Your FREE OAR (Officer Aptitude Rating) Practice Test 2026 – 310+ Q&A

Correct answer: 5

Subtracting 7 from both sides leaves 3x equal to 15, and dividing by 3 gives 5. The value 3 confuses the coefficient with the answer, 4 comes from dividing 15 by 3 and then subtracting one, and 2 comes from subtracting 7 twice, leaving 8 and rounding 8 divided by 3 down.

Correct answer: 60

Average speed is distance divided by time, so 240 miles over 4 hours gives 60 miles per hour. The value 48 divides the same distance by 5 hours, 50 uses a distance of 200 miles, and 55 uses a distance of 220 miles; each keeps the right method but feeds it a figure the question did not give.

Correct answer: 28

Convert the percentage to a decimal and multiply: 0.35 times 80 gives 28. The value 20 is 25 percent of 80. The value 24 is 30 percent of 80, dropping the extra 5 percent. The value 26 takes 30 percent correctly but counts the 5 percent as 2 instead of 4.

Correct answer: 60

Area of a rectangle is length times width, so 12 times 5 gives 60 square units. The value 13 is the diagonal from the 5-12-13 right triangle, 17 simply adds the length and width, and 29 adds two lengths and one width as if finding part of the perimeter.

Correct answer: 10

Adding 9 to both sides gives 2y equal to 20, and dividing by 2 gives 10. The value 11 simply copies the right side and ignores both the minus 9 and the coefficient. The value 22 doubles the 11 instead of halving after moving the 9, and 31 doubles the 11 and then adds the 9.

Correct answer: 43

Four squared is 16 and three cubed is 27, and together they make 43. The value 49 adds 4 and 3 first and then squares the sum, 73 swaps the exponents to give 64 plus 9, and 91 cubes both numbers to give 64 plus 27.

Correct answer: $30

Twenty-five percent of $40 is $10, and taking that off the ticket price leaves $30. The figure $32 takes only 20 percent off, $36 takes only 10 percent off, and $50 adds the 25 percent as a markup instead of subtracting it.

Correct answer: $4.80

Five pencils for $2.00 works out at $0.40 each, and 12 of them at that rate cost $4.80. The figure $3.60 prices only nine pencils, $4.00 doubles the five-pencil price and stops at ten, and $4.40 stops one pencil short at eleven.

Correct answer: 24

The least common multiple is the smallest number that both 6 and 8 divide into exactly, and that number is 24. The values 12, 18 and 30 are each a multiple of 6, but none of them divides by 8 without a remainder, so none can be a common multiple of the pair.

Correct answer: 3/4

The greatest common factor of 18 and 24 is 6, and dividing both parts by 6 leaves 3/4. The value 3/8 divides the 18 by 6 but the 24 by only 3, 3/5 misreads the denominator as 30, and 5/7 subtracts 3 from each part instead of dividing.

Correct answer: 21

With x equal to 4, twice x squared is 32 and three x is 12, so 32 minus 12 plus 1 gives 21. The value 33 drops the minus three x term entirely, 45 adds the 12 instead of subtracting it, and 53 squares 2x to get 64 before subtracting 12 and adding 1.

Correct answer: 30

A triangle covers half the rectangle around it, so half of 10 times 6 gives 30 square units. The value 32 is the perimeter of a 10-by-6 rectangle, not an area. The value 48 adds base and height to 16 and multiplies by half the height. The value 50 halves 10 times 10, using the base as the height.

Correct answer: 0.875

Dividing 7 by 8 gives 0.875, since each eighth is 0.125 and seven of them make 0.875. The value 0.800 is 4/5, a rounder neighbour that some candidates settle on. The value 0.833 is 5/6, a common fraction often mixed up with eighths. The value 0.714 is 5/7, a neighbour from the sevenths.

Correct answer: 25

Fifteen boys fill the three boy units of the ratio, so one unit is 5 students and the five girl units come to 25. The value 30 treats the ratio as 3 to 6, 35 treats it as 3 to 7, and 40 is the size of the whole class rather than the number of girls in it.

Correct answer: 180

The three interior angles of a triangle total 180 degrees, which is why the third angle is fixed once the other two are known. The value 360 is the total for a four-sided figure or a complete turn, 270 is three right angles, and 120 is a complete turn shared equally among three sides.

Correct answer: 36

Multiplying both sides by 4 undoes the division and leaves 36. The value 27 would follow if the equation divided x by 3, 45 if it divided by 5, and 54 if it divided by 6; each one multiplies 9 by a divisor the equation does not use.

Correct answer: 27

The unknown plus 15 makes 42, so subtracting 15 from 42 recovers it as 27. The value 57 adds 15 rather than subtracting it, 42 repeats the total the question already supplies, and 12 subtracts 15 a second time from a figure that was already correct.

Correct answer: 30

Twelve percent is 0.12 as a decimal, and 0.12 multiplied by 250 gives 30. The value 18 applies the same 12 percent to 150, 42 applies it to 350, and 54 applies it to 450; the method is right in each case but the total is not the one given.

Correct answer: 9

A square has four equal sides, so one side is the perimeter divided by 4, and 36 divided by 4 is 9. The value 6 is √36, which would be the side only if 36 were the area, 4 is the number of sides rather than a length, and 8 follows from dividing 32 by 4 after misreading the perimeter.

Correct answer: 11

The bracket is worked first: 8 plus 4 is 12, dividing by 2 leaves 6, and adding 5 gives 11. The value 17 adds 5 to 12 without dividing at all, 15 divides only the 4 before adding, and 21 totals every figure on the line and ignores the operations.

Correct answer: 0.30

Six tenths multiplied by five tenths gives 30 hundredths, written 0.30, because multiplying two one-place decimals produces a two-place decimal. The value 1.10 adds the two decimals instead of multiplying them, 1.20 divides 0.6 by 0.5, and 0.83 divides 0.5 by 0.6.

Correct answer: 3

Four workers for 6 days is 24 worker-days, and 24 shared among 8 workers gives 3 days. The value 4 divides those 24 worker-days by the 6 days instead of by 8 workers, 5 trims just one day off the original 6 instead of halving it, and 7 adds a day as though more workers slowed the job.

Correct answer: 12

A square root is the number that multiplies by itself to give the original, and 12 times 12 is 144. Squaring the others falls wide: 10 gives 100, 14 gives 196, and 16 gives 256, so not one of them returns 144.

Correct answer: 5

Twelve cookies need 2 cups, so each cup makes 6 cookies and 30 cookies need 30 divided by 6, which is 5 cups. A value of 6 rounds the two and a half batches up to three full batches of 2 cups. A value of 7 adds the original 2 cups on top of the 5 needed. A value of 9 divides the 18 extra cookies by the 2 cups instead of scaling the recipe.

Correct answer: x > 6

Dividing both sides by 3 leaves x > 6, and the direction of the sign is unchanged because 3 is positive. The value x > 8 divides 24 by 3 after misreading the right side, x > 4 reads that side as 12, and x > 2 divides by 9 rather than by the coefficient 3.

Correct answer: 18

An average is the total divided by how many values were added: 14 plus 18 plus 22 is 54, and 54 divided by 3 gives 18. The value 16 averages only the first two numbers, 15 drops the carried ten to get a total of 44 and divides that by 3, and 12 adds only 14 and 22 but still divides by 3.

