is 12/60 = 0.2 hour, and 250 x 0.2 = 50. Writing 12 minutes as 0.12 hour gives 250 x 0.12 = 30 miles; dividing 250 by 12 gives about 20.8 miles; and reading 12 minutes as 1.2 hours gives 250 x 1.2 = 300 miles.

Correct answer: 7 gallons

7 gallons is correct. Fuel used is distance divided by fuel economy: 245 / 35 = 7. Stopping the division at 35 x 6 = 210 and dropping the 35 miles left over gives 6 gallons; dividing the other way, 35 / 245, gives about 0.14 gallons; and 8 gallons would cover 8 x 35 = 280 miles, 35 more than the trip.

Correct answer: 4 hours

4 hours is correct. Flying in opposite directions, the aircraft separate at the sum of their speeds, 480 + 520 = 1,000 miles per hour, so 4,000 / 1,000 = 4. Using their average speed of 500 miles per hour gives 4,000 / 500 = 8 hours; using only the westbound speed gives 4,000 / 520, or about 7.7 hours; and using the difference of the speeds, 40 miles per hour, gives 4,000 / 40 = 100 hours.

Correct answer: 36 miles per hour

36 miles per hour is correct. Average speed is total distance over total time: the first 90 miles take 90 / 45 = 2 hours and the next 90 take 90 / 30 = 3 hours, so 180 / 5 = 36. Averaging the two speeds, (45 + 30) / 2, gives 37.5 miles per hour; and 40 miles per hour or 38 miles per hour would mean a total time of 4.5 or about 4.7 hours, not the 5 hours the two legs take.

Correct answer: 36 minutes

36 minutes is correct. The time in hours is 54 / 90 = 0.6 hour, and 0.6 x 60 = 36 minutes. Reading 0.6 hour as if it meant 60 minutes gives 60 minutes; dividing the wrong way, 90 / 54 = about 1.67 hours, gives 100 minutes; and stopping before the conversion leaves 0.6 minutes.

Correct answer: 10:30 a.m.

10:30 a.m. is correct. In its one-hour head start the bus covers 50 miles; the car closes that gap at 70 - 50 = 20 miles per hour, so it needs 50 / 20 = 2.5 hours, and 8:00 a.m. plus 2 hours 30 minutes is 10:30 a.m. Reading 2.5 hours as 2 hours 50 minutes gives 10:50 a.m.; adding 2.5 hours to the bus's 7:00 a.m. start gives 9:30 a.m.; and making both slips gives 9:50 a.m.

Correct answer: 1,440 gallons

1,440 gallons is correct. One hour and 20 minutes is 60 + 20 = 80 minutes, and 18 x 80 = 1,440. Writing the time as 1.2 hours and converting that to 72 minutes gives 18 x 72 = 1,296 gallons; counting only the 20 minutes gives 18 x 20 = 360 gallons; and counting only the 1 hour gives 18 x 60 = 1,080 gallons.

Correct answer: 8 hours

8 hours is correct. The pace is 15 / 5 = 3 miles per hour, so 24 miles takes 24 / 3 = 8 hours. Reasoning that 9 more miles need 9 more hours gives 5 + 9 = 14 hours; stopping at the pace and reporting it gives 3 hours; and dividing the 24 miles by the 5 hours instead of by the 3-mile-per-hour pace gives 24 / 5 = 4.8 hours.

Correct answer: 70 miles per hour

70 miles per hour is correct. The train covers 200 - 60 = 140 miles in the 2 hours from noon to 2:00 p.m., and 140 / 2 = 70. Dividing the 200 marker by 2 hours ignores the starting marker and gives 100 miles per hour; stopping at the distance gives 140 miles per hour; and taking noon to 2:00 p.m. as 12 - 2 = 10 hours gives 140 / 10 = 14 miles per hour.

Correct answer: 1,920 megabytes

1,920 megabytes is correct. The rate is 256 / 8 = 32 megabytes per second, and one minute is 60 seconds, so 32 x 60 = 1,920. Treating a minute as 100 seconds gives 32 x 100 = 3,200 megabytes; multiplying the 256 megabytes by 60 without first finding the per-second rate gives 15,360 megabytes; and making both mistakes, 256 x 100, gives 25,600 megabytes.

Correct answer: 265 miles

265 miles is correct. The first part covers 65 x 2 = 130 miles and the second 45 x 3 = 135 miles, and 130 + 135 = 265. Swapping the times, 65 x 3 + 45 x 2, gives 285 miles; multiplying the average of the two speeds, 55, by the 5 hours gives 275 miles; and stopping after the first part gives 130 miles.

Correct answer: 240 miles per hour

240 miles per hour is correct. From 11:00 a.m. to 4:00 p.m. is 5 hours, so the speed is 1,200 / 5 = 240. Counting the hours 11, 12, 1, 2, 3, 4 as 6 hours gives 200 miles per hour; counting only from noon, 4 hours, gives 300 miles per hour; and subtracting 11 - 4 = 7 hours gives 1,200 / 7, or about 171.4 miles per hour.

Correct answer: 6 miles

6 miles is correct. There are 60 minutes in an hour, so 360 / 60 = 6 miles each minute. Treating an hour as 100 minutes gives 3.6 miles; dividing by the 3,600 seconds in an hour gives 0.1 miles, which is the distance flown each second; and 5 miles a minute would be only 5 x 60 = 300 miles per hour.

Correct answer: 30 feet

Each inch on the blueprint stands for 4 feet, so multiply the whole 7.5 inches by 4: 7.5 x 4 = 30 feet. Scaling only the 7 whole inches gives 28 feet, which drops the half inch and the 2 feet it stands for; tacking the half back on unscaled (28 + 0.5) gives 28.5 feet. Adding the scale instead of multiplying gives 7.5 + 4 = 11.5 feet, which never uses the scale as a multiplier.

Correct answer: 16 navigators

Set up 5/2 = 40/x. Since 40 is 5 x 8, the navigators number 2 x 8 = 16 navigators. Subtracting the 3-point gap between the ratio terms (40 - 3 = 37 navigators) treats a ratio as a fixed difference rather than a multiple. Turning the ratio upside down (40 x 5/2 = 100 navigators) gives more navigators than pilots, which contradicts 5 to 2. Adding pilots and navigators (40 + 16 = 56 navigators) gives the whole group, not the navigators alone.

Correct answer: 15 inches

The width grows from 4 to 10 inches, a scale factor of 10/4 = 2.5, so the height becomes 6 x 2.5 = 15 inches. Adding the same 6 inches to the height (6 + 6 = 12 inches) treats an enlargement as a fixed increase instead of a multiple. Applying the scale factor to the new width instead of the old height (10 x 2.5) gives 25 inches. Setting up the proportion with the height on the wrong side, 4/6 = x/10, gives x = 40/6, about 6.7 inches.

Correct answer: 27 pounds

Nitrogen to phosphorus is 5 to 3, and 45 is 5 x 9, so the phosphorus is 3 x 9 = 27 pounds. Subtracting the 2-point gap between the ratio terms (45 - 2 = 43 pounds) treats the ratio as a difference. Turning the ratio upside down (45 x 5/3 = 75 pounds) gives more phosphorus than nitrogen, which contradicts 5 to 3. Adding the two ingredients (45 + 27 = 72 pounds) gives the whole blend, not the phosphorus.

Correct answer: 14 hours

Fewer pumps take longer, so this is an inverse proportion. The job is 7 x 12 = 84 pump-hours, and 6 pumps need 84 / 6 = 14 hours. Stopping at the work total gives 84 hours, which counts pump-hours, not clock hours. Multiplying the new pump count by the old time (6 x 12 = 72 hours) skips the total-work step. Adding one hour for one fewer pump gives 13 hours, but the time grows in proportion (by 7/6), not by a fixed hour.

Correct answer: 42

The smallest quantity is 4 parts = 28, so one part is 28 / 4 = 7, and the largest (6 parts) is 6 x 7 = 42. The value 7 is the size of one part, a step short of the answer. The value 35 is the middle quantity (5 parts), not the largest. The value 30 adds the 2-part gap between 4 and 6 to 28 as if each part were 1 unit.

Correct answer: $40,000

The ratio has 5 + 4 + 3 = 12 parts, so one part is $96,000 / 12 = $8,000, and fuel's 5 parts come to 5 x $8,000 = $40,000. Stopping at one part gives $8,000. Using training's 3 parts gives $24,000, the share at the other end of the ratio. Dividing the budget by fuel's 5 instead of by the 12 total parts gives $19,200.

Correct answer: 22 sheets

Each sheet yields 1,000 / 8 = 125 emblems, so 2,750 emblems need 2,750 / 125 = 22 sheets. Rounding 2,750 up to 3,000 emblems and using 3 x 8 gives 24 sheets, two more than the job needs. The figure 16 sheets covers only the first 2,000 emblems (2 x 8) and ignores the last 750. The figure 14 sheets covers only the 1,750 emblems beyond the first 1,000 (1,750 / 125) and leaves out the 8 sheets those first 1,000 need.

Correct answer: 20 days

More troops use the rations up sooner, so this is an inverse proportion: 240 x 30 = 7,200 troop-days, and 7,200 / 360 = 20 days. Treating it as a direct proportion (30 x 360/240) gives 45 days, more time for more troops. Cutting the days by the same 50 percent that the troops grew gives 15 days, but a 50 percent rise in troops cuts the days by only a third. Reading 'grows to 360' as 'grows by 360' makes the garrison 240 + 360 = 600 troops, and 7,200 / 600 gives 12 days.

Correct answer: 9 inches

Convert first: 36 feet is 36 x 12 = 432 inches. At a scale of 1 to 48, the model spans 432 / 48 = 9 inches. Dividing 48 by 36 gives about 1.33, which sets the scale upside down and never converts, so 1.33 inches is wrong. Dividing 36 by 48 without converting gives 0.75, a length in feet, so 0.75 inches has the wrong unit. Dividing 36 by 12 instead of multiplying gives 3, which converts in the wrong direction and never applies the scale, so 3 inches is wrong.

Correct answer: 45 turns

The gears turn in the ratio 4 to 3, and 60 is 4 x 15, so the large gear makes 3 x 15 = 45 turns. Multiplying 60 by 3 and forgetting to divide by 4 gives 180 turns. Turning the ratio upside down (60 x 4/3 = 80 turns) has the large gear spinning faster than the small one. Adding both gears' turns (60 + 45 = 105 turns) counts the pair together rather than the large gear alone.

Correct answer: 52 units

Seven units of A trade for 4 of B, and 91 is 7 x 13, so 91 units of A equal 4 x 13 = 52 units of B. Subtracting the 3-unit gap between the rate terms (91 - 3 = 88 units) treats the rate as a difference. Multiplying 91 by 4 and forgetting to divide by 7 gives 364 units, more B than A, although each unit of B is worth more. Adding 91 and 52 to get 143 units mixes the two currencies.

Correct answer: 6 cubic feet

Gravel is 4 parts = 24 cubic feet, so one part is 24 / 4 = 6, and cement (1 part) is 6 cubic feet. Dividing the gravel by the 3 ingredients (24 / 3 = 8 cubic feet) ignores the ratio's parts. The figure 42 cubic feet is the whole batch (7 parts x 6), not the cement. Multiplying 24 by 4 instead of dividing gives 96 cubic feet, far more cement than gravel.

Correct answer: 8 technicians

Each technician calibrates 80 / 5 = 16 instruments a day, so 128 instruments need 128 / 16 = 8 technicians. The figure 3 technicians is only the number to add for the 48 extra instruments (48 / 16), not the whole crew. Adding the growth factor 128 / 80 = 1.6 to the 5 technicians instead of multiplying by it gives 6.6, rounded up to 7 technicians. Rounding the growth factor 1.6 up to 2 and doubling the crew gives 10 technicians.

Correct answer: 36 cups

The parts total 2 + 9 = 11, so one part is 44 / 11 = 4 cups, and the water (9 parts) is 9 x 4 = 36 cups. Stopping at the size of one part gives 4 cups. The figure 8 cups is the concentrate (2 parts), not the water. Subtracting the concentrate's 2 parts as if they were cups (44 - 2 = 42 cups) skips finding the size of a part.

Correct answer: 6 centimeters

Each centimeter stands for 45 / 3 = 15 kilometers, so 90 kilometers is 90 / 15 = 6 centimeters. Stopping at 90 / 45 = 2 centimeters forgets that 45 kilometers takes 3 centimeters on the map, not 1. Stopping at 45 / 3 = 15 gives the kilometers per centimeter, so 15 centimeters is the scale, not a map distance. Dividing 90 by 3 gives 30 centimeters, which divides by the map length instead of by the scale.

Correct answer: 4 days

The crews do 1/12 and 1/6 of the job per day; together that is 1/12 + 2/12 = 3/12 = 1/4 of the job a day, so the job takes 4 days. Averaging the two times gives 9 days, which treats the crews as taking turns rather than working at once. The figure 6 days is the faster crew working alone, and two crews together must finish sooner than that. Halving the faster crew's time gives 3 days, which assumes the slower crew works as fast as the faster one.

