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ASTB-E practice questions

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Question 1Math Skills Test (MST)

Evaluate: 3 + 4 × 2² − 6 ÷ 3

  1. 13
  2. 9
  3. 21
  4. 17 Correct answer.

Explanation

Order of operations requires exponents first (2² = 4), then multiplication and division left to right (4 × 4 = 16 and 6 ÷ 3 = 2), then addition and subtraction. This gives 3 + 16 − 2 = 17.

Question 2Math Skills Test (MST)

What is 2/3 + 1/4?

  1. 11/12 Correct answer.
  2. 5/6
  3. 3/12
  4. 3/7

Explanation

Rewrite both fractions with the least common denominator of 12: 2/3 = 8/12 and 1/4 = 3/12. Adding the numerators gives 11/12, which cannot be reduced.

Question 3Math Skills Test (MST)

What is 15% of 240?

  1. 24
  2. 30
  3. 36 Correct answer.
  4. 48

Explanation

Convert the percent to a decimal and multiply: 0.15 × 240 = 36. Equivalently, 10% of 240 is 24 and 5% is 12, and 24 + 12 = 36.

Question 4Math Skills Test (MST)

A student's five test scores are 78, 85, 92, 68, and 77. What is the mean score?

  1. 76
  2. 79
  3. 80 Correct answer.
  4. 78

Explanation

The mean is the sum of the scores divided by the number of scores. The sum is 78 + 85 + 92 + 68 + 77 = 400, and 400 ÷ 5 = 80.

Question 5Math Skills Test (MST)

How many minutes are there in 3.5 hours?

  1. 195
  2. 350
  3. 240
  4. 210 Correct answer.

Explanation

Since each hour contains 60 minutes, multiply the number of hours by 60: 3.5 × 60 = 210 minutes.

Question 6Math Skills Test (MST)

A rectangle measures 12 inches by 5 inches. What is its area?

  1. 17 square inches
  2. 60 square inches Correct answer.
  3. 120 square inches
  4. 34 square inches

Explanation

The area of a rectangle is length times width, so 12 × 5 = 60 square inches.

Question 7Math Skills Test (MST)

What is the value of 2⁵?

  1. 64
  2. 16
  3. 32 Correct answer.
  4. 10

Explanation

An exponent tells how many times to use the base as a factor: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.

Question 8Math Skills Test (MST)

If 4 identical pens cost $6, how much do 10 of the same pens cost?

  1. $15.00 Correct answer.
  2. $10.00
  3. $18.00
  4. $12.00

Explanation

Find the unit price first: $6 ÷ 4 = $1.50 per pen. Then multiply by the new quantity: $1.50 × 10 = $15.00.

Question 9Math Skills Test (MST)

Solve for x: 5x − 7 = 3x + 11

  1. 18
  2. 9 Correct answer.
  3. 2
  4. −9

Explanation

Subtract 3x from both sides to get 2x − 7 = 11, then add 7 to both sides to get 2x = 18, and divide by 2 to get x = 9.

Question 10Math Skills Test (MST)

A recipe that makes 6 servings calls for 1.5 cups of rice. At the same rate, how many cups are needed for 10 servings?

  1. 0.9 cups
  2. 3 cups
  3. 2.25 cups
  4. 2.5 cups Correct answer.

Explanation

Set up the proportion 1.5/6 = x/10 and cross-multiply to get 6x = 15, so x = 2.5 cups. The per-serving amount is 0.25 cup, and 0.25 × 10 = 2.5.

Question 11Math Skills Test (MST)

A jacket's price rises from $80 to $92. What is the percent increase?

  1. 12%
  2. 13%
  3. 30%
  4. 15% Correct answer.

Explanation

Percent change equals the amount of change divided by the original amount: 12 ÷ 80 = 0.15, or 15%.

Question 12Math Skills Test (MST)

A student scores 88 and 92 on two tests and 85 on a final exam that counts twice as much as each test. What is the weighted average?

  1. 85.0
  2. 88.3
  3. 86.5
  4. 87.5 Correct answer.