Correct answer: 43.96

Circumference is twice pi times the radius, so 2 times 3.14 times 7 gives 43.96. The value 31.40 works from a radius of 5, 37.68 from a radius of 6, and 50.24 from a radius of 8; the formula is right in each case but the radius is not the one given.

Correct answer: 17/20

Rewriting both fractions over a denominator of 20 gives 12/20 plus 5/20, which totals 17/20. The value 13/20 converts the fifths but leaves the quarter as 1/20, 16/20 turns that quarter into 4/20, and 11/20 subtracts the stray 1/20 instead of adding a properly converted quarter.

Correct answer: 3 hr 30 min

From 2:15 to 5:15 is three whole hours, and the further stretch to 5:45 adds half an hour, giving 3 hr 30 min. The value 3 hr 00 min ignores the minutes even though they move from quarter past to quarter to, while 4 hr 30 min and 2 hr 30 min miscount the whole hours between 2 and 5 as four and as two.

Correct answer: 5

Dividing both sides by 2 leaves x plus 3 equal to 8, and taking 3 off gives 5. The value 8 stops at that intermediate total and reports it as x, while 6 and 7 come from subtracting the 3 before dividing, which leaves 13 to be halved and then rounded one way or the other.

Correct answer: 36

Working left to right, 144 divided by 12 is 12, and that quotient multiplied by 3 gives 36. The value 12 stops at the quotient and never multiplies, while 60 and 84 multiply the quotient by 5 and by 7 in place of the 3 the question names.

Correct answer: 20%

The price falls by $12, and a percent decrease measures that fall against the original price, so 12 divided by 60 is 0.20, or 20%. The value 25% divides the fall by the $48 sale price instead of the starting price, 30% treats the fall as $18, and 40% doubles the fall to $24.

Correct answer: 120

A factorial multiplies every whole number from the given one down to 1, so 5 times 4 times 3 times 2 times 1 gives 120. The value 720 is the factorial of 6, which is what an off-by-one at the top of the chain produces when the run is started one number too high. The value 625 is 5 raised to the fourth power, from multiplying 5 by itself once for each of the four numbers below it instead of multiplying by those numbers. The value 360 comes from losing place in the descending run and writing the 3 twice, 5 times 4 times 3 times 3 times 2.

Correct answer: 175

Each map inch stands for 50 miles, so 3.5 inches is 3.5 times 50, which is 175 miles. The value 125 works from 2.5 inches. The value 155 adds the half inch as a flat 5 miles after the 150. The value 160 counts the half inch as 10 miles instead of half of 50.

Correct answer: 7

Solving x squared equals 49 means finding the number that multiplies by itself to give 49, and 7 times 7 is 49. Squaring the others falls short: 2 gives 4, 4 gives 16, and 6 gives 36, so none of them satisfies the equation.

Correct answer: 162

Each term is three times the term before it, since 2 becomes 6, 6 becomes 18 and 18 becomes 54, so 54 times 3 gives 162. The value 216 multiplies 54 by 4, 324 doubles the correct term, and 486 runs the pattern one step too far by tripling 162 as well.

Correct answer: 150

Thirty percent of the number is 45, so ten percent is 15 and the whole number is ten times that, 150. The value 135 multiplies 45 by 3 instead of dividing by 0.3. The value 120 counts only eight tens of 15. The value 115 adds the remaining 70 to 45 as though the other 70 percent were 70 units.

Correct answer: 3 in 12

The box holds 4 plus 3 plus 5, or 12 marbles, and 3 are blue, so the probability is 3 in 12, one quarter. The figure 2 in 11 is the chance of a second blue after one blue has already been drawn and kept out. The figure 3 in 9 compares blue to non-blue marbles, which gives odds rather than a probability. The figure 2 in 12 removes a blue marble but forgets to shrink the total.

Correct answer: 17

Order of operations puts multiplication before addition and subtraction, so 6 times 2 is 12, and then 9 plus 12 minus 4 gives 17. The value 30 works left to right and also drops the final step, adding 9 and 6 to reach 15 and doubling it. The value 21 handles the product correctly but leaves out the subtraction of 4. The value 26 works strictly left to right, reaching 30 and then subtracting 4.

Correct answer: 24 cu ft

Volume of a rectangular tank is length times width times height, so 2 times 3 times 4 gives 24 cu ft. The figure 16 cu ft is the combined area of the two 2 by 4 faces, which is an area and not a volume. The figure 20 cu ft adds the 3 by 4 face to the 2 by 4 face, mixing areas with volume again. The figure 28 cu ft doubles the 2 by 3 and 2 by 4 faces, a partial surface area rather than the space enclosed.

Correct answer: 90 nm

The ships end up 90 nm apart, that is 90 nautical miles. Each ship covers its speed times 3 hours, so one runs 54 nm north and the other 72 nm east, and because the two courses are perpendicular the gap is the hypotenuse of a 54 by 72 right triangle, which is 90. The figure 30 is only the rate at which the ships separate, in knots, and still has to be multiplied by the 3 hours. The figure 54 is the northbound leg alone and 72 is the eastbound leg alone; neither one measures the distance between the two ships.

Correct answer: 4.5

The run takes 4.5 hours. Speed is distance over time, so 105 divided by 3.5 gives 30 knots, and 135 divided by 30 gives 4.5 hours. The figure 3.5 just repeats the time given for the first run and answers nothing. The figure 4.0 comes from dropping the remainder when dividing 135 by 30. The figure 5.0 comes from reading the second distance as 150 rather than 135.

Correct answer: 80%

80% of the recruits passed. Divide the number who passed by the number who took the drill: 92 divided by 115 is 0.80, which is 80 percent. The figure 77% comes from treating the 23 who failed as a percentage and subtracting that from 100. The figure 83% comes from dividing 92 by 110 after misreading the total. The figure 74% comes from dividing by 125 instead of 115.

Correct answer: x = 9

The answer is x = 9. Adding the two equations cancels y and leaves 2x equal to 18, so x is 9 and y is 5. The reading x = 5 gives the value of y, the other unknown, not the one the question asks for. The reading x = 8 comes from adding 14 and 4 as 16 before halving. The reading x = 4 is the stated difference between the two numbers rather than either number itself.

Correct answer: x = 2 or x = 3

The roots are x = 2 or x = 3. The trinomial factors into x minus 2 times x minus 3, because that pair multiplies to positive 6 and adds to negative 5. The pair x = 6 or x = 1 multiplies to 6 as well but adds to 7, so it cannot produce the middle term. The pair x = 0 or x = 5 comes from dropping the constant and factoring only x squared minus 5x. The pair x = 5 or x = 6 reads the coefficient and the constant straight off the equation as though they were the roots.

Correct answer: 128

The product is 128. Powers of the same base combine by adding exponents, so 2 to the fourth times 2 cubed is 2 to the seventh, which is 128; multiplying 16 by 8 gives the same figure. The figure 112 comes from using the exponent sum as a multiplier and computing 16 times 7. The figure 96 comes from reading 2 cubed as 2 times 3 and computing 16 times 6. The figure 144 comes from confusing 2 cubed with 3 squared and computing 16 times 9.