Correct answer: $34

Each bolt costs $20 / 250 = $0.08, so 425 bolts cost 425 x $0.08 = $34. The figure $14 prices only the 175 bolts beyond the first 250. Turning the proportion upside down (250 x $20 / 425) gives about $11.76, less money for more bolts. Dividing the 425 bolts by the $20 price gives 21.25, a count of bolts per dollar, so $21.25 is not the cost.

Correct answer: 270 miles

Each inch stands for 60 miles, so 4.5 inches is 4.5 x 60 = 270 miles. Scaling only the 4 whole inches (4 x 60) gives 240 miles, which drops the half inch and the 30 miles it stands for. Adding the scale (60 + 4.5) gives 64.5 miles, and dividing 60 by 4.5 gives about 13.3 miles; neither uses the scale as a multiplier.

Correct answer: 84

Thirty-five percent is 0.35, and 0.35 x 240 = 84. Multiplying by 0.65 instead gives 156, the 65 percent that remains after 35 percent is taken away. Splitting it as 30 percent (72) plus 5 percent (12) gives 84; stopping at the 30 percent gives 72, and adding a plain 5 instead of 5 percent gives 77.

Correct answer: $612

The discount is 0.15 x $720 = $108, and $720 - $108 = $612. The figure $108 is the amount saved, not the price paid. Subtracting 15 dollars instead of 15 percent gives $705. Adding the 15 percent instead of subtracting it gives $720 x 1.15 = $828.

Correct answer: 85 percent

A percent score is points earned over points possible: 68 / 80 = 0.85, or 85 percent. Reading the raw score as a percent gives 68 percent. Dividing the other way (80 / 68) gives about 118 percent, more than a perfect score. Taking the 12 points missed as a percent gives 12 percent, which is neither the score nor its share of 80.

Correct answer: $55,120

The raise is 0.06 x $52,000 = $3,120, and $52,000 + $3,120 = $55,120. Using 0.006 instead of 0.06 adds only $312 and gives $52,312. Subtracting the raise instead of adding it gives $48,880. Using 0.6 instead of 0.06 adds $31,200 and gives $83,200.

Correct answer: $140

After a 30 percent discount the jacket costs 70 percent of the original, so the original is $98 / 0.70 = $140. Adding 30 percent back to the sale price ($98 x 1.30 = $127.40) takes 30 percent of the wrong base. Adding 30 dollars instead of 30 percent gives $128. Dividing by the 30 percent that was taken off instead of the 70 percent that was paid ($98 / 0.30) gives about $326.67.

Correct answer: 15 liters

Antifreeze is 25 percent of the 60 liters: 0.25 x 60 = 15 liters. Dividing 60 by 25 gives 2.4 liters, which treats the percent as a divisor. Subtracting 25 from 60 gives 35 liters, which is not a percentage at all. Reading the 25 percent as 25 liters gives 25 liters, which takes the rate for the amount.

Correct answer: 15 percent

Percent decrease is the change over the original value: (80 - 68) / 80 = 12 / 80 = 0.15, or 15 percent. Dividing the change by the new reading (12 / 68) gives about 17.6 percent, which uses the wrong base. Dividing 68 by 80 gives 85 percent, the share of the reading that remains rather than the drop. Reading the 12-point drop itself as 12 percent skips dividing the change by the original 80.

Correct answer: 156 gallons

Sixty-five percent of 240 is 0.65 x 240 = 156 gallons. Subtracting 65 from 240 gives 175 gallons, which is not a percentage at all. Using 60 percent and dropping the 5 gives 0.60 x 240 = 144 gallons. The figure 84 gallons is the empty 35 percent of the tank, not the fuel in it.

Correct answer: $50

The tip is 18 percent of the meal, so $9 = 0.18 x price and the price is $9 / 0.18 = $50. The figure $59 adds the tip back on, giving the whole bill rather than the meal price. Multiplying 9 by 18 gives $162, which multiplies where the price must be found by dividing. Adding 18 dollars to the $9 instead of working with 18 percent gives $27.

Correct answer: 16 gallons

The salt stays fixed at 0.50 x 24 = 12 gallons. At 30 percent, those 12 gallons are 0.30 of the new total, so the total is 12 / 0.30 = 40 gallons, and the water added is 40 - 24 = 16 gallons. The figure 40 gallons is the new total, not the water added. Taking 30 percent of the original 24 gallons gives 7.2 gallons, which applies the new strength to the old volume. Taking the 20-point drop in strength as 20 percent of 24 gives 4.8 gallons, which treats the change in strength as a share of the volume.

Correct answer: 10 pounds

The batch holds 0.15 x 40 = 6 pounds of tin. Adding x pounds gives 6 + x = 0.32 x (40 + x), so 6 + x = 12.8 + 0.32x, then 0.68x = 6.8 and x = 10 pounds. Keeping the total at 40 (12.8 - 6) gives 6.8 pounds, forgetting that the added tin raises the total weight too. The figure 12.8 pounds is all the tin a 40-pound batch would hold at 32 percent, not the amount to add, and 6 pounds is the tin already in the batch.

Correct answer: 4 percent below

Start at 100: a 20 percent rise gives 120, and a 20 percent cut of 120 removes 24, leaving 96, so the final value is 4 percent below the original. The two changes do not cancel to leave the value the same as the original, because the cut is taken from the larger value. Thinking the rise outweighs the cut gives a value higher than the original, but the cut of 24 is bigger than the rise of 20. Counting only the final cut gives 20 percent below; the answer must combine both steps.

Correct answer: 50 ounces

The bleach is 12 percent of the total, so 6 = 0.12 x total and the total is 6 / 0.12 = 50 ounces. Multiplying instead of dividing gives 6 x 12 = 72 ounces or 6 x 0.12 = 0.72 ounces. The figure 44 ounces is the water alone (50 - 6), not the whole solution.

Correct answer: 25 percent

The sorties not completed number 56 - 42 = 14, and 14 / 56 = 0.25, or 25 percent. The figure 75 percent is the share that was completed (42 / 56), not the share left undone. Reading the count of 14 sorties as a percent gives 14 percent, and reading the count of 42 completed sorties as a percent gives 42 percent, which makes both mistakes at once.

Correct answer: $1,200

Simple interest is principal x rate x time: $8,000 x 0.05 x 3 = $1,200, or $400 a year for 3 years. Compounding the interest ($8,000 x 1.05^3 - $8,000) gives about $1,261, but simple interest is never charged on earlier interest. The figure $9,200 is the balance, principal plus interest, not the interest. The figure $9,261 is the compounded balance, which makes both mistakes.

Correct answer: $1,144

Regular pay is 40 x $22 = $880. The 8 overtime hours pay 1.5 x $22 = $33 each, or $264, so the week pays $880 + $264 = $1,144. Paying all 48 hours at $22 gives $1,056, which leaves out the overtime premium. Paying all 48 hours at $33 gives $1,584. Swapping the rates, with the first 40 hours at $33 and the last 8 at $22, gives $1,320 + $176 = $1,496.

Correct answer: 460 recruits

Ninety-two percent of 500 is 0.92 x 500 = 460 recruits. Subtracting 92 from 500 gives 408 recruits, which is not a percentage at all. Taking 90 percent (450) and adding a plain 2 instead of 2 percent gives 452 recruits. The figure 40 recruits is the 8 percent who did not pass.

Correct answer: 15 liters

Let x be the liters of 70 percent solution, so 40 - x liters are 30 percent. The acid gives 0.70x + 0.30 x (40 - x) = 0.45 x 40 = 18, so 12 + 0.40x = 18, then 0.40x = 6 and x = 15 liters. The figure 25 liters is the amount of 30 percent solution. Stopping at 0.40x = 6 without dividing by 0.40 gives 6 liters. Splitting the 40 liters evenly gives 20 liters, but an even split makes a 50 percent solution.

Correct answer: $233.20

The discount is 0.12 x $250 = $30, leaving $220. The tax on $220 is 0.06 x $220 = $13.20, so the total is $220 + $13.20 = $233.20. Netting the two rates into a 6 percent discount gives $235.00, which taxes the full price instead of the discounted one. The figure $220.00 stops after the discount and leaves out the tax. Subtracting the tax instead of adding it gives $206.80.

Correct answer: $9.00

The beans cost 8 x $6 + 12 x $11 = $48 + $132 = $180 for 20 pounds, so the blend costs $180 / 20 = $9.00 per pound. Averaging the two prices, ($6 + $11) / 2 = $8.50, ignores that there are more pounds of the pricier beans. Swapping the weights (12 x $6 + 8 x $11 = $160, and $160 / 20) gives $8.00. Dividing only the $132 paid for the pricier beans by the 20 pounds gives $6.60, which leaves out the cost of the cheaper beans.

Correct answer: 8,000 gallons

The 6,400 gallons are 80 percent of capacity, so capacity is 6,400 / 0.80 = 8,000 gallons. Multiplying by 0.80 instead gives 5,120 gallons, less than the water already held. Adding 20 percent of 6,400 gives 7,680 gallons, which takes the missing 20 percent from the wrong base. Adding 80 to 6,400 gives 6,480 gallons.

Correct answer: 25 questions

The answer is 25 questions. All 80 questions (50 plus 30) count toward the overall score, and 88 percent of 80 is 70.4, so the trainee has 70 correct in all (70 of 80 is 87.5 percent, which rounds to 88). Subtracting the 45 from the first block leaves 70 minus 45, or 25 of the last 30. Subtracting the 50 questions of the first block instead of the 45 answered correctly gives 20 questions; assuming the trainee kept the first block's 90 percent rate on the last 30 gives 27 questions; and reading the drop from 90 to 88 percent as only 2 misses gives 30 minus 2, or 28 questions.

Correct answer: 37.5 miles per hour

The answer is 37.5 miles per hour. Eight minutes is 8/60 of an hour, so the speed is 5 divided by 8/60, which is 5 x 60/8 = 37.5 miles per hour. Treating 8 minutes as 0.08 hour gives 5/0.08, or 62.5 miles per hour; dividing 60 by 8 and dropping the 5 miles gives 7.5 miles per hour; and treating 8 minutes as one-eighth of an hour gives 5 x 8, or 40 miles per hour.

Correct answer: Perceptive

Astute means perceptive: quick to see how a situation really stands and to turn that to advantage, as an astute negotiator does. 'Austere' looks similar but means stern or severely plain; 'studious' means devoted to study, which is diligence rather than sharp judgment; and 'persuasive' means good at convincing others, a skill an astute person may use but not what the word means.

Correct answer: Diminish

To abate is to diminish, to become or make less in force or amount, as a storm abates. 'Escalate' is the reverse, to grow in size or intensity; 'abet' looks similar but means to help or encourage, usually in wrongdoing; and 'abandon' shares the opening letters but means to leave behind or give up.

Correct answer: Careful

Prudent means careful, showing good judgment that avoids needless risk, as in a prudent investment. 'Prudish' looks similar but means easily shocked by matters of propriety; 'cowardly' means lacking courage, which is fear rather than good judgment; and 'heedless' means paying no attention to risk, close to the opposite.

Correct answer: Coherent

Lucid means coherent, clearly expressed and easy to follow, as in a lucid explanation. 'Lurid' looks similar but means shocking or sensational; 'eloquent' means fluent and moving in speech or writing, which can still be hard to follow; and 'muddled' means confused and disordered, close to the opposite.

Correct answer: Prompt

Timely means prompt, happening at the right moment, as in a timely warning. 'Untimely' means happening at a bad or too-early moment, the opposite; 'timeless' shares the root but means never going out of date; and 'hurried' means done too fast, often carelessly, which is haste rather than good timing.

Correct answer: Sinister

Ominous means sinister, suggesting that something bad is about to happen, as in ominous storm clouds. 'Onerous' looks similar but means burdensome; 'mysterious' means hard to explain or understand, which need not threaten anything; and 'auspicious' means promising good fortune, the opposite kind of omen.

Correct answer: Reinforce

To bolster is to reinforce, to support something and make it stronger, as in bolstering morale. 'Undermine' is the reverse, to weaken from below; 'bluster' looks similar but means to talk loudly and aggressively; and 'upholster' shares the ending and the cushion sense of a bolster but means to fit furniture with padding and covers.

Correct answer: Thorough

Meticulous means thorough, giving close attention to every detail. 'Careless' is close to the opposite; 'ponderous' means slow and labored, which careful work may look like but is not what the word means; and 'ambitious' means eager to succeed, which describes drive rather than care with details.

Correct answer: Shorten

To curtail is to shorten or cut back, as in curtailing a visit or curtailing spending. 'Lengthen' is the reverse; 'postpone' means to put off until later, which delays an event without cutting it short; and 'conceal' means to hide, a sense suggested only by the word's resemblance to curtain.