Explanation

Weight the tests as 1 each and the final as 2: (88 + 92 + 2 × 85) ÷ 4 = 350 ÷ 4 = 87.5.

Question 13Math Skills Test (MST)

A boat travels 150 miles in 3 hours at a constant speed. At that same speed, how long does it take to travel 250 miles?

  1. 6 hours
  2. 4 hours
  3. 4.5 hours
  4. 5 hours Correct answer.

Explanation

The speed is 150 ÷ 3 = 50 miles per hour. Time equals distance divided by speed: 250 ÷ 50 = 5 hours.

Question 14Math Skills Test (MST)

Solve for x: 2(x − 3) = 4x + 8

  1. −5.5
  2. −3
  3. −7 Correct answer.
  4. 7

Explanation

Distribute the 2 to get 2x − 6 = 4x + 8. Subtract 2x from both sides to get −6 = 2x + 8, then subtract 8 to get −14 = 2x, so x = −7.

Question 15Math Skills Test (MST)

A circle has a radius of 7 units. What is its area, in terms of π?

  1. 49π Correct answer.
  2. 14π
  3. 196π
  4. 7π

Explanation

The area of a circle is A = πr². Substituting r = 7 gives A = π × 49 = 49π.

Question 16Math Skills Test (MST)

A bag holds 4 red, 6 blue, and 2 green marbles. If one marble is drawn at random, what is the probability that it is red?

  1. 2/3
  2. 1/2
  3. 1/3 Correct answer.
  4. 1/4

Explanation

There are 4 + 6 + 2 = 12 marbles in all, and 4 are red, so the probability is 4/12 = 1/3.

Question 17Math Skills Test (MST)

Which expression is equivalent to √50?

  1. 5√2 Correct answer.
  2. 2√5
  3. 10√5
  4. 25√2

Explanation

Factor out the largest perfect square: 50 = 25 × 2, so √50 = √25 × √2 = 5√2.

Question 18Math Skills Test (MST)

If 2x + y = 11 and x − y = 1, what is the value of y?

  1. 7
  2. 3 Correct answer.
  3. 2
  4. 4

Explanation

Adding the equations eliminates y: 3x = 12, so x = 4. Substituting back into x − y = 1 gives y = 3.

Question 19Math Skills Test (MST)

A $60 jacket is marked down 25%, and then an additional 10% is taken off the reduced price. What is the final price?

  1. $45.00
  2. $42.00
  3. $40.50 Correct answer.
  4. $39.00

Explanation

The first markdown gives 60 × 0.75 = $45. The second discount applies to that new price: 45 × 0.90 = $40.50.

Question 20Math Skills Test (MST)

One pipe can fill a tank in 6 hours and a second pipe can fill it in 12 hours. Working together, how long will they take?

  1. 4 hours Correct answer.
  2. 2 hours
  3. 18 hours
  4. 9 hours

Explanation

Add the rates: 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 tank per hour. The reciprocal gives 4 hours to fill the tank.

Question 21Math Skills Test (MST)

If x + 1/x = 5, what is the value of x² + 1/x²?

  1. 24
  2. 27
  3. 23 Correct answer.
  4. 25

Explanation

Square both sides: (x + 1/x)² = x² + 2 + 1/x² = 25. Therefore x² + 1/x² = 25 − 2 = 23.

Question 22Math Skills Test (MST)

How many liters of a 20% acid solution must be added to 10 liters of a 50% acid solution to obtain a 30% solution?

  1. 20 liters Correct answer.
  2. 10 liters
  3. 25 liters
  4. 15 liters

Explanation

Let x be the liters added: 0.20x + 0.50(10) = 0.30(x + 10). This gives 0.20x + 5 = 0.30x + 3, so 2 = 0.10x and x = 20 liters.

Question 23Math Skills Test (MST)

$2,000 is invested at 5% annual interest compounded annually. What is the balance after 2 years?

  1. $2,205 Correct answer.
  2. $2,200
  3. $2,210
  4. $2,100

Explanation

Compound interest multiplies the balance by 1.05 each year: 2000 × 1.05 = 2100 after one year, and 2100 × 1.05 = $2,205 after two years.