Correct answer: 6√2

The simplified form is 6√2. Take the largest perfect square out of 72: it is 36 times 2, and √36 is 6. The form 3√8 carries the same value but is not simplified, because 8 still holds the perfect square 4; a simplified radical must have no square factor left. The form 6√3 would require 36 times 3, which is 108, not 72. The form 8√3 would require 64 times 3, which is 192.

Correct answer: 11/24

The difference is 11/24. Over the common denominator 24, 5/6 becomes 20/24 and 3/8 becomes 9/24, leaving 11/24. The figure 37/48 converts 5/6 to 40/48 but subtracts the unscaled 3. The figure 31/48 converts 5/6 to forty-eighths but 3/8 only to 9 twenty-fourths, mixing denominators. The figure 58/48 adds 40/48 and 18/48 instead of subtracting them.

Correct answer: 3/2

The quotient is 3/2. Dividing by a fraction means multiplying by its reciprocal, so 2/3 times 9/4 is 18/12, which reduces to 3/2. The figure 8/27 comes from multiplying straight across without flipping the divisor. The figure 2/3 comes from dividing the wrong way round, taking 4/9 divided by 2/3. The figure 27/8 comes from inverting the first fraction rather than the second and then multiplying.

Correct answer: 7/10

The probability is 7/10: the bag holds 10 chips and 3 are white, so 7 are not white. The figure 8/10 is the chance of not drawing red, which excludes the wrong color. The figure 9/10 removes only one white chip instead of all three. The figure 6/10 also subtracts the drawn chip from the total, which is not part of a single draw.

Correct answer: 75

The fourth score is 75. Four scores averaging 82 must total 4 times 82, or 328, and the three known scores add to 253, so the missing one is 328 minus 253. The figure 84 is the average of the three known scores and ignores the total the fourth score has to produce. The figure 82 assumes the missing score equals the mean, which holds only when the other scores already average 82. The figure 78 comes from rounding the known total to 250 before subtracting.

Correct answer: 187.5

Five inches stands for 187.5 miles. The scale gives 75 divided by 2, or 37.5 miles to the inch, and 5 times 37.5 is 187.5. The figure 375.0 comes from multiplying 5 by 75 and never dividing by the 2 inches in the scale. The figure 225.0 comes from counting 6 inches rather than 5. The figure 262.5 comes from adding the 2 scale inches to the 5 and working from 7 inches.

Correct answer: 210

The perimeter is 210 yards: 60 plus 45 is 105, and a rectangle has two of each side, so 105 doubled is 210. The figure 165 counts three sides, 60 plus 60 plus 45, and misses a width. The figure 190 slips on the first addition, taking 60 plus 45 as 95 before doubling. The figure 195 counts the 60-yard length once and the 45-yard width three times.

Correct answer: 53

The other angle is 53 degrees. Complementary angles add to a right angle, so the missing measure is 90 minus 37. The figure 63 comes from subtracting 37 from 100 rather than from 90. The figure 43 subtracts from 80, and the figure 73 subtracts from 110; each uses a total that no pair of complementary angles can reach. Subtracting from 180 would give a supplement instead, which the question does not ask for.

Correct answer: 445

The sum is 445. Round 197 up to 200, add it to 248 for 448, then take back the 3 that was added. Worked in columns, 8 + 7 = 15 carries a one into the tens, and 4 + 9 + 1 = 14 carries a one into the hundreds. The figure 435 drops the carry from the ones column, 345 drops the carry into the hundreds column, and 335 drops both carries.

Correct answer: -5

The value of x is -5. Subtracting 3x from both sides leaves -2 equal to 2x plus 8, and subtracting 8 leaves -10 equal to 2x, so x is -5. The figure 5 has the right size and the wrong sign, which is what happens when the negative is dropped at the final division. The figure -3 comes from combining -2 and 8 as -6 rather than -10. The figure 3 makes that same combining error and loses the sign as well.

Correct answer: y = 4

The line crosses the y-axis at y = 4. A graph meets that axis where x is 0, so the equation becomes 3y equal to 12 and y is 4. The reading y = 6 is the x-intercept, which comes from setting y to 0 instead of x. The reading y = 9 comes from subtracting 3 from 12 rather than dividing by it. The reading y = 2 is just the coefficient of x read straight off the equation.

Correct answer: 150

Full capacity is 150 gallons: if three fifths is 90 gallons, one fifth is 30 and five fifths is 150. The figure 120 adds only one more fifth to the 90 instead of two. The figure 126 adds two fifths of 90 rather than two fifths of the tank. The figure 144 adds three fifths of 90 to the 90, treating the fraction as a growth rate.

Correct answer: 120

The sample holds 120 grams of zinc. With a 5 to 3 ratio and 200 grams of copper, each ratio unit is 200 divided by 5, or 40 grams, so three zinc units are 120 grams. The figure 125 treats 200 grams as the whole sample and takes five eighths of it, 320 is the weight of the whole alloy rather than the zinc, and 333 inverts the ratio by multiplying 200 by five thirds.

Correct answer: 25%

The price rose by 25%. Percent increase is the change divided by the original amount: the rise is 20 dollars and 20 divided by 80 is 0.25. The figure 20% divides that same rise by the new price of 100 rather than by the starting price. The figure 22% divides by 90, the average of the two prices, which answers a different question. The figure 27% comes from dividing by 75 after misreading the starting price.

Correct answer: 90

The result is 90: 60 percent of 500 is 300, and 30 percent of 300 is 90. The figure 60 uses the leftover 40 percent, 200, in place of 60 percent of 500. The figure 75 estimates 60 percent of 500 as half, 250, before taking 30 percent. The figure 80 slips on 0.3 times 0.6, writing 0.16 instead of 0.18, and applies that to 500.

Correct answer: 15

The value is 15. Clear the parentheses first to get 3, then take division and multiplication left to right: 12 divided by 3 is 4, and 4 times 2 is 8, so 7 plus 8 is 15. The figure 11 stops after the division and never multiplies by 2. The figure 22 adds the 7 in before multiplying, giving 11 times 2. The figure 19 adds 7 and 12 and ignores the rest of the expression.

Correct answer: 24

There are 24 codes. The first slot has 4 letters to choose from, the second has 3 and the third has 2, and 4 times 3 times 2 is 24. The figure 36 leaves 3 choices in the last slot, forgetting that a second letter has already been used. The figure 48 leaves 4 choices in the second slot, which would allow a letter to repeat. The figure 60 counts five available letters rather than the four the question supplies.

Correct answer: 0

The value is 0. Work left to right: negative 8 plus 5 gives negative 3, and subtracting negative 3 is the same as adding 3, so negative 3 plus 3 leaves 0. A result of 3 comes from stopping at the intermediate total of negative 3 and reporting its size without the sign. A result of 8 comes from dropping the leading term altogether and evaluating only 5 minus negative 3. A result of 6 comes from reading the first term as positive 8 and then working 8 minus 5 plus 3.

Correct answer: 10 ft

The ladder is 10 ft long. The wall and the ground meet at a right angle, so the ladder is the hypotenuse: square 8 and 6 to get 64 and 36, add them to get 100, and take the square root to get 10. A length of 14 ft comes from adding the two legs instead of working with their squares. A length of 16 ft doubles the 8 ft the ladder reaches up the wall. A length of 12 ft doubles the 6 ft from the wall to the base in the same way.