Correct answer: Strong

Robust means strong, sturdy and healthy, as in a robust frame or a robust economy. 'Feeble' means weak, the opposite; 'bulky' means large and awkward to handle, which describes size rather than strength; and 'rustic' sounds a little like robust but means plain and countrified.

Correct answer: Succinct

Concise means succinct, saying a great deal in few words. 'Verbose' means using more words than needed, the opposite; 'precise' looks similar but means exact or accurate, which a long statement can also be; and 'incisive' shares the ending but means sharp and penetrating in thought.

Correct answer: Passionate

Zealous means passionate, full of energetic devotion to a cause or goal. 'Indifferent' means having no interest or concern, the opposite; 'jealous' looks and sounds similar but means envious or possessive; and 'industrious' means hardworking, which describes steady effort rather than fervor.

Correct answer: Impede

To hamper is to impede, to get in the way of progress or movement, as bad weather hampers a search. 'Hasten' means to speed something up, the opposite; 'pamper' rhymes with hamper but means to indulge with comfort; and 'hammer' differs by one letter but means to strike repeatedly.

Correct answer: Crucial

Vital means crucial, absolutely necessary to something's success or survival, as in vital supplies. 'Trivial' means of little importance, the opposite; 'visual' looks similar but means relating to sight; and 'urgent' means needing action right away, which concerns timing rather than importance.

Correct answer: Dwindle

To wane is to dwindle, to decrease gradually in size or strength, as the moon wanes after it is full. 'Prosper' means to grow and thrive, close to the opposite; 'waver' looks similar but means to sway or hesitate; and 'wean' uses nearly the same letters but means to accustom someone to doing without something.

Correct answer: Prosperous

Affluent means prosperous, having plenty of money and comfort. 'Fluent' shares the root but means speaking or writing smoothly; 'influential' means having power over others, which wealth can bring but which is a different quality; and 'fashionable' means in keeping with current style, which costs money but does not mean having it.

Correct answer: Perplex

To baffle is to perplex, to confuse someone so completely that they cannot understand. 'Clarify' means to make something clear, the opposite; 'deceive' means to make someone believe something false, which misleads rather than bewilders; and 'babble' looks similar but means to talk rapidly and foolishly.

Correct answer: Severe

Stern means severe, serious and strict in manner, as a stern warning is. 'Merciful' means kind and forgiving, close to the opposite; 'stubborn' means unwilling to change one's mind, which is fixed rather than harsh; and 'sterile' looks similar but means free of germs or unable to produce offspring.

Correct answer: Start

To commence is to start, as a ceremony commences at noon. 'Conclude' means to bring to an end, the opposite; 'commend' looks similar but means to praise; and 'announce' means to declare publicly, which may come before a start without being one.

Correct answer: Fault

A flaw is a fault, an imperfection that spoils something, such as a flaw in a gem or in an argument. 'Merit' is a good quality, close to the opposite; 'flair' looks similar but means a natural talent; and 'quirk' means an odd habit or peculiarity, which is unusual rather than defective.

Correct answer: Shortfall

A deficit is a shortfall, the amount by which something falls short of what is needed, as when spending exceeds income. 'Surplus' is an excess, the opposite; 'deposit' looks similar but means money placed in an account; and 'liability' means a debt or obligation owed, which a deficit may create but which is not the gap itself.

Correct answer: Nimble

Agile means nimble, able to move quickly and easily. 'Awkward' means clumsy and ungainly, the opposite; 'fragile' shares the ending but means easily broken; and 'hasty' means done too quickly and carelessly, which is rushing rather than moving with ease.

Correct answer: Remedy

To rectify is to remedy, to put right something that is wrong, as in rectifying an error. 'Impair' means to damage or weaken, close to the opposite; 'ratify' looks similar but means to approve formally, as with a treaty; and 'verify' means to check that something is true, which confirms a fact without putting anything right.

Correct answer: Error

A blunder is an error, especially a careless or clumsy one. 'Triumph' is a great success, close to the opposite; 'plunder' rhymes with blunder but means goods taken by force; and 'gamble' is a risky move, which may pay off and is not a mistake in itself.

Correct answer: Commonplace

Mundane means commonplace, ordinary and lacking excitement, as in mundane chores. 'Exceptional' means far beyond the usual, the opposite; 'mandatory' looks a little similar but means required by rule, which describes obligation rather than dullness; and 'superficial' means concerned only with the surface, which describes a lack of depth rather than a lack of excitement.

Correct answer: Friendly

Amiable means friendly, pleasant and good-natured in manner. 'Abrasive' means harsh and rude in manner, close to the opposite; 'amenable' looks similar but means willing to go along with a suggestion; and 'capable' shares the ending but means able to do something well.

Correct answer: Curb

To inhibit is to curb, to hold back or restrain an action or process, as cold inhibits the growth of bacteria. 'Provoke' means to stir up or set off a reaction, close to the opposite; 'inhabit' looks similar but means to live in a place; and 'inherit' means to receive property or traits from those who came before.

Correct answer: Static

Stagnant means static, not moving or flowing and showing no change, as in stagnant water or a stagnant economy. 'Rippled' describes a surface stirred into small waves, the look of moving water; 'shallow' describes water that is not deep, whether it flows or not; and 'filthy' means very dirty, which stagnant water may become but which is not what the word means.

Correct answer: Real

Genuine means real, truly what it claims to be rather than counterfeit. 'Bogus' means fake, the opposite; 'generous' looks similar but means giving freely; and 'valuable' means worth a great deal, which a genuine item may or may not be.

Correct answer: Tolerant

Lenient means tolerant, mild rather than severe in judging or punishing, as a lenient sentence is. 'Stringent' means strict and demanding, the opposite; 'negligent' means failing to take proper care, which is carelessness rather than mercy; and 'indolent' shares the ending but means lazy and avoiding effort.

Correct answer: Part

A portion is a part, a share of something larger, as in a portion of the meal. 'Entirety' means the whole of something, the opposite; 'potion' looks similar but means a drink with supposed medicinal or magical power; and 'position' means a place or stance, which only resembles portion in spelling.

Correct answer: Intense

Vivid means intense, strikingly bright or clear, as in vivid colors or a vivid memory. 'Subdued' means toned down and soft, the opposite; 'livid' looks similar but means furious or bruise-colored; and 'glossy' means smooth and shiny, which describes a surface rather than the strength of a color.

Correct answer: Disconnect

To detach is to disconnect, to separate one thing from what it was joined to, as when detaching a trailer from a truck. 'Fasten' means to join or attach, the opposite; 'detain' looks similar but means to hold someone back or keep them in custody; and 'distribute' means to hand out or spread among many, which divides a supply rather than unfastening a part.

Correct answer: Energetic

Brisk means energetic, quick and active, as in a brisk walk. 'Leisurely' means unhurried and relaxed, the opposite; 'brittle' looks similar but means hard and easily broken; and 'frantic' means wild with fear or hurry, which is panic rather than healthy energy.

Correct answer: Conform

To comply is to conform, to act as a rule, order or request requires. 'Disobey' means to refuse to follow an order, the opposite; 'compile' looks similar but means to gather material into a list or collection; and 'protest' means to object publicly, which voices disagreement rather than going along.

Correct answer: Paltry

Meager means paltry, too small in amount to be enough, as in a meager ration. 'Lavish' means plentiful and generous, the opposite; 'eager' looks similar but means keen or impatient to do something; and 'bland' means lacking flavor or interest, which describes taste rather than amount.

Correct answer: Luminous

Radiant means luminous, shining brightly or glowing with light or happiness. 'Somber' means dark and gloomy, close to the opposite; 'radical' looks similar but means extreme or fundamental; and 'fragrant' shares radiant's -ant ending but means sweet-smelling.

Correct answer: Observe

To heed is to observe, to pay careful attention to advice or a warning and act on it. 'Neglect' means to ignore or fail to attend to, the opposite; 'delay' means to put off until later; and 'heckle' means to interrupt a speaker with jeers.

Correct answer: Shallow

Superficial most nearly means shallow: concerned only with the surface of something and lacking depth. 'Profound' is close to the opposite, describing deep thought or feeling; 'artificial' shares the same ending and is often confused with superficial, but it means made by people or fake, not lacking depth; and 'beneficial' also shares that ending but means helpful or useful.

Correct answer: Gain

Acquire most nearly means gain, to come to have or get something. 'Lose' is the opposite, to stop having it; 'require' looks and sounds similar but means to need; and 'request' means to ask for something, which may come before getting it but is not the same as getting it.

Correct answer: Tiresome

Tedious most nearly means tiresome: long, dull, and wearying. 'Lively' is close to the opposite, full of energy and interest; 'studious' looks similar but means devoted to study; and 'arduous' means hard and demanding, while a tedious task can be quite easy and simply dull.

Correct answer: Lessen

Diminish most nearly means lessen, to make or become smaller or less. 'Increase' is the opposite; 'demolish' looks similar but means to tear down or destroy completely; and 'divide' means to split into parts, which leaves the total amount the same.

Correct answer: Expert

Adept most nearly means expert, highly skilled at something. 'Clumsy' is close to the opposite; 'adaptable' looks and sounds similar but means able to adjust to new conditions; and 'confident' means sure of yourself, which a person can be without having real skill.

Correct answer: Unfriendly

Hostile most nearly means unfriendly, openly opposed or showing dislike. 'Amicable' is close to the opposite, meaning friendly and peaceable; 'volatile' means likely to change suddenly or flare up, which describes an unstable mood rather than open opposition; and 'suspicious' means distrustful, which a person can feel quietly without acting against anyone.

Correct answer: Forbid

Prohibit most nearly means forbid, to refuse to allow something by rule or authority. 'Permit' is the opposite, to allow; 'exhibit' shares the same ending but means to show or display; and 'condemn' means to declare something wrong or to sentence someone, which judges an act rather than forbidding it ahead of time.

Correct answer: Vary

Fluctuate most nearly means vary, to rise and fall or change irregularly. 'Settle' is close to the opposite, to become steady; 'rise' describes movement in one direction only, while something that fluctuates goes both up and down; and 'falter' means to lose strength or hesitate, not to move up and down.

Correct answer: Miserly

The word most nearly opposite to generous is miserly, unwilling to spend or give. 'Lavish' means giving or spending freely, which is close to generous rather than opposite; 'grateful' sounds related but means thankful for what you receive; and 'gracious' means kind and courteous, which also sits close to generous.

Correct answer: Shrink

The word most nearly opposite to expand is shrink, to become smaller. 'Inflate' and 'enlarge' both mean to make or grow bigger, so they are close to expand rather than opposite; and 'expend' looks almost the same but means to spend or use up.

Correct answer: Transient

The word most nearly opposite to permanent is transient, lasting only a short time. 'Durable' and 'persistent' both describe something that lasts or keeps going, which is close to permanent; and 'stationary' means not moving, which describes position rather than how long something lasts.

Correct answer: Cowardly

The word most nearly opposite to brave is cowardly, lacking courage in the face of danger. 'Fearless' means much the same as brave; 'brash' means bold in a rude or reckless way, which is too much daring rather than too little; and 'disloyal' means unfaithful to a person or cause, a different failing from a lack of courage.

Correct answer: Admirable

In this sentence meritorious means admirable, deserving praise and reward. 'Reckless' would criticize the squadron for careless risk rather than honor it; 'notorious' shares the same ending but means famous for something bad; and 'dangerous' describes the conditions under heavy fire, not the merit of the rescue itself.

Correct answer: Unclear

In this sentence ambiguous means unclear, open to more than one reading, which is why no one knew the real objective. 'Precise' is close to the opposite, exact and clearly defined; 'ambitious' looks similar but means eager to succeed; and 'secretive' means inclined to hide information, while the trouble with this briefing was that its meaning was uncertain, not that it was hidden.

Correct answer: Poise

In this sentence composure means poise, staying calm and self-controlled under pressure. 'Panic' is the opposite; 'posture' looks similar and suits an inspection, but it means the way the body is held; and 'courage' means bravery in the face of danger, while composure is about keeping calm.

Correct answer: Entrust

In this sentence delegate means entrust, to hand a task and the responsibility for it to someone else. 'Perform' is close to the opposite, doing the tasks yourself; 'debate' looks similar but means to argue a question; and 'oversee' means to watch over people as they work, which a commander may do after delegating but which is not the act of handing tasks off.

Correct answer: Mistaken

In this sentence erroneous means mistaken, containing errors, which is what a faulty sensor produces. 'Faultless' is the opposite, free of any error; 'erratic' looks similar but means irregular or unpredictable, and a reading can jump around and still be correct; and 'excessive' means more than is needed, while an erroneous reading can be too high or too low.

Correct answer: Defensible

In this sentence tenable means defensible, able to be held and supported against challenge, which is why the instructor praised it. 'Flimsy' is close to the opposite, weak and easily knocked down; 'tangible' looks similar but means able to be touched or clearly real; and 'unbeatable' goes too far, since a tenable argument can be defended but may still lose the debate.