Question 24Math Skills Test (MST)

How many different groups of 3 can be selected from 7 people?

  1. 42
  2. 35 Correct answer.
  3. 210
  4. 21

Explanation

Because order does not matter, use the combination formula C(7,3) = 7!/(3!4!) = (7 × 6 × 5)/(3 × 2 × 1) = 35.

Question 25Math Skills Test (MST)

A rectangular box has edge lengths 3, 4, and 12. What is the length of the longest diagonal through the interior of the box?

  1. 19
  2. 13 Correct answer.
  3. 12
  4. 15

Explanation

The space diagonal of a rectangular box is √(a² + b² + c²). Here that is √(9 + 16 + 144) = √169 = 13.

Question 26Math Skills Test (MST)

What is the value of 12 ÷ 3 + 2 × 5?

  1. 4
  2. 10
  3. 14 Correct answer.
  4. 30

Explanation

Order of operations requires multiplication and division to be completed before addition, working left to right: 12 ÷ 3 = 4 and 2 × 5 = 10, so the expression becomes 4 + 10 = 14.

Question 27Math Skills Test (MST)

What is the least common multiple of 12 and 18?

  1. 216
  2. 6
  3. 72
  4. 36 Correct answer.

Explanation

Write each number in prime factorization: 12 = 2² × 3 and 18 = 2 × 3². The least common multiple takes the highest power of every prime that appears, giving 2² × 3² = 36.

Question 28Math Skills Test (MST)

The average of five numbers is 14. If four of the numbers are 10, 12, 15, and 16, what is the fifth number?

  1. 15
  2. 13
  3. 17 Correct answer.
  4. 14

Explanation

The total of all five numbers must equal the average times the count: 14 × 5 = 70. The four known numbers add to 53, so the missing number is 70 − 53 = 17.

Question 29Math Skills Test (MST)

Which expression represents the number 0.00042 in scientific notation?

  1. 4.2 × 10⁴
  2. 4.2 × 10⁻⁴ Correct answer.
  3. 4.2 × 10⁻³
  4. 4.2 × 10⁻⁵

Explanation

Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of 10. Moving the decimal point from 0.00042 to 4.2 requires four places to the right, which corresponds to a factor of 10⁻⁴.

Question 30Math Skills Test (MST)

If 3^(x + 1) = 27^(x − 1), what is the value of x?

  1. 3/2
  2. 1
  3. 5/2
  4. 2 Correct answer.

Explanation

Rewrite both sides with the same base: 27 = 3³, so 27^(x − 1) = 3^(3x − 3). Since the bases match, the exponents must be equal, giving x + 1 = 3x − 3, and solving yields 2x = 4, so x = 2.

Question 31Reading Comprehension Test (RCT)

The hovercraft rides on a cushion of air trapped beneath its hull. Because that cushion replaces direct contact with the water, the craft can cross shallow flats, mud, and even ice that would stop a conventional boat. The same design, however, makes steering sluggish, since the craft has almost no grip on the surface beneath it. Which statement best expresses the main idea of the passage?

  1. The air cushion makes the hovercraft versatile but hard to steer. Correct answer.
  2. Conventional boats cannot operate over ice at all.
  3. Hovercraft are generally safer than conventional boats when operating in shallow water.
  4. Air cushions are the only practical way to cross mud and ice.

Explanation

A main-idea statement must cover the passage as a whole, and this passage presents both a benefit of the air cushion (crossing difficult surfaces) and a cost (poor steering). Options that develop only one side of that contrast, or that exaggerate it into a universal rule, capture a detail or overreach.

Question 32Reading Comprehension Test (RCT)

Before a flight, a pilot must obtain a weather briefing covering the route, the destination, and any alternate airports. The briefing includes forecasts, reports of turbulence, and notices of temporary restrictions along the way. According to the passage, which item is part of a preflight weather briefing?

  1. Fuel prices at the destination
  2. The aircraft maintenance log
  3. Notices of temporary restrictions Correct answer.
  4. The passenger manifest

Explanation

The passage lists three components of a briefing: forecasts, turbulence reports, and notices of temporary restrictions. Only the restrictions item appears anywhere in that list, so the other choices are outside the passage's scope.