Correct answer: 48

Three quarters of 64 is 48: one quarter is 64 divided by 4, which is 16, and three of those quarters make 48. A value of 60 subtracts the denominator 4 from 64 instead of dividing by it. A value of 52 subtracts 3 times 4 from 64. A value of 56 is seven eighths of 64, the result of misreading the fraction.

Correct answer: 7

The number is 7. Twice the number plus 6 equals 20, so twice the number is 14, and half of 14 is 7. A value of 14 stops at that intermediate step and reports twice the number rather than the number. A value of 10 halves 20 first and never removes the 6. A value of 20 simply repeats the total stated in the question, which is the result of the operations and not the number they were applied to.

Correct answer: 9

The median is 9. Put the five values in order as 3, 7, 9, 11, 15 and take the one in the middle position, which is 9. A value of 15 is the middle number of the list only as it is printed, and the list has to be sorted before a middle position means anything; 15 is in fact the largest value. A value of 12 is the range, the largest value less the smallest, which measures how spread out the numbers are rather than where their center is. A value of 10 comes from averaging a middle pair, which is the rule for a list with an even count; this list holds five values, so a single value stands alone in the middle and nothing is averaged.

Correct answer: $6 \times 10^{7}$

The product is $6 \times 10^{7}$. Multiply the coefficients, 3 times 2, to get 6, and add the exponents, 4 plus 3, to get 7. A coefficient of 5 comes from adding 3 and 2 rather than multiplying them. An exponent of 1 comes from subtracting 3 from 4 rather than adding. The choice showing a coefficient of 5 with an exponent of 1 makes both of those slips at once.

Correct answer: 78.5

The area is 78.5. Area equals pi times the radius squared, so 3.14 times 25 gives 78.5. A value of 31.4 is the circumference, found by multiplying pi by twice the radius instead of by the radius squared. A value of 62.8 applies that same circumference formula after mistaking the diameter of 10 for the radius. A value of 50.0 squares the radius correctly but then doubles the 25 instead of multiplying it by pi.

Correct answer: 6

The solution is 6. Take 2x from both sides to leave 2x minus 3 equals 9, add 3 to both sides to get 2x equals 12, and halve that to get 6. A value of 9 reaches 12 and then subtracts the 3 again instead of halving, 8 subtracts the leading coefficient 4 from 12 instead of dividing by 2, and 7 moves the 2x across as a plain 2, giving 2x equals 14.

Correct answer: 3/8

The fraction is 3/8. Read 0.375 as 375 thousandths, then divide the top and the bottom by 125 to reach 3/8. The fraction 3/4 is 0.75, which is twice as large, and comes from reducing by 500 instead of 125. The fraction 5/8 is 0.625, the part left over when 0.375 is taken from a whole. The fraction 1/3 is about 0.333 and only resembles 0.375 in its leading digit.

Correct answer: 64 cu in

The volume is 64 cu in. Volume of a cube is the edge multiplied by itself three times, so 4 times 4 times 4 gives 64. A value of 16 cu in squares the edge and stops, which gives the area of one face. A value of 48 cu in multiplies that face area by 3 for the three dimensions instead of by the edge. A value of 24 cu in multiplies the edge by the six faces of the cube, which counts faces rather than filling space.

Correct answer: 20.0%

The decrease is 20.0%. The quantity falls by 50, and 50 divided by the original 250 is 0.2, which is 20 percent. A figure of 25.0% divides the same 50 by the new value of 200 rather than by the starting value. A figure of 50.0% reports the raw drop of 50 units as though units were already percent. A figure of 40.0% doubles the drop to 100 before dividing by 250.

Correct answer: 19

The value is 19. Absolute value strips the sign, so negative 12 becomes 12 and 7 stays 7, and 12 plus 7 is 19. A value of 5 keeps the sign on the first term and works out negative 12 plus 7 as a subtraction. A value of 12 reports only the first absolute value and never adds the second. A value of 24 doubles that first absolute value instead of adding the 7.

Correct answer: 17

The largest is 17. Call the integers n, n plus 1 and n plus 2; their sum is 3n plus 3, so 3n is 45 and n is 15, making the three integers 15, 16 and 17. A value of 15 is the smallest of that trio rather than the largest. A value of 19 comes from adding the 3 instead of subtracting it, which gives n as 17 and pushes the trio up by two. A value of 21 comes from making that same sign slip and also stepping the terms up in twos, and 19 plus 20 plus 21 is far more than 48.

Correct answer: 3

The slope is 3. Slope is the change in y over the change in x, so 11 minus 2 is 9, 4 minus 1 is 3, and 9 divided by 3 is 3. A value of 9 reports only the rise and never divides by the run. A value of -3 subtracts the coordinates in opposite orders, taking 2 minus 11 over 4 minus 1. A value of -9 makes that reversal and also skips the division.

Correct answer: 1/4

The probability is 1/4. The flips are independent, so multiply 1/2 by 1/2, and the four equally likely results are HH, HT, TH and TT, only one of which is two heads. A probability of 1/8 multiplies three halves together and answers for three flips instead of two. A probability of 1/3 counts the results as two heads, one head and no heads, which are not equally likely. A probability of 3/4 is the chance of getting at least one head, the opposite of what is asked.

Correct answer: x + 12

The expression simplifies to x + 12. Distributing the 3 gives 6x + 12, and taking 5x from 6x leaves x, so the result is x + 12. The form x + 4 multiplies only the 2x by 3 and leaves the 4 alone. The form 6x + 7 subtracts a plain 5 from the 12 instead of 5x from the 6x, and 6x - 1 makes both of those slips together.

Correct answer: $828

The pay is $828. The first 40 hours pay 40 times 18, which is 720, and the 4 extra hours pay 27 an hour, which adds 108, for 828 in total. A total of $792 pays all 44 hours at the flat rate of 18 and ignores the overtime premium. A total of $864 pays the 4 extra hours at double the rate rather than at one and a half times. A total of $756 adds only the half-rate premium of 9 an hour for the 4 extra hours and drops their base pay.

Correct answer: 80%

The answer is 80%. Dividing 4 by 5 gives 0.8, and multiplying a decimal by 100 turns it into a percent, so 0.8 becomes 80%. A figure of 45% simply writes the two digits of the fraction side by side, and 54% writes them in reverse order. A figure of 75% is the value of 3/4, the neighbouring fraction a candidate may confuse with four fifths.

Correct answer: 282.6

The volume is 282.6. Volume of a cylinder is pi times the radius squared times the height, so 3.14 times 9 times 10 gives 282.6. A value of 94.20 multiplies pi by the radius once instead of squaring it. A value of 28.26 squares the radius correctly but leaves the height out altogether. A value of 188.4 is the curved side area, found from two times pi times radius times height rather than from the squared radius.

Correct answer: 12

The value is 12. Dividing 56 by 7 gives x as 8, and adding 4 to that 8 gives 12. A value of 60 adds the 4 to the 56 before dividing, or simply adds it to the wrong quantity. A value of 52 subtracts the 4 from the 56 instead. A value of 32 finds x correctly as 8 but multiplies it by 4 rather than adding.