Correct answer: Hurried

In this sentence cursory means hurried, quick and done without close attention. 'Thorough' is the opposite, careful and complete; 'cursive' looks similar but describes joined-up handwriting; and 'critical' means looking closely for faults, which takes far more care than a cursory glance.

Correct answer: Jointly

In this sentence in tandem means jointly, working together on the same task. 'Singly' is the opposite, one at a time and alone; 'randomly' looks similar but means without plan or pattern; and 'steadily' describes a constant, even pace, not working together.

Correct answer: 6

Subtract 13 from both sides to get 6x = 36, then divide both sides by 6, so x = 6; check: 6 times 6 plus 13 is 49. -6 subtracts in the wrong order, 13 - 49 = -36, before dividing by 6. 36 stops one step early, at the value of 6x rather than x. -36 makes both slips, subtracting in the wrong order and then stopping at 6x.

Correct answer: 8

Subtract 2k from both sides to get 3k - 18 = 6, add 18 to get 3k = 24, and divide by 3, so k = 8. 24 stops at the value of 3k and never divides by 3. -4 moves the 18 across without changing its sign, giving 3k = 6 - 18 = -12. 4 subtracts the constants in the wrong order, 18 - 6 = 12, so 3k = 12.

Correct answer: 17x - 35

Distribute the 7 to both terms in the brackets, 7(2x - 5) = 14x - 35, then add the other x term, 14x + 3x = 17x, giving 17x - 35. 17x - 5 multiplies only the 2x by 7 and leaves the 5 alone. 14x - 32 combines the 3x with the constant -35 as if they were like terms. 14x - 2 makes both slips: it leaves the 5 undistributed and then combines 3x with -5.

Correct answer: x < -2

Subtract 8 from both sides to get 3x < -6, then divide by 3; dividing by a positive number keeps the direction, so x < -2. x > -2 flips the sign even though nothing was divided by a negative. x < -6 stops at 3x < -6 and never divides by 3. x > -6 makes both slips, skipping the division and flipping the sign.

Correct answer: x < -4

Subtract 3 from both sides to get -4x > 16, then divide by -4; dividing by a negative number reverses the inequality, so x < -4. x > -4 divides correctly but forgets to reverse the sign. x < -5.5 adds 3 instead of subtracting it, giving -4x > 22, then divides and reverses correctly. x > -5.5 makes both slips.

Correct answer: (x + 3)(x + 8)

Look for two numbers that multiply to 24 and add to 11: 3 and 8 do both, so the factored form is (x + 3)(x + 8). (x + 4)(x + 6) multiplies to 24, but its middle term is 10x, not 11x. (x + 4)(x + 7) and (x + 2)(x + 9) both give 11x, but their constants are 28 and 18 rather than 24, so each checks only the sum.

Correct answer: (x + 2)(x - 7)

Look for two numbers that multiply to -14 and add to -5: 2 and -7 do both, so the factored form is (x + 2)(x - 7). (x - 2)(x + 7) puts the signs on the wrong factors and expands to x^2 + 5x - 14. (x + 1)(x - 14) uses another pair with product -14, but that pair adds to -13. (x - 1)(x + 14) uses the same pair with the signs reversed, giving a middle term of 13x.

Correct answer: 3

Adding the two equations cancels y: 5x + 5x = 10x and 24 + 6 = 30, so 10x = 30 and x = 3. 6 adds the equations but counts only one 5x, solving 5x = 30. 4.5 is the value of y (15 + 2y = 24), not x. 1.8 subtracts the constants while adding the x terms, solving 10x = 18.

Correct answer: x^2 + 3x - 28

Multiply each pair of terms: x times x = x^2, the outer and inner products -4x and 7x combine to 3x, and 7 times -4 = -28, so the product is x^2 + 3x - 28. x^2 - 3x - 28 gets the sign of the middle term wrong, as if it were 4x - 7x. x^2 + 3x + 28 drops the negative sign when multiplying 7 by -4. x^2 - 3x + 28 makes both sign slips.

Correct answer: 4

Multiply both sides by 2 to get 4x + 6 = 22, subtract 6 to get 4x = 16, and divide by 4, so x = 4. 7 adds the 6 instead of subtracting it, solving 4x = 28. 2.5 divides only the 4x by 2, leaving 2x + 6 = 11. 8.5 makes both slips, solving 2x = 17.

Correct answer: 28

Substitute r = 6 and s = -4: 6^2 + 2(-4) = 36 - 8 = 28. 4 doubles r instead of squaring it, giving 12 - 8. -2 forgets to square r at all, giving 6 - 8. 20 doubles r and also drops the negative sign on s, giving 12 + 8.

Correct answer: 5

Distribute on both sides to get 4p + 12 = 2p + 22, subtract 2p to get 2p + 12 = 22, subtract 12 to get 2p = 10, and divide by 2, so p = 5. 17 moves the 12 across as +12, solving 2p = 34. 7 multiplies only the p in each bracket, giving 4p + 3 = 2p + 11, and then also moves the 3 as +3, solving 2p = 14. 10 stops at 2p = 10 and never divides by 2.

Correct answer: -5

The roots of x^2 - 2x - 35 = 0 add to 2 and multiply to -35, so the other root r satisfies 7 + r = 2, giving r = -5; check: (x - 7)(x + 5) = 0. 5 takes the sum of the roots as -2 and also moves the 7 with the wrong sign (-2 + 7). -9 takes the sum as -2 but moves the 7 correctly (-2 - 7). 9 uses the right sum but moves the 7 with the wrong sign (2 + 7).

Correct answer: 20

Over the common denominator 10, x/2 + x/5 = 5x/10 + 2x/10 = 7x/10, so 7x = 140 and x = 20. 98 adds the denominators, solving x/7 = 14. 49 adds the numerators and the denominators, solving 2x/7 = 14. 70 writes both fractions over 10 but leaves each numerator as x, solving 2x/10 = 14.

Correct answer: 5t + 7

Group like terms: 8t - 3t = 5t and -5 + 12 = 7, so the expression simplifies to 5t + 7. 8t + 7 combines the constants but leaves out the -3t term. 5t - 7 works out 5 - 12 instead of -5 + 12, so the constant takes the wrong sign. 8t - 7 makes both slips.

Correct answer: 30

Multiply both sides by 6/5, the reciprocal of 5/6: 25 times 6 = 150, and 150 divided by 5 = 30. 150 multiplies by 6 but never divides by 5. 125 multiplies 25 by the 5 instead of dividing by it and never uses the 6. 25 skips both steps and treats the left side as plain x.

Correct answer: 6

Subtract 6x from both sides to get 3x - 7 = 11, add 7 to get 3x = 18, and divide by 3, so x = 6. 15 subtracts the 3 instead of dividing by it (18 - 3). 18 stops at 3x = 18 and never divides by 3. 3 divides 18 by 6, the coefficient from the right side, instead of by 3.

Correct answer: x ≥ 2

Subtract 14 from both sides to get -7x ≤ -14, then divide by -7; dividing by a negative number reverses the inequality, so x ≥ 2. x ≤ 2 forgets to reverse the sign. x > 2 reverses correctly but drops the 'or equal to' part, although x = 2 makes 14 - 7x exactly 0. x < 2 makes both slips.

Correct answer: 2x + 6

Distribute both factors: 4(2x - 1) = 8x - 4 and -2(3x - 5) = -6x + 10. Then 8x - 6x = 2x and -4 + 10 = 6, giving 2x + 6. 2x - 14 multiplies -2 by -5 as -10 instead of +10. 2x + 9 multiplies only the 2x by 4 and leaves the -1 alone. 2x - 11 makes both slips.

Correct answer: 12

Substitute 2 for x and square before multiplying: 4(2^2) - 3(2) + 2 = 16 - 6 + 2 = 12. 60 multiplies before squaring, (4 times 2)^2 = 64, then 64 - 6 + 2. 4 forgets to square, using 4 times 2 = 8, then 8 - 6 + 2. 15 subtracts 3 instead of 3x, giving 16 - 3 + 2.

Correct answer: (4x - 3)(4x + 3)

16x^2 - 9 is a difference of squares: 16x^2 is (4x)^2 and 9 is 3^2, so it factors as (4x - 3)(4x + 3), which multiplies back to 16x^2 - 9. (8x - 3)(8x + 3) halves 16 instead of taking its square root and expands to 64x^2 - 9; (4x - 9)(4x + 9) leaves the 9 unrooted and expands to 16x^2 - 81; (8x - 9)(8x + 9) makes both slips and expands to 64x^2 - 81.

Correct answer: 4

Subtract 3v from both sides to get 14 = 5v - 6, add 6 to get 20 = 5v, and divide by 5, so v = 4 (check: 3 times 4 plus 14 is 26, and 8 times 4 minus 6 is 26). 20 stops at 5v = 20 without dividing by 5; -4 comes from a sign slip that writes -5v = 20; -20 makes both slips.

Correct answer: 5

Adding the two equations cancels y and leaves 8x = 40, so x = 5 (and then y = 17 - 15 = 2). 2 is the value of y, not x; 8 comes from dividing 40 by 5 instead of by 8; 20 comes from subtracting 3x from 5x to get 2x = 40 while still adding the right-hand sides.

Correct answer: c^2 - 81

Multiply each pair of terms: c times c is c^2, the middle terms -9c and +9c cancel, and 9 times -9 is -81, so the product is c^2 - 81, a difference of squares. c^2 + 81 gives 9 times -9 as +81; c^2 - 18c + 81 is (c - 9)^2 and c^2 + 18c + 81 is (c + 9)^2, each squaring one factor instead of multiplying the two different factors.

Correct answer: 7n + 4

The product of seven and n is 7n, and four more than that product adds 4 after multiplying, so the expression is 7n + 4. 4n + 7 swaps the roles of the two numbers; 7(n + 4) adds 4 to n before multiplying, which is seven times four more than n; 4(n + 7) makes both slips.

Correct answer: 4

Divide both sides by 5 to get x^2 = 16, then take the positive square root, so x = 4 (check: 5 times 16 is 80). 8 halves 16 instead of taking its square root; 16 stops at x^2 = 16 without taking the square root; 20 multiplies 80 by 5 instead of dividing and then takes the square root of 400.

Correct answer: 1

Distribute -4 to get 20 - 4x - 12 = 4, so 8 - 4x = 4, then -4x = -4 and x = 1. 7 comes from writing -4 times 3 as +12, which gives 32 - 4x = 4; -1 drops the sign when dividing -4x = -4; -7 makes both sign slips.

Correct answer: 5

Substitute 4x for y: 2x + 4x = 30, so 6x = 30 and x = 5 (then y = 20). 20 is the value of y, not x; 13 substitutes 4 instead of 4x, giving 2x + 4 = 30; 6 drops the coefficient 2 and solves x + 4x = 30.

Correct answer: 17

Absolute value is the distance from zero on the number line, and a distance is never negative, so the absolute value of -17 is 17. -17 keeps the sign instead of dropping it; 1/17 confuses absolute value with the reciprocal; -1/17 is the opposite of the reciprocal, a different operation again.

Correct answer: 9 and -9

The absolute value of x is 9 whenever x is 9 units from zero, and both 9 and -9 are, so the solutions are 9 and -9. The set '9 only' forgets the negative solution; '3 and -3' treats absolute value like a square root and solves as if x^2 = 9; '3 only' makes both slips.

Correct answer: 1024

4^5 means five factors of 4: 4 times 4 is 16, times 4 is 64, times 4 is 256, and times 4 is 1024. 20 multiplies the base by the exponent; 4096 uses six factors of 4 instead of five; 625 swaps the base and the exponent, working out 5^4.

Correct answer: 11

Division comes before addition, so 6 divided by 3 is 2 and 9 + 2 = 11. 5 adds first and then divides 15 by 3; 27 multiplies 6 by 3 instead of dividing, giving 9 + 18; 15 adds 9 and 6 and drops the division altogether.

Correct answer: 39

Parentheses first: 9 - 6 = 3, and 3 cubed is 27; then 4 times 3 is 12, and 27 + 12 = 39. 15 drops the exponent and adds 3 + 12; 21 squares 3 instead of cubing it (9 + 12); 34 adds 4 and 3 instead of multiplying them (27 + 7).

Correct answer: w^12

When powers of the same base are multiplied, the exponents add: 6 + 6 = 12, so the product is w^12 with no coefficient. w^36 multiplies the exponents instead of adding them; 2w^12 adds the exponents but also puts a 2 in front, as if the two factors had been added; 2w^36 makes both slips.

Correct answer: p^7

When powers of the same base are divided, subtract the exponents: 12 - 5 = 7, so the result is p^7. p^17 adds the exponents, the rule for multiplying; p^60 multiplies them, the rule for a power of a power; p^2.4 divides 12 by 5, which is not an exponent rule at all.