Question 33Reading Comprehension Test (RCT)

Reef coral depends on microscopic algae that live inside its tissue and supply it with food. When water temperatures rise a few degrees above normal for too long, the coral expels the algae and turns white, a condition called bleaching. If the heat persists, the coral starves. What can be inferred about a bleached coral?

  1. It has migrated to cooler water.
  2. It has already died and cannot recover.
  3. It produces extra algae in warm water.
  4. It can recover if the water cools in time. Correct answer.

Explanation

Bleaching is defined as the loss of algae, and starvation follows only if the heat persists. That conditional structure implies the coral survives in a bleached state for some period, so cooling before starvation can allow recovery.

Question 34Reading Comprehension Test (RCT)

The committee's report was terse: three pages, no diagrams, and every recommendation stated in a single sentence. Reviewers who expected a lengthy analysis were surprised. As used in the passage, "terse" most nearly means

  1. brief Correct answer.
  2. disorganized
  3. hostile
  4. inaccurate

Explanation

Context clues define the word: three pages, no diagrams, and one-sentence recommendations, set against reviewers who expected a lengthy analysis. These clues point to shortness of expression, not to error, anger, or disorder.

Question 35Reading Comprehension Test (RCT)

To replace a bicycle's brake pads, first loosen the cable clamp and slide the old pad out of the caliper. Insert the new pad so that its angled end points forward, tighten the clamp bolt, and then center the caliper by turning the adjustment screw a quarter turn at a time. The author's primary purpose is to

  1. urge readers to buy new brakes
  2. explain a procedure Correct answer.
  3. amuse readers with an anecdote
  4. trace the history of bicycle design

Explanation

The passage consists of ordered imperatives telling the reader how to perform a task, which is the structure of an explanation of procedure. Persuasion, history, and entertainment would each require a different kind of content, such as claims, dates, or a story.

Question 36Reading Comprehension Test (RCT)

The bridge carries four lanes of traffic and a separated walkway. It replaced a two-lane ferry service. The bridge opened in March after two years of construction. The walkway is the project's most attractive feature. Which sentence from the passage states an opinion rather than a fact?

  1. The walkway is the project's most attractive feature. Correct answer.
  2. The bridge carries four lanes of traffic and a separated walkway.
  3. The bridge opened in March after two years of construction.
  4. It replaced a two-lane ferry service.

Explanation

A statement is an opinion when it depends on a judgment of value that cannot be verified by observation. Calling one feature the most attractive ranks it aesthetically, whereas lane counts, dates, and the service the bridge replaced can all be checked.

Question 37Reading Comprehension Test (RCT)

To brew green tea properly, heat water to about 175 degrees, well below a rolling boil. Pour it over the leaves and steep for two to three minutes, then remove the leaves. Steeping longer than four minutes draws out bitter compounds. According to the passage, what should be done immediately after steeping for two to three minutes?

  1. Let the tea stand for four minutes
  2. Remove the leaves Correct answer.
  3. Heat the water to a rolling boil
  4. Add a second measure of leaves

Explanation

The passage gives the steps in order: heat the water, pour it over the leaves, steep two to three minutes, then remove the leaves. The next step listed after steeping is therefore removal of the leaves.

Question 38Reading Comprehension Test (RCT)

The lighthouse keeper's log for October contains 31 entries. Of these, nine describe fog and fourteen describe clear skies. The remaining entries describe rain. Visitors are noted on only two days. How many October entries describe rain?

  1. 2
  2. 9
  3. 8 Correct answer.
  4. 14

Explanation

The log has 31 entries, of which 9 and 14 are accounted for by fog and clear skies. Subtracting those from the total leaves 8 entries for rain; the visitor count is a separate detail and does not enter the calculation.

Question 39Reading Comprehension Test (RCT)

Studies of long-haul truck drivers found that drivers who took a 20-minute nap during a mandatory rest stop reported fewer near-misses in the following four hours than drivers who drank coffee instead. Alertness tests given at the end of the shift showed the same pattern. Which conclusion is best supported by the passage?