Correct answer: 12

The greatest common factor is 12. Both numbers break down into 12 times something, since 24 is 12 times 2 and 36 is 12 times 3, and no larger number divides both. A value of 72 is the least common multiple, the smallest number both divide into, which answers the opposite question. A value of 24 divides the first number but leaves a remainder in 36. A value of 36 divides the second number but is larger than 24 and so cannot divide it.

Correct answer: $65

The selling price is $65. A markup of 30 percent on $50 adds 0.30 times 50, which is $15, so the price rises to $65. A price of $15 stops at the markup amount and never adds it to the cost. A price of $53 treats the 30 percent as $3, and a price of $55 applies only a 10 percent markup.

Correct answer: 1231

Because 4 = 2², each base-4 digit stands for two binary digits, grouped from the right: 1 | 10 | 11 | 01 gives 1, 2, 3, 1, so the answer is 1231 (check: 64 + 32 + 12 + 1 = 109 = 1101101 in binary). Grouping from the left instead (11 | 01 | 10 | 1) produces 3121, and writing the groups in reverse order produces 1321. Reading each bit pair backward turns 10 into 1 and 01 into 2, which gives 1132.

Correct answer: 33

10110 in base 2 is 16 + 4 + 2 = 22, and 23 in base 4 is 2 × 4 + 3 = 11, so the sum is 33. Getting 45 means adding 22 to 23 as if the base-4 numeral were already base 10. Getting 36 reads the base-4 digits in reverse (32 in base 4 = 14), and getting 24 reads the binary digits in reverse (01101 = 13).

Correct answer: −5

Work inside the parentheses first: 3 ◆ 2 = 2(3) − 2² = 6 − 4 = 2. Then 2 ◆ (−3) = 2(2) − (−3)² = 4 − 9 = −5. The answer 13 comes from turning −b² into +9 because b is negative, but the square is 9 and it is still subtracted. The answer −19 comes from grouping the other way, 3 ◆ (2 ◆ −3) = 3 ◆ (−5), and the answer 10 comes from treating b² as 2b.

Correct answer: 234°

Since π radians equals 180°, multiply by 180/π: 13π/10 × 180/π = 13 × 18 = 234°. The answer 468° uses 360° for π (that is 2π), and 117° uses 90° for π. The answer 54° is the reference angle, 234° − 180°, not the angle's own measure.

Correct answer: 4π/3

The minute hand makes a full turn of 2π radians (360°) in 60 minutes, so in 40 minutes it turns 40/60 × 2π = 4π/3 (240°). The answer 2π/3 treats a full turn as π instead of 2π. The answer 3π/4 inverts the fraction 4/3, and 2π/9 converts 40 minutes as if it were 40°.

Correct answer: 5,400 revolutions

One hertz is one cycle per second, so 45 Hz is 45 revolutions per second, or 45 × 60 = 2,700 RPM; over 2 minutes that is 2,700 × 2 = 5,400 revolutions. Stopping at 2,700 gives the revolutions in one minute, not two. The answer 90 multiplies 45 by 2 as if Hz were per minute, and 1,350 divides 2,700 by 2 instead of multiplying.

Correct answer: 76 feet per second

A knot is one nautical mile per hour, so 45 knots is 45 × 6,080 = 273,600 feet per hour; dividing by 3,600 seconds gives 76 feet per second (45/3,600 = 1/80, and 6,080/80 = 76). The answer 66 uses the 5,280-foot statute mile. The answer 23 uses 1,852, the number of meters in a nautical mile, as if it were feet, and 52 is about 45 × 1.15, the speed in miles per hour rather than feet per second.

Correct answer: −13

The exponent applies before the negative sign in −2⁴, so it equals −16, while (−3)² = 9 because the parentheses include the sign. Then 9 × 2 ÷ (−6) = −3, and −16 − (−3) = −13. Treating −2⁴ as (−2)⁴ = 16 gives 19, and treating (−3)² as −9 gives −19. Making both sign errors gives 13.

Correct answer: $96.00

Successive percent changes multiply: cost × 1.25 × 0.80 = cost × 1.00, so the sale price equals the cost and the jacket cost $96.00. Answers near $91 come from adding the percents as a net 5% markup and then removing 5%, either by dividing by 1.05 ($91.43) or by taking 95% ($91.20). The $86.40 answer undoes the changes with the wrong operations, adding 20% and then taking 25% off.

Correct answer: $24.32

Simple interest is 5,000 × 0.04 × 3 = $600. Compounded annually, the balance grows to 5,200, then 5,408, then 5,624.32, so the interest is $624.32 and the difference is $24.32. The $24.00 answer counts $8 of interest on interest in year 2 and $16 in year 3 but forgets that year 3 also earns interest on year 2's extra $8. The $16.32 and $16.00 answers count only one year's worth of the extra.

Correct answer: $300.00

The cost was $300.00, because a 30% markup then a 30% cut multiply the cost by 1.3 times 0.7, or 0.91, and $273 divided by 0.91 is $300. The tempting $273.00 assumes an equal percent increase and decrease cancel out, but the cut is taken from a larger base, so the pair loses 9%. The $297.57 adds 9% back to the sale price instead of dividing by 0.91, and $248.43 reverses each step by multiplying instead of dividing.

Correct answer: $1,224

She has $1,224 left: rent leaves $1,800, savings leaves 80% of that or $1,440, and the car payment leaves 85% of that or $1,224. The tempting $1,080 takes the car payment as 15% of the full $2,400 instead of 15% of the $1,440 remaining. The $1,122 takes savings as 20% of the full pay, and $960 subtracts all three percents from $2,400 at once.

Correct answer: The credit union loan, by $160.50

The credit union loan is cheaper by $160.50: it costs $2,400 in interest, while the dealership costs $20,000 times (1.055 squared minus 1), or $2,260.50, plus the $300 fee, for $2,560.50. The tempting answer that favors the dealership by $139.50 forgets the fee. Favoring the credit union by only $100.00 treats the dealership's rate as simple interest, and favoring the dealership by $200.00 drops both the fee and the compounding.

Correct answer: -5x^3/y^2

A cube root divides each exponent by 3 and keeps the sign of a negative radicand, since -5 cubed is -125, giving -5x^3 y^-2, or -5x^3/y^2. The tempting 5x^3/y^2 drops the negative sign as if an odd root of a negative number had to be positive. The two x^6/y^3 forms subtract 3 from each exponent instead of dividing by 3.

Correct answer: 2(√5 + 1)

Multiplying the top and bottom by the conjugate √5 + 1 makes the denominator (√5)^2 - 1^2 = 4, so the result is 8(√5 + 1)/4, or 2(√5 + 1). The tempting 2(√5 - 1) multiplies by √5 - 1 instead of the conjugate and then wrongly squares √5 - 1 as 5 - 1. The forms divided by 3 compute the denominator as 5 + 1 = 6 instead of 5 - 1 = 4.

Correct answer: 69π square feet

The circumference 20π gives an inner radius of 10, so the outer radius is 13 and the walkway is the ring between them: π(13^2 − 10^2) = 69π square feet. The tempting 60π multiplies the inner circumference by the width, which ignores that the outer edge is longer. The value 129π uses 20 as the radius, and 156π adds the 3-foot width to both sides of the radius, making the outer radius 16.