Correct answer: 30

Division and multiplication come before addition: 54 divided by 9 is 6 and 4 times 6 is 24, so 6 + 24 = 30. 60 works strictly left to right (6 + 4 = 10, then 10 times 6); 16 adds 4 and 6 instead of multiplying them; 144 multiplies 6 by 24 at the last step instead of adding.

Correct answer: 729

A power raised to a power multiplies the exponents: 3 times 2 is 6, and 3^6 = 729 (the same as 27 squared). 243 adds the exponents to get 3^5; 54 multiplies 27 by 2 instead of squaring it; 216 multiplies the base 3 by the outer exponent 2 to get 6 and then cubes that.

Correct answer: 95

The exponent comes first, then the division, then the subtraction: 5^2 = 25, 25 divided by 5 is 5, and 100 - 5 = 95. 15 subtracts before dividing, (100 - 25) divided by 5; 98 doubles 5 instead of squaring it, so it subtracts 10 divided by 5; 18 makes both slips, (100 - 10) divided by 5.

Correct answer: 1/16

A negative exponent means the reciprocal of the positive power, so 4^-2 is 1 divided by 4^2, which is 1/16, a positive number. 1/8 multiplies 4 by 2 instead of squaring it; -1/16 takes the reciprocal but wrongly makes the result negative; -1/8 makes both slips.

Correct answer: 54

Parentheses first: 8 - 5 = 3; then the exponent: 3^2 = 9; then the multiplication: 6 times 9 = 54. 9 stops after squaring and never multiplies by 6; 324 multiplies 6 by 3 before squaring, giving 18^2; 234 squares 8 and 5 separately, 6 times (64 - 25).

Correct answer: 8x^7

Multiply the coefficients and add the exponents of x: 4 times 2 is 8 and 4 + 3 is 7, so the product is 8x^7. 6x^7 adds the coefficients instead of multiplying them; 8x^12 multiplies the exponents instead of adding them; 6x^12 makes both slips.

Correct answer: 1

By the zero-exponent rule, any nonzero number raised to the power 0 equals 1, so 6^0 = 1 (6 divided by 6 is both 6^0 and 1). 0 treats the exponent as a multiplier, 6 times 0; 6 leaves the base unchanged; 1/6 confuses a zero exponent with a negative one, since 6^-1 is 1/6.

Correct answer: 14

The square root of 196 is the number that multiplies by itself to give 196, and 14 times 14 = 196, so the answer is 14. 49 divides 196 by the perfect square 4 (196 = 4 times 49) and then never takes a square root; 98 halves 196 instead of taking its square root; 16 is too large, since 16 times 16 is 256, not 196.

Correct answer: 23

Inside the parentheses, multiplication comes first: 4 times 6 is 24 and 3 + 24 = 27; then 50 - 27 = 23. 8 works left to right inside the parentheses, (3 + 4) times 6 = 42, and 50 - 42 = 8; 47 subtracts only the 3 and drops the 4 times 6; 37 adds the 4 and the 6 instead of multiplying them, so it takes 3 + 4 + 6 = 13 from 50.

Correct answer: 17

Evaluate each power first: 5^2 is 25 and 2^3 is 8, so 25 - 8 = 17. 16 swaps the base and exponent of 2^3 and subtracts 3^2 = 9; 2 writes 5^2 as 5 times 2 = 10, giving 10 - 8; 4 writes both powers as products, giving 10 - 6.

Correct answer: 7.3 x 10^5

Scientific notation puts one nonzero digit before the decimal point: 730,000 is 7.3 times 100,000, and the decimal point moves 5 places, so the number is 7.3 x 10^5. 7.3 x 10^4 counts the four zeros instead of the five places the decimal point moves; 7.3 x 10^-5 uses a negative exponent, which describes a number smaller than 1; 7.3 x 10^-4 makes both slips.

Correct answer: 16

Take each square root first: the square root of 100 is 10 and the square root of 36 is 6, so 10 + 6 = 16. 46 roots the 100 but forgets to root the 36 (10 + 36); 106 roots the 36 but not the 100 (100 + 6); 136 adds the two numbers without taking either root.

Correct answer: 35

Exponent first: 4^2 = 16; then multiplication: 2 times 16 = 32; then add and subtract from left to right: 8 + 32 = 40 and 40 - 5 = 35. 67 multiplies 2 by 4 before squaring, so it adds (2 times 4)^2 = 64; 19 doubles 4 instead of squaring it, so it adds 2 times 8 = 16; 155 adds 8 and 2 first and multiplies 10 by 16 before subtracting 5.

Correct answer: 6^5

When powers of the same base are multiplied, keep the base and add the exponents: 3 + 2 = 5, so the product is 6^5. 6^6 multiplies the exponents instead of adding them; 12^5 adds the bases as well as the exponents, but the base stays 6; 12^6 adds the bases and also multiplies the exponents.

Correct answer: 9

The fraction bar groups the whole top: 24 + 12 = 36, and 2^2 = 4, so 36 divided by 4 is 9. 30 divides only the 12, and by 2 instead of 4, then adds 24; 6 divides only the 24 by 4 and loses the 12; 18 divides 36 by 2 and ignores the exponent.

Correct answer: 40 square inches

The area of a triangle is one-half times base times height: one-half of 16 times 5 is one-half of 80, which is 40 square inches. 80 square inches forgets the one-half and gives the area of a 16 by 5 rectangle; 42 square inches is the perimeter of that rectangle, 2 times (16 + 5), not an area; 13 square inches halves the base to 8 and then adds the 5 instead of multiplying.

Correct answer: 17

By the Pythagorean theorem the hypotenuse squared is 8^2 + 15^2 = 64 + 225 = 289, and the square root of 289 is 17. 23 adds the legs without squaring them; 529 squares the sum of the legs, (8 + 15)^2, instead of adding their squares, and stops before the root; 289 stops before taking the square root.

Correct answer: 33 centimeters

An equilateral triangle has three equal sides, so its perimeter is 3 times 11 = 33 centimeters. 121 centimeters squares the side, 11 times 11, which is the area of a square rather than a perimeter; 14 centimeters adds 3 to 11 instead of multiplying; 22 centimeters counts only two of the three sides.

Correct answer: 60 degrees

The interior angles of a triangle add to 180 degrees, so the third angle is 180 - 45 - 75 = 60 degrees. 105 degrees subtracts only the 75-degree angle; 135 degrees subtracts only the 45-degree angle; 120 degrees adds the two given angles instead of subtracting them from 180.

Correct answer: 25.12

Circumference is pi times the diameter, so 3.14 times 8 = 25.12. 200.96 uses the area formula with the diameter as the radius, 3.14 times 8 times 8; 50.24 puts the diameter into 2 times pi times the radius, doubling the answer; 2.55 divides 8 by 3.14 instead of multiplying.

Correct answer: 120 cubic units

The volume of a rectangular box is length times width times height: 6 times 4 is 24, and 24 times 5 = 120 cubic units. 24 cubic units stops at the area of the 6 by 4 base; 29 cubic units adds the height instead of multiplying by it; 148 cubic units is the surface area, 2 times (24 + 30 + 20), not the volume.

Correct answer: 65 degrees

Complementary angles add to 90 degrees, so the other angle is 90 - 25 = 65 degrees. 155 degrees uses 180, the sum for supplementary angles; 75 degrees and 55 degrees are borrowing slips in 90 - 25: 75 takes the smaller digit from the larger in each place, and 55 borrows one ten too many.

Correct answer: 5

The horizontal change is 4 - 1 = 3 and the vertical change is 6 - 2 = 4, so the distance is the square root of 3^2 + 4^2 = 25, which is 5. 7 adds the two changes without squaring them, the distance along the grid lines; 25 stops at 3^2 + 4^2 = 25 and skips the square root; 12.5 halves 25 instead of taking its square root.

Correct answer: 115 degrees

Supplementary angles add to 180 degrees, so the other angle is 180 - 65 = 115 degrees. 25 degrees uses 90, the sum for complementary angles; 245 degrees adds 65 to 180 instead of subtracting; 155 degrees makes both slips and adds 65 to 90.

Correct answer: Octopuses became remarkably clever although they and mammals evolved separately.

Octopuses became remarkably clever although they and mammals evolved separately. That is the main idea: the passage lists the octopus's skills and then says what makes them remarkable is that it achieved them "along an evolutionary path entirely separate from that of mammals." The options "Octopuses are able to open jars to reach the food inside them." and "Octopuses are able to recognize the individual human handlers who look after them." are true supporting examples, but each covers only one detail, not the passage as a whole. The option "Unlike octopuses, most invertebrates have not been considered intelligent." generalizes about other invertebrates, which is never the focus of the passage.

Correct answer: A high price is not a reliable sign of quality because expectation shapes our judgment

The central point is that a high price is not a reliable sign of quality because expectation shapes our judgment: the passage sets up the belief that price signals quality, knocks it down with blind taste tests, and ends by saying much of what we pay for is the expectation a price creates. 'Blind taste tests show that the cheaper products taste better than the costly ones' goes beyond the evidence, which shows only that people often cannot tell the two apart. 'Stores raise prices because shoppers believe that a high price means a better product' is never claimed; the passage says nothing about how stores set prices. 'Shoppers cannot tell costly products from the cheap ones once the labels are taken off' is the supporting evidence, not the point that evidence is used to make.

Correct answer: The reef was built up over ages from the skeletons of billions of tiny polyps

The main idea is that the reef was built up over ages from the skeletons of billions of tiny polyps: the passage corrects the picture of a single living structure and calls the reef the lasting record of countless small lives. 'The reef is a single living creature that grew larger over thousands of years' repeats the very image the first sentence says is mistaken. 'Each one of the tiny polyps in a colony secretes its own hard outer skeleton' is one step in the process, not the idea the whole passage builds toward. 'The largest formations on Earth are the work of countless small living things' stretches a point about one reef into a claim about every large formation, which the passage never makes.

Correct answer: The delay is being caused by a mechanical problem with the aircraft itself

The most reasonable inference is that the delay is being caused by a mechanical problem with the aircraft itself: the maintenance crew brings equipment to the right engine, mechanics open a panel and confer, and connecting passengers are rebooked because the wait will be long. 'The delay is being caused by a storm moving toward the destination airport' has no support, since the passage mentions no weather at all. 'The passengers have to wait while heavy freight gets loaded onto the plane' misreads the heavy equipment, which the maintenance crew rolls to the engine rather than loading as cargo. 'The passengers have asked to switch over to flights on another airline' reverses who acts; the gate agent begins the rebooking, and nothing says passengers asked for it.

Correct answer: Life found at the vents disproved the old belief in a barren deep ocean

The main idea is that life found at the vents disproved the old belief in a barren deep ocean: the passage moves from the old assumption to the vent creatures and ends by saying the discovery overturned ideas about where life can exist. 'The deep ocean is far too dark and cold to hold much life of any kind' is the assumption the passage says was overturned. 'Creatures at the deep vents draw on a chemical source instead of sunlight' is a true detail about the vent creatures, but it supports the main idea rather than stating it. 'Scientists now believe the first creatures on Earth lived in the deep sea' claims more than the passage says; it is about where life can exist, not where life began.

Correct answer: The vendors are leaving early because a storm seems to be on its way

The inference is that the vendors are leaving early because a storm seems to be on its way: they fold their awnings and load crates in a hurry while glancing again and again at the darkening sky to the west. 'The vendors are packing up early since their goods have already sold out' fits the empty market but ignores the darkening sky, and nothing mentions sales. 'The vendors are moving their stalls to a new market just west of the town' misreads the glances west, which are at the sky, not toward a new site. 'The vendors are closing at midmorning as they do on most days of the week' contradicts the passage, which calls the marketplace usually crowded.

Correct answer: Goldfish have a much longer memory than the popular myth suggests

The main idea is that goldfish have a much longer memory than the popular myth suggests: the passage states the few-seconds belief, then shows goldfish remembering learned tasks weeks later, and says the myth has little basis in fact. 'Goldfish forget most of what they learn within just a few seconds' is the myth the passage rejects. 'Goldfish can be trained to push levers and find their way through mazes' lists the evidence, not the point the evidence proves. 'Careful experiments show that goldfish are smarter than most other fish' adds a comparison with other fish that the passage never makes.

Correct answer: His work on the audit has earned him new recognition

The most reasonable inference is that his work on the audit has earned him new recognition: he went unnoticed for years, and only after the audit did the handshakes, the warm mention, and the parking space appear. 'He is being rewarded for his many long years of service at the firm' misses the timing, since those years passed without notice and the praise began after the audit. 'He has been promoted to take over from the owner as head of the firm' reads far more into a parking space and a warm mention than the passage supports. 'The managers hope to win him over in their dispute with the owner' invents a conflict; the owner praises him too, so nothing suggests a dispute.

