ASVAB — All Questions

What are the coordinates of the midpoint of the segment joining (-3, 5) and (7, 1)?

• a.(4, 6)
• b.(2, 6)
• c.(5, 2)
• d.(2, 3)✓

A midpoint is the average of the endpoints, handled one coordinate at a time: x = (-3 + 7) / 2 = 2 and y = (5 + 1) / 2 = 3, giving (2, 3). Adding without halving gives (4, 6), and halving the difference of the coordinates rather than their sum gives (5, 2).

At what value of x does the line y = -2x + 9 cross the x-axis?

• a.x = 4.5✓
• b.x = 9
• c.x = 2
• d.x = -9

A line meets the x-axis where y is 0, so set -2x + 9 = 0, move the term across to get 2x = 9, and divide: x = 4.5. The number 9 is the y-intercept, where the line crosses the other axis, and -9 comes from moving the 9 across but never dividing by the coefficient.

What is the slope of a line perpendicular to the line that passes through the points (0, 5) and (2, 0)?

• a.0.4✓
• b.2.5
• c.-2.5
• d.-0.4

First get the slope of the given line, rise over run: (0 - 5) / (2 - 0) = -2.5. A perpendicular line has the negative reciprocal, so flip it to 2/5 and switch the sign, giving 0.4. Only flipping leaves -0.4, and only switching the sign leaves 2.5.

A rectangle has vertices at (1, 2), (9, 2), (9, 8), and (1, 8). What is its area?

• a.48 square units✓
• b.28 square units
• c.14 square units
• d.24 square units

Read the side lengths straight off the coordinates. The horizontal side runs from x = 1 to x = 9, a length of 8, and the vertical side runs from y = 2 to y = 8, a height of 6. Area is 8 x 6 = 48 square units. The value 28 is the perimeter, 2 x (8 + 6), and 14 is 8 + 6.

The endpoints of a diameter of a circle are (2, 3) and (10, 9). What is the radius of that circle?

• a.7 units
• b.5 units✓
• c.10 units
• d.8 units

The distance between the two endpoints is the diameter. The legs are 10 - 2 = 8 and 9 - 3 = 6, so the distance is the square root of 64 + 36, which is 10. The radius is half of that, 5 units. Stopping at 10 units reports the diameter, 8 units is only one leg, and 7 is the average of the legs.

What is the greatest common factor of 48 and 72?

• a.48
• b.24✓
• c.12
• d.16

Break both numbers into primes: 48 = 2 x 2 x 2 x 2 x 3 and 72 = 2 x 2 x 2 x 3 x 3. Take the primes they share, three 2s and one 3, and multiply: 8 x 3 = 24. The value 12 is a common factor but not the greatest, 16 divides 48 but not 72, and 48 is merely the smaller number.

How many prime numbers are there between 20 and 40?

• a.5
• b.3
• c.4✓
• d.6

A prime has no factors besides 1 and itself, so test the odd numbers only. Ruling out 21, 27, 33 and 39 as multiples of 3, and 25 and 35 as multiples of 5, leaves 23, 29, 31 and 37, so the count is 4. Counting 27 or 33 by mistake is how people arrive at 5 or 6.

Which of the numbers 4,518, 3,724, 5,231 and 6,142 is divisible by 9?

• a.3,724
• b.6,142
• c.4,518✓
• d.5,231

A number divides evenly by 9 exactly when the sum of its digits is a multiple of 9. For 4,518 the digits give 4 + 5 + 1 + 8 = 18, which is 9 x 2, so it works. The other digit sums come to 16, 11 and 13, none of them multiples of 9, so no long division is needed.

In how many different orders can 4 runners cross the finish line if there are no ties?

• a.10 orders
• b.16 orders
• c.12 orders
• d.24 orders✓

Arrangements of n distinct items come to n factorial. There are 4 choices for first place, 3 left for second, 2 for third and 1 for last, so 4 x 3 x 2 x 1 = 24 orders. Working out 4 x 4 gives 16, which would count orders only if a runner could repeat, and adding gives 10.

If n is an odd integer, which of the expressions n + 2, 3 x n, n x n and n + 5 must be an even integer?

• a.3 x n
• b.n + 5✓
• c.n x n
• d.n + 2

Odd plus odd is even, odd plus even is odd, and odd times odd is odd. Adding 5, itself odd, to an odd n gives an even result every time. Adding 2 keeps it odd, and both 3 x n and n x n multiply two odd numbers, so they stay odd. Try n = 7: the values are 9, 21, 49 and 12.