Correct answer: 109.12 m²

The rectangle is 96 m², the semicircle of radius 4 adds half of 16π, or 25.12 m², and the notch removes half of 8 × 3, or 12 m², giving 109.12 m². The value 134.24 m² counts a full circle instead of a semicircle. The value 97.12 m² forgets the one-half in the triangle formula, and 133.12 m² adds the notch instead of subtracting it.

Correct answer: 18 feet

Setting (4/3)πr^3 = 972π gives r^3 = 972 × 3/4 = 729, so r = 9 and the diameter is 18 feet. The tempting 9 feet is the radius, not the diameter the question asks for. The value 18√3 feet comes from using the surface-area formula 4πr^2, and 54 feet comes from squaring the radius instead of cubing it.

Correct answer: 54

A 27-fold volume means every length is multiplied by the cube root of 27, which is 3, and surface area grows by 3^2 = 9, so the larger tank needs 6 × 9 = 54 gallons. The tempting 162 scales the paint by the full volume factor of 27, but paint covers area, not volume. The value 18 scales by the length factor alone, and 486 divides 27 by 3 to get a length factor of 9 instead of taking the cube root.

Correct answer: 34 + 4π meters

The perimeter is 34 + 4π meters. The outline is the two 12-meter sides, the semicircle's arc (half of 8π, so 4π), and the two slanted triangle sides, each the hypotenuse of a 3-4-5 right triangle, so 12 + 12 + 5 + 5 = 34 plus 4π. The tempting 42 + 4π also counts the 8-meter side under the semicircle, which is now inside the figure. The answers with 8π use the full circle's circumference instead of half of it.

Correct answer: 288π cubic inches

The second sphere's volume is 288π cubic inches. From (4/3)πr³ = 36π, the first radius is 3; from 4πr² = 144π, the second radius is 6, so the volume is (4/3)π(216) = 288π, which is 8 times the first because doubling the radius cubes the scale factor. The tempting 144π multiplies the volume by 4, applying the surface-area ratio to volume, and 72π only doubles it, applying the radius ratio.

Correct answer: 10/36

The probability is 10/36. Six outcomes give a sum of at least 10 and six are doubles, but 5-5 and 6-6 are in both lists, so inclusion-exclusion gives 6 + 6 − 2 = 10 outcomes. The tempting 12/36 adds the lists without removing the overlap, and 11/36 removes only 6-6, missing that 5-5 also sums to 10. The value 8/36 drops the shared outcomes entirely instead of counting them once.

Correct answer: 8/663

The probability is 8/663. Ace then king is 4/52 × 4/51 = 4/663, and king then ace is the same, so the two orders together give 8/663. The tempting 4/663 counts only one order, and 2/169 keeps both orders but uses 52 as the second denominator, as if the first card were put back. The value 1/169 makes both mistakes.

Correct answer: 60

There are 60 arrangements. Treat TT as one block, leaving five units (TT, L, E, E, R) with the E repeated, so 5!/2! = 60. The tempting 120 forgets to divide for the repeated E, and 30 also divides by 2 for the T's, even though the two T's inside the block cannot be told apart and so create no extra orderings. The value 180 is every arrangement of LETTER, ignoring the condition.

Correct answer: 0.26

The probability is 0.26. Weather only is 0.2 × 0.9 = 0.18 and maintenance only is 0.8 × 0.1 = 0.08, so exactly one is 0.26. The tempting 0.28 is the chance of at least one, 1 − 0.8 × 0.9, which still includes the 0.02 chance of both. The value 0.30 adds the two as if they could never happen together, and 0.72 is the chance of neither.

Correct answer: 315

There are 315 committees. All 4-person committees number 11C4 = 330, and the all-women committees number 6C4 = 15, so 330 − 15 = 315 include at least one man. The tempting 600 picks one man first and then any 3 of the other 10, which counts each committee with two or more men several times. The value 345 adds the all-women committees instead of subtracting them, and 330 ignores the condition.

Correct answer: She wants to live beside the tower she guarded

Elena turns down the town retirement and moves into a cottage within sight of the tower she had faithfully kept, so she wants to live beside the tower she guarded. The passage records no objection to the automated equipment, so she wants to resist the systems she now doubts is not stated. No successor appears anywhere in the account, so she wants to train the keeper she thinks ready is invented. The passing vessels are described as company during her working years, not as a reason for staying, so she wants to watch the ships she safely guided misreads the ending.

Correct answer: Warmer surrounding seawater

The passage says rising ocean temperatures make polyps expel the algae that feed and color them, and it names that expulsion as bleaching, so warmer surrounding seawater is the stated cause. Failing carbonate skeletons would slow reef building rather than trigger the loss of algae. Unchecked marine harvesting is never raised anywhere in the passage. A persistent shelter shortage is presented as a consequence for the organisms living on a dying reef, not as the trigger for bleaching.

Correct answer: The council approved the trimmed initial mile

After months of hearings the council backed a scaled down version that paid for one mile and left the rest of the route undecided, so the council approved the trimmed initial mile. Nothing in the passage puts the corridor up for sale, so the council auctioned the whole rail corridor is not supported. The plan moved forward rather than being turned down, so the council rejected the greenway trail today reverses the outcome. Funding stopped at the first mile, so the council endorsed the entire cycling route overstates what was agreed.

Correct answer: Fluency comes from steady study plus daily immersion

Marcus finds that being surrounded by the language gave him only fragments until he added daily work with a tutor, and he concludes that fluency comes from steady study plus daily immersion. His own experience abroad disproves the claim that fluency comes from years spent living fully overseas. He credits the tutor for the turn in his progress, so fluency comes from practice once formal tutors leave contradicts him. He treats the fragments he absorbed as evidence of failure, so fluency comes from scattered phrases picked up daily is the position he abandoned.

Correct answer: Shared timetables throughout town

The passage says the clock gave a precise, shared standard so markets, schooling and labor could be coordinated across an entire town, which is shared timetables throughout town. Exact bell schedules across town is wrong because bells were the older, loose way of marking time. Exact solar schedules across town is wrong because the sun's position was also described as loose. Standard time shared across towns overreaches, since the passage speaks only of coordination within a single town.

Correct answer: Low moisture plus acidity blocks bacterial growth

The passage says honey's low moisture content and natural acidity create conditions bacteria cannot survive in, so low moisture plus acidity blocks bacterial growth is the stated reason. Warming is described only as a way to undo crystallization, so gentle warming kills resident bacteria year round misuses that detail. Crystallization is called a harmless natural change, so sugar granules crush harmful microbes fairly fast credits it with something the passage denies. Honey found in ancient tombs kept without modern packaging, so airtight jars exclude outside moisture quite well is not the explanation given.

Correct answer: Careful analysis reveals fixes blame overlooks

The supervisor studies the data instead of faulting the staff, finds fatigue and a badly placed break, and cuts errors by rescheduling, which shows that careful analysis reveals fixes blame overlooks. The long standing schedule is what produced the afternoon spike, so older factory routines produce stronger output is contradicted. The passage credits rescheduling rather than discipline, so punishing tired workers ends afternoon defects is the approach she declined. She added rest instead of taking it away, so removing midday breaks raises afternoon output reverses her fix.

Correct answer: Deserts sustain creatures through clever adjustment

The passage lists nocturnal habits, water-storing stems, waxy coatings and spines as the reasons life flourishes, so deserts sustain creatures through clever adjustment is its view. Deserts house richer wildlife than tropical forests overstates the claim, since no comparison with forests is made. Deserts host life because their heat is exaggerated contradicts the punishing heat the passage describes. Deserts host life through stored water in cactuses narrows the view to one plant example and never says animals drink from cacti.