Correct answer: Reducing and reusing are more effective than recycling because they stop waste before it starts

The central message is that reducing and reusing are more effective than recycling because they stop waste before it starts: the passage calls recycling the last and least effective of three steps and says reducing and reusing prevent waste before it begins. 'Recycling is the best answer to the waste problem because it keeps materials out of the landfill' repeats the popular praise the passage pushes back against. 'Recycling should be stopped altogether, since all it does is manage trash headed for the landfill' overstates the point; the passage ranks recycling last but never says to give it up. 'Reusing what we already own is the first step, and recycling is the step that follows' sets out an order the passage never gives, since it names reducing before reusing, and it misses the claim that both beat recycling.

Correct answer: She spotted a danger that she had nearly missed

The inference is that she spotted a danger that she had nearly missed: she reaches confidently for her queen, freezes, scans the far corner, breathes out slowly, and picks a different move, which is what a player does on catching a threat just in time. 'She forgot which piece she had planned to move on this turn' does not fit, since she reached straight for her queen and changed her mind only after scanning the board. 'She was pretending to hesitate so her opponent would grow careless' reads a bluff into the scene with nothing to support it. 'She realized she should wait and let her opponent make the next move' is contradicted by the last line, where she goes on to choose a different move herself.

Correct answer: A sponge cleverly soaks up and releases far more water than its small size suggests

The main idea is that a sponge cleverly soaks up and releases far more water than its small size suggests: the passage calls it a marvel of simple engineering, explains how it holds more water than its size would suggest, and says it gives the water back just as readily. 'Sponges are cheap and handy mainly because they are thrown away after a single use' reverses the passage, which calls the sponge endlessly reusable. 'A great many household tools are clever feats of engineering that people take for granted' turns a point about the sponge into a claim about household tools in general. 'The countless small pores of a sponge draw water in through a natural pulling force' is one detail of how it works, not the idea the passage is built around.

Correct answer: The rookie ran the final lap much faster than anybody had expected

The most reasonable inference is that the rookie ran the final lap much faster than anybody had expected: the coach looks at the stopwatch again in disbelief, the assistant laughs, and the two at once start choosing championship races for him. 'The coach thought his stopwatch had given the rookie a false time' misreads the double take; a coach who distrusted the watch would not start planning championship races. 'The rookie ran the race so slowly that the coach and assistant laughed' takes the laughter the wrong way, since it leads straight to talk of big races. 'The rookie has already won his place in the upcoming championship race' goes too far; they are only discussing which races to enter him in.

Correct answer: Wheels were used in pottery long before they carried cargo or people

The central point is that wheels were used in pottery long before they carried cargo or people: the passage says the earliest wheels were potters' wheels for shaping clay and that only centuries later did someone roll the idea along the ground. 'The wheel was invented by an early potter in a single flash of insight' repeats the flash-of-insight image the first sentence sets out to correct. 'Carts came first, and potters adopted the wheel many centuries later' reverses the order the passage gives. 'Transport became faster once wheels were invented' may well be true, but the passage says nothing about speed; it is about what the first wheels were used for.

Correct answer: The pupils have rigged the door to play a prank on the teacher

The inference is that the pupils have rigged the door to play a prank on the teacher: an eraser is balanced on top of a door left slightly open, and the students go quiet and bite back grins as she walks toward it. 'The students are quiet because they respect and fear a new teacher' ignores the hidden grins, which show they are waiting for something to happen. 'The teacher set the eraser on the door to see how a class responds' reverses who set it up, since she is only now walking into the room. 'The eraser fell on the door by accident before the teacher came' cannot explain a carefully balanced eraser or students watching to see her walk under it.

Correct answer: The efficient light of fireflies is inspiring engineers to design more efficient lighting

The main idea is that the efficient light of fireflies is inspiring engineers to design more efficient lighting: the passage describes a cold light that loses almost no energy as heat and says engineers hope to build lighting that wastes far less power than today's bulbs. 'The glow of fireflies comes about by accident when a chemical reaction inside them gives off heat' contradicts the first two sentences, which say the glow is no accident and gives off almost no heat. 'Engineers studying fireflies have already designed bulbs that copy the light these insects make' goes too far; the engineers only hope to design such lighting. 'Modern bulbs waste power because they lack the rare chemical that fireflies use to glow' invents a cause the passage never gives for why bulbs waste power.

Correct answer: Recent changes at the restaurant drove away its loyal customers

The most reasonable inference is that recent changes at the restaurant drove away its loyal customers: a new menu replaced the dishes regulars loved, longtime cooks left, and reviews complain of slow service and smaller portions, and now the tables sit empty. 'The restaurant is now losing customers because a rival opened nearby' names a cause the passage never mentions. 'The restaurant now refuses reservations, so customers no longer come' misreads the first line, which says reservations were once needed weeks ahead, not that they are now refused. 'Cooks left after the restaurant had already lost its loyal customers' turns cause and effect around; the cooks leaving is one of the changes listed as reasons for the empty tables.

Correct answer: The beauty of a bridge depends on the hidden foundations beneath the water

The main idea is that the beauty of a bridge depends on the hidden foundations beneath the water: the passage contrasts the admired spans with the massive foundations below and ends by saying the beauty we see depends on the unseen work beneath. 'The graceful span is the strongest and the most important part of a bridge' reverses the passage, which places the true strength in the hidden foundations. 'The massive foundations beneath the water must be rebuilt as storms hit them' adds a claim about repairs the passage never makes; it says the foundations anchor the bridge against storms and currents. 'People admire the graceful span of a bridge as it rises high above the water' restates the opening detail, not the point the passage makes about it.

Correct answer: He is shaken and needs a short recess to regroup with the client

The inference is that he is shaken and needs a short recess to regroup with the client: a normally confident lawyer pauses longer than usual, shuffles his notes twice, clears his throat, and asks for a brief recess to consult his client, all signs that the question caught him off guard. 'He is stalling and wants a recess to wear down the other party' reads a tactic into what the passage presents as unusual hesitation in a confident man. 'He feels unwell today and wants a recess so he can call his doctor' misreads the throat-clearing; he asks for the recess to consult his client, not a doctor. 'He knows he is beaten and will settle the case with the other side' goes far beyond one awkward question; nothing says the case is lost or that a settlement is planned.

Correct answer: The salt of our body fluids echoes the ancient seas where life began

The main idea is that the salt of our body fluids echoes the ancient seas where life began: the passage notes that blood, sweat, and tears carry salt in proportions close to seawater and links that to the oceans where life first began. 'Humans first evolved in the ocean and later crawled out onto dry land' makes a claim about human evolution that the passage never makes; it speaks only of where life first began. 'Blood, sweat, and tears hold far more salt than the water of the ocean' misreads the passage, which says the proportions are strikingly close to seawater, not higher. 'Scientists have proved the salt in our body fluids came from the ocean' overstates a cautious point; only some scientists see a faint echo, and nothing is said to be proved.

Correct answer: The person who was in the cabin left suddenly and in a great hurry

The most reasonable inference is that the person who was in the cabin left suddenly and in a great hurry: the door swings open, a meal is left half-eaten and still warm, a chair is tipped over, a boot lies at the threshold, and footprints lead away down the trail. 'Someone broke into the cabin and stole the belongings of its owners' adds a theft that nothing in the passage describes. 'The cabin has stood empty for many weeks since its owner moved away' is ruled out by the meal that is still warm. 'The person who was in the cabin went out for a short, easy walk' does not explain the tipped chair, the dropped boot, or the meal left unfinished.

Correct answer: Vaccines train the body to fight a germ before a real infection

The central point is that vaccines train the body to fight a germ before a real infection: the passage explains that a harmless piece or weakened form of a germ teaches the immune system to recognize the threat, so the body is ready when the actual germ appears. 'Vaccines give the body a mild case of the disease a germ causes' is a common misunderstanding; the passage says vaccines use a harmless piece or a weakened form of the germ, not the disease itself. 'The body is unable to fight off a germ unless vaccines train it' stretches the point too far; the passage says vaccines prepare the body in advance, not that it is helpless without them. 'Vaccines kill off a germ after the body has already become sick' reverses the timing, since the passage stresses preparing the body before the germ ever arrives.

Correct answer: He is reluctant to take the eager dog out for a walk in the rain

The inference is that he is reluctant to take the eager dog out for a walk in the rain: he stands at the door with the leash, looks out at the rain, then puts the leash down and turns on the television while the dog waits. 'He has decided to give up the dog he begged for in the first place' reads far too much into one rainy afternoon; nothing suggests he plans to part with the dog. 'He is waiting for the dog to calm down before a walk in the rain' does not fit, since he settles on the couch with the television and the dog is simply waiting by the door. 'He forgot he had promised to take the dog for a walk before supper' is ruled out by the leash already in his hand, which shows he knows about the walk.

Correct answer: The word disaster preserves an old belief that stars caused misfortune

The main idea is that the word disaster preserves an old belief that stars caused misfortune: the passage traces the word to roots meaning bad star and notes that it survives even though the belief behind it has faded. 'People once believed that planets sealed the fate of voyages and battles' is true of the past, but it is the background, not the point the passage makes about the word. 'Most people today still blame their bad luck on the position of stars' contradicts the last sentence, which says almost no one does today. 'The word disaster was first used by sailors to describe their shipwrecks' invents an origin; the passage traces the word to roots meaning bad star.

Correct answer: She is expecting a major event to occur in the night sky

The most reasonable inference is that she is expecting a major event to occur in the night sky: she circled this one date months ago, sets up early, checks the forecast three times, keeps watching the eastern horizon, and turns down every other plan for the evening. 'She is worried that a storm will soon damage the telescope' misreads the forecast checks, which show she wants a clear sky for viewing, not that she fears damage. 'She is testing a new telescope before she uses it for real' does not explain why one date was circled months in advance. 'She has a meeting that night that she is hoping to skip' reverses the passage; she refused other appointments because of the sky, not to dodge one meeting.

Correct answer: The hunt for spices drove voyages that changed how the world was linked

The main idea is that the hunt for spices drove voyages that changed how the world was linked: the passage says the spice trade did more than move goods, listing new sea routes, daring voyages, and cultures meeting for the first time, and ends by saying it reshaped the map of the world. 'The merchants traded spices mainly because pepper and cinnamon were rare' names a reason for the trade that the passage never gives. 'The spice trade did little more than carry pepper and cinnamon to market' contradicts the first sentence, which says the trade did far more than carry spices. 'The spice trade mattered mainly because it made its merchants rich' adds a claim about wealth that the passage never makes.

Correct answer: The players are crushed after losing the big championship game

The inference is that the players are crushed after losing the big championship game: the usually rowdy locker room is silent, players hide under towels, the coach stares at the floor, and the scoreboard still shows the margin of the championship game they just lost. 'The team lost after its coach made several bad decisions in a row' blames the coach, but the passage gives no reason for the loss. 'The players are resting quietly before the final championship match' gets the timing wrong, since the game has already been played and lost. 'The team is upset that the scoreboard showed the wrong final margin' misreads the scoreboard, which simply still shows the real final margin.

Correct answer: Constellations are tricks of perspective, not real groups of related stars

The main idea is that constellations are tricks of perspective, not real groups of related stars: the passage says the stars in a pattern have nothing to do with one another and are joined only by the chance angle from which we view them. 'Stars in the same constellation sit at roughly the same distance from Earth' contradicts the passage, which says they lie at wildly different distances. 'Constellations were first drawn, long ago, to help sailors steer by stars' gives a purpose for constellations that the passage never mentions. 'Some stars in a constellation, though they look near, lie far behind others' is a true detail, but it is evidence for the main idea rather than the idea itself.

Correct answer: The bookstore is about to close after forty years of business

The most reasonable inference is that the bookstore is about to close after forty years of business: a sign thanks customers for decades of loyalty, shelves that were once packed stand half empty, and the owner spends his time with old friends rather than on sales. 'The owner is selling off old books to make room for new ones' does not fit the farewell-style thank-you sign. 'The bookstore is ready to expand thanks to its loyal customers' contradicts the half-empty shelves and the owner's lack of sales. 'The owner is too busy talking with friends to care about sales' takes the chatting at face value and ignores the sign and empty shelves that explain it.

Correct answer: What we call common sense is mostly learned and varies across cultures

The central point is that what we call common sense is mostly learned and varies across cultures: the passage says what counts as obvious differs from place to place and ends by calling so-called common sense largely learned, not born in us. 'A gesture seen as polite in one country can be an insult somewhere else' is the example the passage uses, not the point the example supports. 'Everyone is born with an identical sense of what is obvious and polite' is the assumption the passage rejects. 'Travelers should learn the local customs before they visit another land' is advice the passage never gives.