Obstinate most nearly means

• a.obsolete
• b.yielding
• c.obedient
• d.stubborn✓

An obstinate mule or an obstinate refusal will not be moved by argument or evidence. Latin ob, against, plus stare, to stand: standing against you, the same stare behind stationary and obstacle. Yielding and obedient are its opposites, and obsolete, meaning out of date, only shares the opening letters.

Lucid most nearly means

• a.murky
• b.clear✓
• c.shiny
• d.vivid

A lucid explanation is easy to follow, and a patient who is lucid is thinking clearly. Latin lux, light, runs through translucent and elucidate, and lucid can itself mean bathed in light. Shiny still misses, naming a polished surface rather than a clear one. Murky is its opposite; vivid rates intensity.

Alleviate most nearly means

• a.elevate
• b.relieve✓
• c.deviate
• d.inflame

To alleviate pain or a shortage is to lighten it, making it easier to bear without removing it. Latin levis, light, also gives elevate, lever and levity. Inflame is the exact opposite, making the trouble worse, and deviate merely echoes the ending; it means to stray from a set course.

Fortify most nearly means

• a.obliterate
• b.debilitate
• c.strengthen✓
• d.camouflage

To fortify is to strengthen: fortify a position, fortify cereal with iron. The root fort, strong, shows up in fort, fortress and fortitude. Debilitate is the opposite, draining strength away. Obliterate overshoots, since fortifying builds up rather than wipes out, and camouflage only hides.

Benevolent most nearly means

• a.affluent
• b.generous✓
• c.spiteful
• d.boastful

A benevolent commander wishes his people well and acts on it. Break the word up: bene, good, as in benefit, plus volent, wishing, as in volunteer. Spiteful is the exact reverse. Affluent tempts because we so often hear benevolent donor, but that describes the money, not the goodwill.

Resilient most nearly means

• a.elastic✓
• b.reliant
• c.brittle
• d.radiant

A resilient recruit bounces back from a bad week, and resilient material returns to its shape. Latin re, back, plus salire, to leap, the root behind salient. Brittle is the opposite: it breaks instead of springing back. Reliant sounds close but means dependent on someone else.

Adversary most nearly means

• a.opponent✓
• b.advocate
• c.follower
• d.adjutant

An adversary is the person or side you are up against, in court, in sport or in war. Latin ad plus vertere, to turn against, gives adverse and versus. The other three all name someone on your side: an advocate argues for you, a follower goes along with you, an adjutant assists you.

Inevitable most nearly means

• a.predictable
• b.unavoidable✓
• c.implausible
• d.preventable

An inevitable outcome is one nobody can dodge: winter is inevitable, and so is the paperwork. Latin in, not, plus evitare, to avoid; strip the negative and you are left with evitable, avoidable. Preventable is the precise opposite and the main trap. Predictable is the near-miss: you can foresee a thing you could still stop.

Feasible most nearly means

• a.workable✓
• b.probable
• c.flexible
• d.hopeless

A feasible plan is one that can actually be carried out with the time and money on hand. Latin facere, to do or make, gives fact, factory and feat. Hopeless names the plan that cannot be. Probable is the near-miss worth fixing: feasible says a thing can be done, not that it is likely to happen.

Arid most nearly means

• a.dry✓
• b.wet
• c.big
• d.hot

Arid land is bone dry, getting too little rain to farm; the noun is aridity. Wet is the opposite. Hot is the trap, because we picture deserts baking, yet Antarctica is arid too: the word measures moisture alone, never temperature, and never the size of the country it describes.

Dormant most nearly means

• a.thriving
• b.portable
• c.inactive✓
• d.dominant

A dormant volcano or a dormant account is asleep, inactive for now but able to wake. Latin dormire, to sleep, also gives dormitory. Thriving names something actively growing, the opposite state. Dominant differs by a single letter and means controlling, a common mix-up.

Magnify most nearly means

• a.clarify
• b.deflate
• c.enlarge✓
• d.signify

To magnify is to make something appear larger: magnify an image, magnify a small problem. The root magn, great, runs through magnitude and magnificent. Deflate shrinks instead. Clarify tempts because a lens sharpens print too, and signify only rhymes; the word names size, not sense.

Retract most nearly means

• a.reattach
• b.announce
• c.redirect
• d.withdraw✓

To retract is to pull back what you put out: retract a statement, retract landing gear. Latin trahere, to pull, gives tractor, traction and extract. Announcing is the opposite move, putting the claim out there. Redirect keeps the re but sends the thing elsewhere, not back.

Eradicate most nearly means

• a.eliminate✓
• b.establish
• c.elaborate
• d.extricate

To eradicate a disease or a habit is to wipe it out completely, roots and all. Latin radix, root, gives radish and radical. Establish is the opposite, putting something in place to stay. Extricate and elaborate share its shape and rhythm, but one frees a thing and the other builds it out.