  1. Mandatory rest stops eliminate driver fatigue.
  2. A brief nap may sharpen alertness more than coffee does. Correct answer.
  3. Coffee has no measurable effect on driver alertness.
  4. Long-haul trucking is inherently unsafe.

Explanation

The study compares a nap with coffee and finds the nap group did better on two different measures, which supports a comparative claim stated with appropriate caution. The passage does not show coffee was worthless, that rest stops solve fatigue, or that the occupation itself is unsafe.

Question 40Reading Comprehension Test (RCT)

Early seismographs could record that an earthquake had happened but not where it began. By timing the arrival of different wave types at three widely spaced stations, researchers could fix the epicenter on a map. Modern networks do the same work with hundreds of stations and computers, but the underlying principle has not changed. Which statement best summarizes the passage?

  1. Early instruments were useless because they could not locate epicenters.
  2. Three stations are always sufficient to fix an epicenter.
  3. Comparing arrival times at several stations remains the basis for locating a quake. Correct answer.
  4. Modern seismology now relies entirely on computer networks.

Explanation

A summary must cover the whole passage, which traces one method from early instruments to modern networks and stresses continuity of principle. The other choices either take a single detail, overstate a limitation, or turn a described practice into an absolute rule.

Question 41Reading Comprehension Test (RCT)

Because the airfield lies in a valley, cold dense air drains into it after sunset. Moisture in that air condenses into fog, which can persist until the sun is high enough to burn it off. Pilots scheduling night arrivals often face the field's worst visibility. According to the passage, what causes fog to form at the airfield?

  1. Exhaust released by arriving aircraft
  2. Heat rising from the runway during the day
  3. Wind sweeping across the nearby hills
  4. Cold air draining into the valley after sunset Correct answer.

Explanation

The passage states a direct causal chain: the valley location lets cold dense air drain in after sunset, and moisture in that air condenses as fog. The other choices introduce causes the passage never mentions.

Question 42Reading Comprehension Test (RCT)

The senator's remarks were calculated to placate the crowd rather than to inform it: soothing phrases, no numbers, and a promise to "look into the matter." As used in the passage, "placate" most nearly means

  1. provoke
  2. confuse
  3. calm Correct answer.
  4. instruct

Explanation

The colon introduces clues that define the word: soothing phrases and a vague promise, offered in place of information. Those details point to soothing an audience's feelings, which is what calming means.

Question 43Reading Comprehension Test (RCT)

Supporters of the new stadium argue that it will pay for itself through ticket sales and nearby restaurant revenue. But the city's own analysis counted only the tax on tickets, not restaurant revenue, and projected a shortfall of $2 million a year. The supporters' case rests, therefore, on revenue the city never counted. What weakness does the passage identify in the supporters' argument?

  1. It ignores the cost of construction entirely.
  2. It assumes that no one will attend the games.
  3. It counts revenue the city's analysis never included. Correct answer.
  4. It relies on outdated ticket prices.

Explanation

The passage's key move is to show that the supporters' self-financing claim depends on restaurant revenue omitted from the city's accounting, which is why their conclusion differs from the projection. The other choices describe errors the passage neither states nor implies.

Question 44Reading Comprehension Test (RCT)

The vaccine must be kept between 2 and 8 degrees Celsius. In the rural clinics studied, power outages occurred on average three times a week, and none of the clinics owned a backup generator. Potency tests on samples from those clinics failed at twice the national rate. Which conclusion is best supported by the passage?

  1. Power outages are the leading cause of illness nationwide.
  2. Interrupted cooling likely reduced potency at those clinics. Correct answer.
  3. The vaccine is ineffective wherever it is used.
  4. Generators are too expensive for rural clinics.

Explanation

The passage links a strict temperature requirement to frequent outages without backup power and then reports elevated potency failures, which supports a cautious causal inference. The other choices either generalize far beyond the data or invent facts about cost and national disease.