Correct answer: Starting the rival homeroom contest

Participation stayed flat until Priya set the homerooms against one another and posted a running tally, after which collection rates soared, so starting the rival homeroom contest is the strategy that worked. She never eased the quota, so lowering the weekly material target is not in the passage. Nothing was compelled, so making the drive mandatory homework misstates a voluntary effort. The only reward described is a posted tally and a sense of pride, so offering the classmates cash prizes adds an incentive the passage does not contain.

Correct answer: It devours reserves well beyond its small bulk

The passage sets about two percent of body weight against roughly twenty percent of resting energy, so it devours reserves well beyond its small bulk is the point being made. Neurons are described as never fully shutting down, so it switches off entirely once its owner sleeps contradicts the text. The twenty percent figure is a share of energy and not of mass, so it marks twenty percent toward its body weight swaps the two numbers. Resting is exactly when the twenty percent is measured, so it demands nothing further once its owner naps reverses the finding.

Correct answer: It broke down whenever thick fog arrived

Flying by landmarks worked in clear weather and stopped working at night or in heavy cloud, so it broke down whenever thick fog arrived is why the method was unreliable. Landmarks are rivers, roads and rail lines, so it suited flights above wide ocean water inverts the conditions it needed. Radio equipment belongs to the later fix rather than to the method itself, so it needed costly onboard radio sets then confuses the two eras. No prohibition appears anywhere, so it met official bans from air regulators is invented.

Correct answer: It saved the aged facade behind updated interiors

The architect offered a middle course that kept the historic front and refitted the inside for community use, and it won support, so it saved the aged facade behind updated interiors. The plan moved forward at once, so it left the empty building awaiting further study describes the deadlock the compromise ended. Demolition was the position the compromise defeated, so it sent the whole theater toward rapid demolition names the losing side. The refitted space is for community events, so it turned the theater toward rented office suites changes the purpose.

Correct answer: Sleep quality matters beyond mere duration

Because broken cycles leave a person unrested even when the hours are unchanged, the passage concludes that sleep quality matters beyond mere duration. Deep sleep quality alone decides your rest ignores the dreaming stage, which the passage also credits with a real job. Deep sleep duration can offset poor cycles contradicts the point that disrupted cycles harm rest whatever the time spent. Dream sleep counts more than deep sleep ranks two stages the passage treats as equally necessary.

Correct answer: Unclear duties froze routine decisions

Fast growth left nobody sure who owned what, and work halted while people waited on each other, so unclear duties froze routine decisions names the problem. Money is never mentioned, so limited startup investor cash reserves is outside the passage. The company had grown quickly and had people to spare, so meager experienced employee head count misreads the situation. The founder added a chain of approval as the cure, so heavy written internal approval habits describes the fix rather than the fault.

Correct answer: It releases very little wasted heat

The passage contrasts the glow with a household bulb and says it produces almost none of the heat a bulb wastes, so it releases very little wasted heat is the stated reason for calling it efficient. Luciferin and its enzyme are named as the mechanism, so it avoids the chemical trigger step denies the very process described. Duration is never discussed, so it lasts through an animal lifetime is not supported. Brightness is never claimed either, so it throws a startlingly bright glow is beside the point the passage makes.

Correct answer: Sound fundamentals plus patient effort

The coach set aside the scoreboard and praised improvement instead, which is why sound fundamentals plus patient effort describes what he put first. Players began arriving early rather than practicing less, so shorter weekly squad practice sessions reverses what happened. He worked with the squad he inherited, so fresh outside player recruitment trips adds something the passage never mentions. Chasing silverware is exactly what he declined to do at the start, so instant championship game trophy plans is the opposite of his approach.

Correct answer: They endanger ice fed supplies miles downstream

Rivers carrying drinking water and irrigation to millions are fed by glacial melt, and scientists warn those supplies are at risk as the ice shrinks, so they endanger ice fed supplies miles downstream. Snowfall is what fails to replace the ice rather than something the glaciers reduce, so they cut yearly snowfall over frozen reservoirs reverses the relationship. Salt content is never raised in the passage, so they raise inland river salinity levels steeply is invented. Melting ice adds water rather than removing it, so they slowly lower sea levels across communities runs the wrong way.

Correct answer: A stiff formal library setting

Parents told the librarian the hush and formality put young children off, so a stiff formal library setting is what kept the room empty. No charge is mentioned anywhere, so a steady weekly reading charge is invented. Opening times are never raised as an obstacle, so a poor daily opening timetable is unsupported. The passage says the collection was generous, so a small picture book selection contradicts the text directly.

Correct answer: By briefly cooling the surface using reflected light

Ash and gases spread around the globe and reflect sunlight back into space, causing a temporary drop in surface temperature, so by briefly cooling the surface using reflected light matches the passage. By briefly warming the air while the gases trap heat describes a greenhouse effect the passage never mentions. By slowly cooling the surface while ash absorbs heat names the wrong mechanism, absorption rather than reflection, and the wrong pace. By lastingly chilling the planet as gases block heat ignores that the cooling is called temporary.

Correct answer: It pulled the distant neighbors together

With screens dark, families ate on porches, strangers introduced themselves and people checked on the elderly, so it pulled the distant neighbors together is the unexpected effect. Phones were dimmed and televisions dark, so it deepened the household phone routines is the reverse of what the passage reports. Damage to property is never described, so it wrecked the nearby porches completely is invented. Residents stayed and later missed the quiet days, so it propelled the longtime residents away contradicts the ending.

Correct answer: The voyage occupies several lifetimes

No individual butterfly finishes the whole circuit; offspring carry on a route their parents started, so the voyage occupies several lifetimes is what the passage calls remarkable. Time of day is never discussed, so the butterflies travel past nightfall is not supported. The passage stresses precision and a return to the same forests, so the route changes considerably yearly contradicts it. The text states outright that no single butterfly makes the full round trip, so single insects complete the roundtrip is the claim it denies.

Correct answer: Naming the hidden interests behind positions

The mediator told both sides to look past their stated demands to what each actually needed, they found their goals compatible, and the deal closed, so naming the hidden interests behind positions is what broke the deadlock. The agreement was signed rather than dropped, so quietly abandoning the stalled deal entirely reverses the ending. A mediator rather than a hard bargainer was brought in, so hiring the toughest possible outside advisor misreads the role. Both sides feared looking weak and neither gave way, so conceding the disputed clause fairly quickly is the move they avoided.

Correct answer: Tougher bacterial strains gradually multiply

The passage says survivors pass their resistance on until strains emerge that no longer respond, so tougher bacterial strains gradually multiply is the consequence described. Patients' immune systems resist common drugs misplaces the resistance in the person rather than the bacteria. Microbes mutate faster after every drug dose is not stated; resistance is inherited by survivors, not sped up. Common flu strains return each winter season describes a seasonal viral pattern the passage never mentions.