Meticulous most nearly means

• a.zealous
• b.careful✓
• c.orderly
• d.hurried

A meticulous mechanic checks every torque value and writes each one down, so meticulous means careful about small details. Hurried is the opposite. Orderly is the near-miss, since meticulous work is exact rather than merely neat, and zealous rates enthusiasm instead of attention to detail.

Abrupt most nearly means

• a.absurd
• b.sudden✓
• c.steady
• d.polite

An abrupt stop comes with no warning, and an abrupt reply is rudely short, which is why polite is one of its opposites and steady is the other. Latin ab, off, plus rumpere, to break, the root in rupture and interrupt: broken off short. Absurd shares those letters but means ridiculous.

Coarse most nearly means

• a.smooth
• b.gritty✓
• c.costly
• d.hoarse

Coarse means rough and grainy to the touch, or crude in manner: coarse sandpaper, coarse language. Smooth or fine is the opposite. Hoarse is the trap, since it nearly rhymes and also describes roughness, but only of a voice. Its homophone course, a path or a class, is the other mix-up.

Nimble most nearly means

• a.meek
• b.slow
• c.numb
• d.spry✓

Nimble means quick and light in movement, and it stretches to thinking: nimble fingers, a nimble mind. Spry says the same of someone still light on their feet. Slow is the opposite, meek means mild rather than quick, and numb, unable to feel, only echoes the opening sound.

Somber most nearly means

• a.shabby
• b.gloomy✓
• c.boring
• d.joyful

A somber mood or ceremony is dark, quiet and serious. Picture the Spanish sombra, shade, the shadow a sombrero casts. Joyful is the opposite. Boring is the near-miss, since a hushed ceremony can drag, but somber names the weight of the mood. Shabby describes wear, not feeling.

Rebuke most nearly means

• a.revoke
• b.praise
• c.berate✓
• d.rebuff

To rebuke is to criticize sharply and openly, the way an officer berates a recruit for a sloppy uniform. Praise is the opposite. Rebuff is the near-miss, meaning to reject an offer rather than to scold, and revoke, to cancel a licence or an order, differs by only a couple of letters.

Conspicuous most nearly means

• a.capricious
• b.indistinct
• c.suspicious
• d.noticeable✓

Something conspicuous stands out and gets noticed: a conspicuous scar, conspicuous gallantry. Latin con plus spicere, to look, the spec in spectator and inspect, which is also why suspicious tempts. Indistinct is the opposite, and capricious, meaning whimsical, only echoes the ending.

Apathy most nearly means

• a.compassion
• b.enthusiasm
• c.resentment
• d.detachment✓

Apathy is a complete lack of interest or concern: voter apathy, an apathetic shrug at bad news. Greek a, without, plus pathos, feeling, the pathos in sympathy and pathetic. Compassion is the tempting one, since it is feeling with someone. Enthusiasm and resentment are both feeling, not its absence.

Innate most nearly means

• a.intact
• b.taught
• c.inborn✓
• d.ornate

An innate talent is one you were born with rather than trained into. Latin in plus natus, born, gives native, nature and prenatal. Taught is the precise opposite and the main trap. Ornate rhymes with it but describes heavy decoration, and intact, meaning undamaged, only shares the start.

Depict most nearly means

• a.deposit
• b.portray✓
• c.predict
• d.distort

To depict is to show or describe: a painting depicts a battle, a report depicts conditions. The root pict, painted, gives picture and pictorial. Distort is the near-miss, depicting something falsely. Predict sounds almost identical but concerns the future instead.

Concur most nearly means

• a.agree✓
• b.argue
• c.defer
• d.incur

To concur is to agree: the board concurred with the recommendation. Latin con, together, plus currere, to run, the same root in current and concurrent, so concurring minds run together. Arguing is the opposite. Defer means to yield or postpone, and incur, to bring trouble on yourself, shares only that run.

Precede most nearly means

• a.step back
• b.follow on
• c.go before✓
• d.hang back

To precede is to come before in time or order: a warning order precedes the operation. Latin prae, before, plus cedere, to go, as in recede and predecessor. Following on is the exact opposite, the job of succeed. Proceed, which means to go forward, is the spelling people confuse with it.

Deplete most nearly means

• a.deplore
• b.restock
• c.exhaust✓
• d.deflate

To deplete is to draw a supply down until little is left: deplete the fuel, deplete the reserves. Think de plus plenus, full, the plen in plenty and replenish, running in reverse. Restocking is the opposite. Deplore, to regret deeply, shares those first letters, and deflate applies to air, not stock.