Question 45Reading Comprehension Test (RCT)

The manual's section on carburetor adjustment is a masterpiece of ambiguity. It advises the reader to "turn the screw until the engine sounds right," without ever defining what right sounds like. One suspects the author had never held a wrench. The author's attitude toward the manual is best described as

  1. frightened
  2. reverent
  3. indifferent
  4. mocking Correct answer.

Explanation

Tone shows up in word choice: calling the section a "masterpiece of ambiguity" and doubting the author's experience are ironic jabs. That ridicule signals a mocking attitude rather than respect, neutrality, or fear.

Question 46Reading Comprehension Test (RCT)

Unlike the diesel engines in most long-haul trucks, the turbine in the experimental rig has far fewer moving parts and runs on almost any liquid fuel. Its drawback is fuel consumption: at cruising load it burns roughly 30 percent more than a comparable diesel, a penalty that no amount of maintenance can offset. According to the passage, what is the turbine's principal disadvantage?

  1. It cannot run at cruising load.
  2. It has far too many moving parts.
  3. It requires a special grade of fuel.
  4. Its fuel consumption is higher than a diesel's. Correct answer.

Explanation

The passage names the drawback in a single clause: the turbine burns about 30 percent more fuel at cruising load, and maintenance cannot offset it. The other choices contradict details the passage states outright.

Question 47Reading Comprehension Test (RCT)

Which sentence would best begin the following paragraph? ______. The first models weighed nearly 30 pounds and could store only a few minutes of audio. By the 1990s, solid-state memory had shrunk the devices to the size of a matchbox while multiplying their capacity many times over.

  1. Music has been an important part of daily life for many centuries.
  2. Solid-state memory is difficult to manufacture.
  3. Matchboxes are inexpensive to produce.
  4. Portable audio players have changed greatly over time. Correct answer.

Explanation

A topic sentence should announce the idea the rest of the paragraph develops, and the details that follow trace a change in size and capacity over decades. The other choices either address a single supporting detail or introduce a topic the paragraph never pursues.

Question 48Reading Comprehension Test (RCT)

Under the marina's rules, a slip may be sublet only to a member in good standing and only with the harbormaster's written approval. Subletting without approval results in a 30-day suspension of slip privileges. A member sublets her slip to a member in good standing but does not obtain written approval. Under the rules, what is the result?

  1. A 30-day suspension of slip privileges. Correct answer.
  2. Permanent loss of the slip.
  3. A fine set at the harbormaster's discretion.
  4. Nothing, because the subtenant is a member in good standing.

Explanation

The rules state two conditions for a valid sublet, and the described situation satisfies only one of them. The stated consequence for subletting without approval is therefore a 30-day suspension, and nothing in the passage authorizes a different penalty.

Question 49Reading Comprehension Test (RCT)

It is tempting to treat the Antikythera mechanism as a lone miracle of ancient engineering. In fact, ancient writers describe dozens of geared astronomical devices, most now lost. The mechanism is remarkable not because it was unique but because it survived. The author's main point about the device is that it

  1. matters mostly because it survived, not because it was unique Correct answer.
  2. was built by an inventor whose name is unknown
  3. was less sophisticated than scholars once believed
  4. proves that the ancient Greeks had already built mechanical computers

Explanation

The passage corrects the impression that the device was one of a kind and states plainly that its significance lies in survival rather than uniqueness. The other choices either miss that corrective point or attribute claims about sophistication and naming that the passage never makes.

Question 50Reading Comprehension Test (RCT)

The report's headline figure, a 12 percent decline in collisions, was computed from police records alone. Minor collisions settled privately never entered those records, and the same neighborhoods that gained new bike lanes also gained new reporting kiosks. Both changes would push the count in the same direction regardless of what happened on the road. What is the author's central criticism of the report?

  1. The 12 percent figure is too small to be meaningful.
  2. Police records are never reliable sources of data.
  3. The decline may reflect better reporting, not safer roads. Correct answer.
  4. Bike lanes generally increase the number of collisions.

Explanation

The passage shows that reporting changes, not road conditions, could produce the measured drop, since new kiosks and shifts in private settlement both alter what enters the records. That is a challenge to the validity of the inference, not a claim about the size of the figure or a blanket dismissal of all police data.