Correct answer: The new toys turned bath time into something the toddler enjoys

The inference is that the new toys turned bath time into something the toddler enjoys: the toddler who screamed at every bath now splashes and laughs, and the only change the passage names is the floating toys and the pouring cup his mother added. 'The toddler has outgrown his fear of water as he has grown older' offers a cause the passage never mentions and ignores the toys. 'The mother has warmed the water so the toddler is no longer cold' invents a change to the water; the passage says nothing about its temperature. 'The toddler still dislikes baths but is pretending to be happy' is contradicted by the splashing and the giggles that replace his cries.

Correct answer: Though seen as weeds, dandelions are useful plants with many edible parts

The main idea is that, though seen as weeds, dandelions are useful plants with many edible parts: the passage contrasts the plant's reputation as a weed with leaves for salads, roots for a drink, and flowers for syrup. 'Dandelions are useless pests that most gardeners are right to fight' reverses the passage, which says nearly every part of the plant is useful. 'Dandelions are now widely farmed around the world for both food and medicine' changes the past to the present; the passage says the plant was once valued as food and medicine. 'Most weeds, such as dandelions, are more useful than people realize' stretches a point about one plant into a claim about most weeds.

Correct answer: She is eagerly waiting to greet a person she loves at the gate

The most reasonable inference is that she is eagerly waiting to greet a person she loves at the gate: she checks her watch, scans each arriving passenger with rising eagerness, hides a bouquet, and then drops the flowers and runs to a man in uniform. 'She is a florist who brings flowers to a passenger at the gate' cannot explain why she drops the bouquet and runs to him. 'She is nervous about meeting a stranger who is due at the gate' misreads her rising eagerness and her run toward him, which show joy, not nerves. 'She is late for her own flight and is now rushing to the gate' misreads the watch-checking; she is already at the gate watching arrivals, not hurrying to catch a plane.

Correct answer: The ten percent idea is a myth because nearly the whole brain is active

The main idea is that the ten percent idea is a myth because nearly the whole brain is active: the passage names the myth, cites scans showing many regions active even in simple tasks, and ends by saying there is no idle reserve. 'Simple tasks light up a few regions of the brain, leaving most idle' contradicts the scans, which show simple tasks lighting up many regions at once. 'People could become smarter by unlocking the idle parts of their brain' restates the myth's promise; the passage says no idle reserve is waiting to be unlocked. 'Brain scans are the best tool because they show the whole brain at work' turns the evidence into a claim about scanning tools that the passage never makes.

Correct answer: The new factory upstream is probably polluting the water in the well

The inference is that the new factory upstream is probably polluting the water in the well: only after the factory opened did the water turn cloudy and several children fall ill, and the council at once called an urgent meeting with the factory's owners. 'The children fell ill from flu that began before the factory opened' contradicts the timing, since the passage says the trouble came after the factory opened. 'The well has dried up since the new factory began drawing river water' misreads the problem; the water turned cloudy, not scarce. 'The villagers are meeting the owners to ask about jobs at the factory' ignores the sick children and cloudy water that make the meeting urgent.

Correct answer: Technology replaced the keepers, leaving the towers as relics of the past

The central message is that technology replaced the keepers, leaving the towers as relics of the past: the passage contrasts the keepers who once tended the flame with today's automated lights and satellite navigation, and calls the towers monuments to a vanished way of life. 'The lighthouses are no longer needed, now that ships use satellite guidance' goes too far; the passage says automated lights replaced the keepers, not that the lights themselves are useless. 'Lighthouse keepers worked hard, keeping their flames lit through the storms' is a detail about the past, not the message about what changed. 'The old lighthouse towers should be protected as monuments to the past' turns a description into advice the passage never gives.

Correct answer: He no longer trusts the charity to spend its money wisely

The most reasonable inference is that he no longer trusts the charity to spend its money wisely: he gave freely last year, but after news reports questioned how the charity spent its funds and a former employee spoke out about waste, he ignores its letter and calls. 'He is upset that the charity keeps asking him for more money' ignores the reports of waste that the passage places right before his silence. 'He has run low on money and can no longer afford a gift' offers a cause the passage never mentions. 'He is angry at the former worker for criticizing the charity' reverses where his doubts point, since the criticism is what turned him away from the charity.

Correct answer: Bone is living tissue which the body constantly breaks down and rebuilds

The main idea is that bone is living tissue which the body constantly breaks down and rebuilds: the passage rejects the picture of dry, lifeless scaffolding and explains that cells keep removing old bone and laying down new material. 'Bone forms an unchanging frame that stays the same in youth and old age' is the view the passage rejects; it says your skeleton today is not the one you had a decade ago. 'Bone cells mostly break down old bone, so the skeleton gets weak with age' leaves out the new material that cells lay down and adds a claim about aging the passage never makes. 'Bone is the most active tissue, so the skeleton grows stronger as it ages' overstates the last sentence, which calls bone among the most active tissues, and adds a claim about strength the passage never makes.

Correct answer: He is reading the signs and expects a storm to arrive soon

The inference is that he is reading the signs and expects a storm to arrive soon: gulls flying inland, a falling barometer, and long swells from the open sea lead him to reef the sails and secure the deck before the sky shows any trouble. 'He is getting the boat ready for a long race on the open sea' misreads the preparations; reefing sails and securing gear make a boat safer in rough weather, not faster. 'He thinks the gulls flying inland show that land is close by' misreads the gulls, which he reads as a weather warning along with the barometer and swells. 'He thinks the barometer is broken and gives bad readings' cannot be right, since he acts on the falling reading at once.

Correct answer: Deserts are defined by low precipitation, so even icy Antarctica counts as one

The main idea is that deserts are defined by low precipitation, so even icy Antarctica counts as one: the passage replaces the hot-sand picture with the real definition, little rain or snow, and applies it to the frozen continent. 'Heat and a lack of plants define a desert, so frozen Antarctica cannot be one' repeats the mistaken picture the passage corrects, since a desert is defined not by temperature. 'Most deserts, like Antarctica, are cold places buried under thick sheets of ice' stretches one example into a claim about most deserts. 'Antarctica receives far too much snow each year to count as a true desert' contradicts the passage, which says the continent gets almost no snow or rain.

Correct answer: Her actions fail to match the openness she promised her staff

The most reasonable inference is that her actions fail to match the openness she promised her staff: she announced an open-door policy, yet her door is usually closed, messages go unanswered for days, and she has no time for the meetings she encouraged. 'She is too busy with important work to meet anyone this month' takes her full schedule at face value and misses the gap between her promise and her conduct. 'The employees have given up trying to reach her with problems' is not stated; the passage shows them noticing the problem, not giving up. 'She has dropped the policy and now keeps her office door shut' invents an announcement; she never withdrew the policy, she simply does not follow it.

Correct answer: The simple paper clip took years of trial and error to get right

The central point is that the simple paper clip took years of trial and error to get right: the passage challenges the idea that the clip is too simple to have a history and explains how earlier fasteners tore, slipped, or rusted until today's design held firmly without a mark. 'The paper clip was invented in a single flash by a clever thinker' contradicts the years of trial and error the passage describes. 'The earliest paper clip failed because it was made of cheap metal' names a cause the passage never gives; it describes the failures but not their material. 'The paper clip used today still slips loose and marks the page' contradicts the last sentence, which says today's clip holds firmly without leaving a mark.

Correct answer: He cares for the widow but keeps his kindness private.

He rarely speaks to anyone, yet he carries her groceries, shovels her walk before dawn, and leaves bread on her step, and he "never knocked or waited to be thanked." The best inference is therefore that he cares for the widow but keeps his kindness private. Because he never waits for thanks, it does not follow that he hopes for thanks from the widow but hides his pride. The passage mentions no job and no grudge, so nothing shows that he works for the widow but resents his endless chores. Nothing in his actions points to romance either, so it is unsupported that he longs for the widow but conceals his true feelings.

Correct answer: Rethinking something familiar can yield major improvements.

The passage ends, "Sometimes a small rethinking of the familiar changes everything," so its main idea is that rethinking something familiar can yield major improvements. The warning about wasted effort is set up only to be qualified with "yet some inventions truly do deserve a second look," so its point is not that rethinking something familiar can be a big waste of effort. It is a true detail of the example, not the main idea, that luggage wheels existed for ages before suitcases rolled well. One example cannot carry a sweeping rule, and the passage never claims that luggage wheels show that most old inventions need a redesign.

Correct answer: The diner has unexpectedly closed, at least for the moment.

The lights are off, the lot is empty by noon, the cook's car is gone, a notice is taped to the door, and the specials board "still showed last week's date," so the most reasonable inference is that the diner has unexpectedly closed, at least for the moment. That stale date shows the closure has lasted days, which rules out the idea that the diner has closed for the afternoon, at least until six. The notice lists only a phone number, so nothing shows that the diner has moved to a new address, listed on the notice. Nothing mentions a sale or a buyer, so it goes too far to say the diner has been sold, and new owners will take over.

Correct answer: A tree's rings keep a detailed yearly record of the conditions it lived through.

Each ring marks a year, its width "records the conditions of that year," and reading the rings "is like reading a diary," so the main idea is that a tree's rings keep a detailed yearly record of the conditions it lived through. The passage's whole point about ring width contradicts the claim that a tree's rings reveal its age but say little about the conditions it lived through. The passage says a wide ring means a wet season and a thin one hints at drought, which reverses the claim that a tree's rings grow widest in the driest years it lived through. The opening line, "The rings inside a tree trunk are more than decoration," rules out the claim that a tree's rings are decoration with no link to the conditions it lived through.

Correct answer: The student's final exam score was lifted by his persistent effort.

After failing two exams he came to office hours every week, turned in extra problems, and stayed late, and "by the final exam he scored among the highest in the class," so the best inference is that the student's final exam score was lifted by his persistent effort. Nothing suggests the test itself changed, so the passage gives no reason to think the student's final exam score improved since the test was easier. The professor's public remark came after the final, so it reverses the order of events to say the student's final exam score rose once the professor praised him. The passage mentions no outside helper, so nothing supports the claim that the student's final exam score rose with help from a private tutor.

Correct answer: The word salary echoes an era when salt itself served as pay.

The passage closes by saying our word for wages "still carries the memory of a time when salt was almost as good as money," so its main idea is that the word salary echoes an era when salt itself served as pay. The first sentence traces the word to "the Latin word for salt," which contradicts the claim that the word salary comes from a Latin term for wages, not salt. Soldiers were "sometimes paid in it or given an allowance to buy it," so it overstates the passage to say Roman soldiers were paid in salt alone instead of with coins. The passage values salt for preserving food, not for taste, so it misreads the text to say Roman cooks prized salt mostly for its flavor in their meals.

Correct answer: The patient is steadily regaining the health he had lost.

After weeks of weakness he now sits up, asks for a full meal, and laughs, and his chart shows "steady improvement in every reading over the past three days," so the most reasonable inference is that the patient is steadily regaining the health he had lost. His asking for a full meal contradicts the claim that the patient is cheerful but still too weak to eat a meal. The chart's improving readings show the change is real, which rules out the idea that the patient is cleverly faking a good mood for visitors. Improving is not the same as being ready to leave, and the passage says nothing about a discharge, so it goes beyond the evidence to say the patient is fit enough to go home to his family today.

Correct answer: Each element gives its flame a distinct color that chemists can use to identify it.

Sodium glows yellow, copper blue-green, and "other elements each lend their own hue," so chemists "identify substances simply by the color they produce"; the central point is that each element gives its flame a distinct color that chemists can use to identify it. The passage names copper and other elements as well, so it is wrong to say sodium is the single metal that chemists can identify by the color of its flame. The passage never connects hue to temperature, so it does not say the color of a flame is what chemists use to identify how hot a burning substance is. The passage is about hue, not brightness, so it misreads the text to say chemists can identify which element is burning by how brightly its flame glows.

Correct answer: The engine has overheated and broken down.

Steam is rising from under the hood, "the temperature gauge had climbed into the red," and the driver has turned on his hazards and is calling for help, so the best inference is that the engine has overheated and broken down. The passage describes steam, not a blast or flames, so it misreads the scene to say the engine has exploded and caught fire. The driver stares at the front of the car, but a flat tire would not send steam from the hood or push the gauge into the red, so nothing shows the front tire has burst and gone flat. No collision is mentioned, and a crash would not explain the gauge either, so the passage gives no support to the idea that the front bumper has hit a deer and crumpled.

Correct answer: The Roman calendar needed major reforms before it matched the sun and became the model we use.

The passage says, "Only after major reforms did the calendar finally line up with the sun, giving us the system we still rely on today," so its main idea is that the Roman calendar needed major reforms before it matched the sun and became the model we use. It is a true supporting detail, not the main idea, that the early Roman calendar drifted so far from the seasons that its winter festivals fell in autumn. The early version "drifted badly," which contradicts the claim that the Roman calendar tracked the sun closely from the start, and major reforms changed very little. The festivals landed in autumn because the months wandered, not by design, so it misreads the cause to say the Romans moved their winter festivals to autumn to keep their calendar in step with the seasons.

Correct answer: The surf is too dangerous for anyone to swim.