Cordial most nearly means

• a.reserved
• b.friendly✓
• c.detached
• d.doubtful

A cordial welcome is warm and genuinely friendly, and cordial relations are pleasant ones. Latin cor, heart, gives courage, accord and record, so cordial is hearty. Detached is the opposite. Reserved is the near-miss, because a greeting can be perfectly correct and stiff with no warmth behind it.

Malice most nearly means

• a.goodwill
• b.hot rage
• c.ill will✓
• d.bad luck

Malice is the wish to do someone harm, as in acting with malice or spreading a malicious rumor. The prefix mal, bad, shows up in malfunction and malnutrition. Goodwill is the exact opposite. Bad luck borrows that sense of bad but drops the intent, and hot rage flares without the settled wish.

Devise most nearly means

• a.borrow
• b.divide
• c.invent✓
• d.revise

To devise is to think up and work out: devise a route, devise a training plan. A device is the thing someone devised, and divide is the surprise cousin, since both grew from Latin dividere. Revise is the near-miss, changing something that already exists rather than building it from nothing.

Rectify most nearly means

• a.verify
• b.ratify
• c.worsen
• d.remedy✓

To rectify is to set something right, to remedy it: rectify an error on a pay record. The root rect, straight or right, appears in correct, erect and rectangle. Worsen is the opposite. Ratify is the classic mix-up, meaning to approve an agreement, and verify only checks that a thing is true.

Incessant most nearly means

• a.unpleasant
• b.occasional
• c.successive
• d.continuous✓

Incessant noise never lets up: incessant rain, incessant complaints from the back seat. Take it apart: in, not, plus cessare, to stop, the root of cease, so incessant means never ceasing. Occasional is the opposite. Successive means one after another, which leaves room for a pause, and unpleasant judges rather than times.

Flourish most nearly means

• a.finish
• b.wither
• c.flaunt
• d.thrive✓

To flourish is to grow strongly or do very well: a flourishing business, plants that flourish in shade. Latin flor, flower, gives floral and flora, so the picture is blooming. Wither is the opposite. Finish sounds close but means to end, and flaunt catches only the sense of waving something about.

Peculiar most nearly means

• a.punctual
• b.ordinary
• c.uncommon✓
• d.polished

Peculiar means strange, out of the common run: a peculiar smell, a peculiar answer. It comes from peculium, one's own property, so what is peculiar belongs to nobody else. Ordinary is the exact opposite and the main trap. Punctual and polished share only its shape and its opening letter.

Subsequent most nearly means

• a.recurrent
• b.preceding
• c.resultant
• d.following✓

Subsequent events come after the one just named: the raid and the subsequent inquiry. Latin sub, after, plus sequi, to follow, gives sequence and sequel. Preceding is the exact opposite. Resultant is the trap, since it claims one thing caused another, not merely that it came later.

Vex most nearly means

• a.scold
• b.annoy✓
• c.amuse
• d.relax

To vex is to irritate or trouble someone: a vexing problem, a child who vexes a tired parent; the noun is vexation. Relax names the opposite effect and amuse the pleasant one. Scold is the near-miss, since a vexed supervisor may well scold, but vex names the irritation, not the telling-off.

Ominous most nearly means

• a.reassuring
• b.foreboding✓
• c.monotonous
• d.mysterious

Ominous means giving the feeling that something bad is coming: ominous clouds, an ominous silence. It is the adjective of omen, a sign of what lies ahead, which is exactly what a foreboding sky is. Reassuring is the opposite, and mysterious is the near-miss: ominous points at harm, not the unknown.

Aspire most nearly means

• a.settle
• b.strive✓
• c.admire
• d.expire

To aspire is to aim high and work toward it: aspire to a commission. Latin ad, toward, plus spirare, to breathe, the root of inspire and respiration. Settling for less is the opposite. Expire and admire rhyme with it but mean to run out and to regard with respect.

Static most nearly means

• a.increasing
• b.electrical
• c.motionless✓
• d.changeable

Static means not moving and not changing: a static display, sales that stayed static all quarter. The word is Greek, from statikos, causing to stand, the same standing that sits in stasis and thermostat. Changeable and increasing both describe movement, the opposite. Electrical plays on static electricity.

Vehement most nearly means

• a.measured
• b.forceful✓
• c.reckless
• d.lukewarm

A vehement denial is intense and forceful, and someone vehemently opposed leaves no doubt. Vehement shares Latin vehere, to carry, with vehicle: the vehement speaker is carried away by feeling. It rates that force, not whether it is wise or rash, so measured and reckless miss. Lukewarm is the opposite.