A red flag flies, a warning is posted, and the few people present watch "the unusually high, fast-breaking waves" from the sand, so the most reasonable inference is that the surf is too dangerous for anyone to swim. The day is described as sunny, so nothing suggests the weather is too chilly for anyone to swim. Nothing mentions pollution, so it goes beyond the passage to say the water is too polluted for anyone to swim. The usually busy beach is described as empty, which contradicts the claim that the beach is too crowded for anyone to swim.

Correct answer: Honey's makeup keeps it fit to eat for exceedingly long periods.

Honey "never truly spoils," stays edible for thousands of years, and outlasts "nearly every other food" because of its low water content and acidity, so the main idea is that honey's makeup keeps it fit to eat for exceedingly long periods. The passage gives low water and natural acidity as the cause, so it misreads the text to say honey's sweetness is the main reason bacteria cannot grow in it. The tomb finds are evidence of honey's long life, not of its purpose, so nothing supports the claim that honey's presence in tombs shows it was mainly a burial offering. The passage credits honey's own chemistry rather than where it was kept, so it is wrong to say honey's shelf life depends mostly on being sealed inside tombs.

Correct answer: He was impressed and is likely to advance her.

He leaned forward, took notes, smiled at her answers, raised the salary range "without being asked," and "said the team was excited to move forward," so the best inference is that he was impressed and is likely to advance her. Smiling at her answers contradicts the idea that he was unconvinced and is likely to reject her. Leaning in and jotting notes show close attention, which rules out the claim that he was distracted and is likely to forget her. Telling her the team is excited to move forward goes well beyond politeness, so it does not fit that he was gracious and is likely to turn her down.

Correct answer: The word museum reflects its beginnings as a home for study.

The first such institution was "a center for scholars to study and create," and "even now, the word carries that older sense," so the main idea is that the word museum reflects its beginnings as a home for study. That last sentence contradicts the claim that the word museum has drifted far from its roots in study. The passage says the first was "less a hall of objects" than a place of study, which reverses the claim that the first museums were built as a showcase for rare objects. The passage links the word to the Muses, goddesses of art and learning, not to honoring artists, so nothing supports the claim that the first museums were built by scholars to glorify artists.

Correct answer: The cook was satisfied that the soup was seasoned perfectly.

He tasted the soup, "reached for neither salt nor pepper," nodded to himself, and served it "without changing a thing," so the most reasonable inference is that the cook was satisfied that the soup was seasoned perfectly. His nod of approval contradicts the idea that the cook was unhappy with the soup but too rushed to fix it. He never reached for the salt at all, so nothing suggests the cook was sure that the soup needed salt but had run out. His nod points to a finished soup, not to a plan to leave the job to diners, so it is unsupported that the cook was content to let the customers season the soup.

Correct answer: The yellows and oranges of fall leaves are present all year but hidden until the green wanes.

The colors "are there all along," green pigment masks them through spring and summer, and "only when the green fades" do they show, so the central point is that the yellows and oranges of fall leaves are present all year but hidden until the green wanes. The last sentence says the hidden colors finally show themselves, which contradicts the claim that the yellows and oranges of fall leaves remain hidden all summer and disappear with the green. The passage corrects the idea that new color is made in fall, so it is wrong to say cold autumn nights make the leaves produce new yellow and orange pigments that replace green. The passage's point is that those colors were there all along, which is more than the bare detail that autumn leaves turn brilliant shades of yellow and orange.

Correct answer: The town is springing back to life after hard times.

The town "had emptied during the factory's decline," and now new families are moving in, shops are reopening, and the school is reopening a closed wing, so the best inference is that the town is springing back to life after hard times. New families moving into vacant houses contradicts the claim that the town is still losing families to larger cities. The passage never says the factory reopened; its decline is what emptied the town, so it is unsupported that the town is thriving since its old factory reopened. The newcomers are families settling into houses, not visitors, so nothing suggests the town is being turned into a resort for tourists.

Correct answer: Inertia

Newton's first law is also called the law of inertia, because it describes an object's tendency to stay at rest or keep moving at constant velocity unless a net force acts on it. Acceleration belongs to the second law, which links net force to acceleration. Momentum is the quantity that stays constant in collisions, a result tied to the third law rather than a name for the first, and action and reaction is the third law itself, which says every force comes with an equal and opposite force.

Correct answer: Newton's first law

Newton's first law explains the motion: an object in motion keeps moving in a straight line at constant speed unless a net force acts on it, and far from any star or planet nothing is pushing or pulling the craft. Newton's third law describes equal and opposite force pairs, which matter only while the engines are firing. Kepler's first law says planets orbit the sun in ellipses, and Kepler's third law relates a planet's orbital period to its distance from the sun; both describe orbits around a star, and this craft is not orbiting anything.

Correct answer: Force is mass times acceleration

Newton's second law is usually written as force is mass times acceleration (F = ma): the net force on an object equals its mass multiplied by the acceleration that force produces. The statement that momentum is mass times velocity is the definition of momentum, a different quantity, not the second law. Mixing the two up gives statements that are simply wrong: saying force is mass times velocity confuses force with momentum, and saying momentum is mass times acceleration confuses momentum with force.

Correct answer: Half as much acceleration as the car

The truck will have half as much acceleration as the car. By Newton's second law, acceleration equals net force divided by mass, so with the same force, doubling the mass halves the acceleration. Twice as much acceleration as the car gets the relationship backward by treating acceleration as growing with mass. Just as much acceleration as the car ignores the mass entirely, and four times as much acceleration as the car both reverses and squares the effect.

Correct answer: Newton's third law

This pair of forces illustrates Newton's third law: for every action force there is an equal and opposite reaction force, so your foot's backward push on the ground is matched by the ground's forward push on you. The law of inertia (Newton's first law) describes an object keeping its state of motion, not a pair of forces between two objects. Newton's second law relates net force to acceleration on a single object, and the law of gravity describes attraction between masses, which pulls downward rather than producing the forward push.

Correct answer: 2.5 m/s squared

The acceleration is 2.5 m/s squared: by Newton's second law, acceleration equals force divided by mass, so 25 newtons divided by 10 kilograms gives 2.5. Multiplying instead of dividing gives 250 m/s squared, and dividing the mass by the force (10 / 25) gives 0.4 m/s squared. Dividing by the cart's weight (about 98 newtons) instead of its mass gives about 0.26 m/s squared, but the second law uses mass in kilograms.

Correct answer: Move apart in opposite directions at equal speeds

They will move apart in opposite directions at equal speeds. By Newton's third law each skater pushes the other with an equal and opposite force, and with equal masses they gain equal speeds in opposite directions. To travel in the same direction at equal speeds, both would need a push the same way, which a push-off cannot give. The two forces act on different skaters, so they do not cancel, which rules out the claim that they stay at rest because the paired forces cancel out. They push on each other, not on the ice, so the idea that they stay at rest because frictionless ice has no grip is also wrong.

Correct answer: Keep moving ahead due to its inertia

The passenger's body tends to keep moving ahead due to its inertia. By Newton's first law, the body continues at the bus's original speed while the brakes slow the bus, so it lurches forward relative to the bus. If the body could slow down to the same pace as the bus, there would be no lurch at all. No forward force acts on the passenger: the brakes act on the bus, not on the body, so nothing causes the body to be flung forward by the braking force, and weight acts straight down, so it cannot be pulled forward by its own weight.

Correct answer: Increase by a factor of three

The acceleration will increase by a factor of three. By Newton's second law, with mass held constant acceleration is directly proportional to net force, so tripling the force triples the acceleration. To decrease by a factor of three would treat acceleration as inversely proportional to force, which is how it depends on mass, not force. To increase by a factor of nine squares the factor, as if the relationship were a square law, and to decrease by a factor of nine applies an inverse-square rule like the one for gravity, which does not describe force and acceleration.

Correct answer: A massive flywheel that resists changes to its spin rate

The clearest example of inertia is a massive flywheel that resists changes to its spin rate: its large mass makes it hard to start turning and just as hard to stop, which is exactly the resistance to a change in motion that inertia describes. A loaded sled that slowly grinds to a stop on rough ground shows friction changing an object's motion. A rubber ball that speeds up as it rolls down steep ground shows gravity causing acceleration, and a toy balloon that darts forward as air leaves its neck shows Newton's third law, action and reaction.

Correct answer: Downward push of the rocket on the exhaust gases

The upward thrust is the reaction to the downward push of the rocket on the exhaust gases. By Newton's third law, when the rocket forces the gases down, the gases push the rocket up with an equal and opposite force, which is why rockets work even in the vacuum of space. An upward push of the rocket on the exhaust gases has the direction backward: the rocket throws the gases down, not up. A downward push of the exhaust gases on the ground and an upward push of the ground on the exhaust gases are forces between the gases and the ground, not forces on the rocket, and they vanish once the rocket climbs, yet the thrust continues.

Correct answer: 3 m/s squared in the same direction as the force

The acceleration is 3 m/s squared in the same direction as the force. Newton's second law gives acceleration as net force divided by mass, so 18 newtons divided by 6 kilograms is 3 m/s squared, and acceleration always points the same way as the net force. Answers of 0.33 m/s squared in the same direction as the force or 0.33 m/s squared opposite to the force come from dividing mass by force (6 / 18), and 3 m/s squared opposite to the force has the right size but the wrong direction.

Correct answer: The force on an object's mass due to gravity

Weight is the force on an object's mass due to gravity, so it is measured in newtons and changes with the local strength of gravity. The amount of matter that makes up an object is the definition of mass, which is measured in kilograms and stays the same everywhere. The resistance of an object's mass to changes in motion describes inertia, and the total volume that an object takes up is a measure of size; neither is weight.

Correct answer: Direction

The car is accelerating because it changes its direction. Acceleration is any change in velocity, and velocity includes direction as well as speed, so steering around a curve is acceleration even at constant speed. A change in position alone is just motion: an object moving in a straight line at constant velocity changes position without accelerating. A change in elevation is the same, since a car climbing a straight ramp at steady speed is not accelerating, and a change in mass is not part of the definition of acceleration at all.

Correct answer: Period

A horizontal row on the periodic table is called a period, and properties change gradually as you move across it. A group, also called a family, is a vertical column of elements with similar chemical behavior. A series is a name for a run of related elements, such as the lanthanide series, not the standard term for a row, and a block is a region of the table, such as the s-block or the p-block, sorted by which type of orbital is filling.

Correct answer: Protons inside the nucleus

The atomic number gives the number of protons inside the nucleus, and that count is what identifies the element. The number of neutrons inside the nucleus can differ between isotopes of the same element, so it cannot define the atomic number. The number of electron shells in the atom matches the element's period on the table, and the number of outer electrons in the atom (the valence electrons) relates to its group; neither is the atomic number.

Correct answer: O

The chemical symbol for oxygen is the single capital letter O. Os is the symbol for osmium and Og is the symbol for oganesson, two different elements. Ox looks like a natural shortening of the name, but it is not the symbol of any element.

Correct answer: Very unlikely to react chemically

The noble gases are very unlikely to react chemically, because their outer electron shells are already full and they have almost no tendency to form bonds. Being very likely to react chemically is the opposite of that behavior. Being very eager to gain more electrons describes the halogens in the column just to their left, such as fluorine and chlorine, and being very eager to give away electrons describes the alkali metals on the far left, such as sodium.

Correct answer: Electrons and protons

A neutral atom always has equal numbers of electrons and protons, so the negative and positive charges cancel and the atom carries no overall charge. Neutrons have no charge, so the neutron count does not have to match anything: protons and neutrons are equal in some light atoms, such as carbon-12, but not in most heavier ones, so neither protons and neutrons nor neutrons and electrons must always match. Isotopes and molecules are not particles inside a single atom at all, so their numbers have nothing to do with an atom's charge.

Correct answer: Reactants to the products

The arrow points from the reactants to the products: the starting materials are written on the left, the new substances on the right, and the arrow shows the direction of the change. Products to the reactants reverses that direction. Coefficients (the numbers in front of each formula) and subscripts (the small numbers inside a formula) appear on both sides of the equation, so an arrow from coefficients to the subscripts or from subscripts to the coefficients does not describe what the arrow separates.

Correct answer: Element

Such a substance is an element: it contains only one kind of atom and cannot be broken down into anything simpler by ordinary chemical means. A compound contains two or more elements chemically bonded together and can be broken down chemically. An isotope is one form of an element with a particular number of neutrons, not the name for the kind of substance, and a molecule is a single particle of bonded atoms, which in many substances, such as water, joins more than one element.

Correct answer: Ion

An atom that loses or gains electrons and becomes charged is called an ion: losing electrons makes a positive ion and gaining them makes a negative ion. An isotope is a form of an element with a different number of neutrons, which does not change the charge. A radical is a particle with an unpaired electron, defined by that unpaired electron rather than by a charge, and an isomer is one of two or more compounds with the same formula but a different structure.