Correct answer: Early turnover fell and recent hires felt readier

Surveys after the redesign showed staff feeling better prepared and connected while departures in the first year declined, so early turnover fell and recent hires felt readier. The new day was full of tours, questions and sample problems, so basic training shrank and newer hires knew little misstates the change. Paperwork was what the redesign removed, so paperwork stacks grew and office morale sank fast reverses it. Lectures were replaced by activities, so sessions ran longer and duller lectures came back describes the old format.

Correct answer: Continuous lunar tidal attraction

The passage opens by saying tides come chiefly from the moon drawing the oceans toward it, so continuous lunar tidal attraction is the primary cause. Spin alone is never given as a cause, so ordinary daily planetary rotation is unsupported. Heat is never mentioned in connection with tides, so changing ocean temperature layers is invented. Only the sun is credited with a secondary role, so persistent offshore wind patterns names a force the passage never raises.

Correct answer: It allowed the counter staff longer chats

Taking orders online lifted the phone work off the counter and left more room for talking with people in the shop, so it allowed the counter staff longer chats. Staff were still needed and simply did different work, so it abolished the need for shop assistants overstates the change. New customers found the shop through its website, so it shrank the weekly customer count badly is the opposite of what happened. The owner's fear proved unfounded, so it made the bakery itself feel impersonal is the outcome the passage rules out.

Correct answer: The recently perfected printing press

The passage credits one technology with carrying the new thinking across the continent at unprecedented speed, so the recently perfected printing press is the factor named. Trade is never discussed, so the sharply reduced overseas commerce is outside the text. Classical works were being rediscovered rather than lost, so the widening classical text shortages reverses the situation. Wealthy patrons are described as funding artists and thinkers, so the gradual wealthy patron withdrawal contradicts the passage.

Correct answer: The body needs unhurried days adjusting upward

The guide insists on a measured pace and frequent halts because acclimatizing takes time, and the climbers who obeyed reached the top, so the body needs unhurried days adjusting upward. The passage says months of preparation left them unready for the thin air, so hard training erases the whole climbing danger is refuted in its opening line. The climber who hurried had to turn back, so quicker climbers reach the summit ahead anyway is contradicted by the ending. Frequent rest is the guide's central instruction, so rest proves needless across the highest slopes denies it.

Correct answer: It expanded past one patch toward shared ground

One teacher's vegetable bed drew curious neighbors until the lot held dozens of beds and became a place to trade seeds, recipes and stories, so it expanded past one patch toward shared ground. Ownership never changes hands, so it passed quietly toward one large produce farm is invented. Fresh vegetables are the starting point and the produce is named throughout, so it grew showy blossoms alone lacking food crops contradicts the text. Neighbors joined rather than left, so it sat unused once its local neighbors departed reverses the story.

Correct answer: Camouflage adopts widely varied physical shapes

The passage lists mimicry of dangerous animals, color change to match surroundings, and bodies shaped like twigs or leaves, so camouflage adopts widely varied physical shapes is its main idea. These strategies are presented as effective ways of avoiding becoming prey, so camouflage rarely fools alert hunting predators works against the text. Insects are one example among several, so camouflage occurs solely among crawling insects narrows the passage wrongly. Variety is the whole point, so camouflage follows one identical natural method states the reverse.

Correct answer: Vital findings deserve prominent early placement

The warning went unread until the author moved it to the front, and the closing line tells writers to put the most important material where readers will actually look, so vital findings deserve prominent early placement. Length is never praised, so lengthy reports outperform shorter clearer texts is unsupported. Burying the warning is the mistake the episode corrects, so serious warnings deserve quiet protective burial states the error as a rule. The executives did read the summary and only missed what was hidden later, so busy executives avoid opening summaries entirely misreads them.

Correct answer: As a generous perilous presence

The people along the banks learned to respect the river's generosity and its dangers together and shaped their lives around both, so as a generous perilous presence is how they saw it. They built their lives around the river rather than trying to be rid of it, so as a menace needing eradication misses the balance. Merchants used it as a highway for goods, so as a worthless shipping channel contradicts the passage. Floods ruined fields and homes, so as a wholly beneficial neighbor leaves out half of what the passage says.

Correct answer: Confident memories are sometimes seriously mistaken

The passage closes by cautioning that confidence in a memory is no guarantee of its truth, so confident memories are sometimes seriously mistaken. They are not invariably entirely faithful, because recall fills gaps with assumptions and details borrowed from later experiences. They are not permanently fixed recordings, since the brain rebuilds an event every time it is retrieved rather than storing it like video. And they are not single unrepeatable episodes; the passage describes the same memory being recalled again and again.

Correct answer: Coaching the village helpers with faraway expert backup

Care improved by coaching the village helpers with faraway expert backup: a nonprofit trained local volunteers, gave them simple tools, and put them on a radio link to distant physicians. Supplying the village itself with salaried city doctors never happened, and the passage says the place still had no doctor of its own. Treating the village sick with distant monthly journeys is the problem the program removed, not the remedy it supplied. Providing the village elders with costly hospital wards is exactly what the closing line says meaningful health gains do not require.

Correct answer: Spreading the strain evenly around the frame

A successful design distributes stresses so that no single part bears too much, which is spreading the strain evenly around the frame. Polishing the surface alone around the front fails because the passage says elegance lies in the invisible balance of forces rather than in appearance. Choosing the heaviest metals around the deck only adds to the steady dead weight that the passage lists as one of the loads a design must already carry. Ignoring the gusting winds around the valley contradicts the requirement to account for dynamic forces such as wind and earthquakes.

Correct answer: Using remembered learning instead of the passage

A well-informed test-taker goes wrong when using remembered learning instead of the passage. The text says those who rely on outside facts they happen to know, rather than the material in front of them, pick answers that merely seem true in general. Hurried impressions and confident intuition are never named as the cause, and the section is scored on the given material, so instruction wording is not what the answer must rest on.

Correct answer: Naming the view that sentences jointly reinforce

A reader finds the main idea by naming the view that sentences jointly reinforce. The passage says the main idea is the single point every sentence works to support, and that details, examples and figures are evidence building toward it rather than the point itself. Marking the sentences that introduce the passage or selecting the sentences that stretch the longest judges layout, not meaning, and trusting the sentences that surprise the readers mistakes a striking figure for the point it serves.

Correct answer: It builds on the reason that the passage supplies

A sound inference is the one that builds on the reason that the passage supplies, staying close to the text and going only one small step beyond it. Riding on guesswork the passage denies fails, since answers that demand large assumptions or contradict the text are wrong. Feeding on phrases the passage reprints yields a stated fact rather than an inference, and trading on drama the passage withholds adds information the text never provides.

Correct answer: The order covered too brief a deployment

She revised it because the order covered too brief a deployment: the quantities had been calculated for four weeks while the ship was to stay at sea for an additional six. The chief wanted a smaller reserve order is backward, since she raised the quantities and flagged the shortfall for him. The order met a planned deployment fully contradicts the mismatch she found, and a lighter stores load was never her aim, because leaving the crew short before resupply was the risk she was avoiding.

Correct answer: To convene and be numbered

In this passage 'muster' most nearly means to convene and be numbered. The text defines a muster as an assembly at which personnel are accounted for, and says the call to muster at stations is a call to gather and be counted. To march and be dispatched describes setting out on a task, to repair and be inspected describes work on equipment, and to disperse and be excused is the opposite of assembling, so none of them fits the sense the passage gives.

Correct answer: Checklists shield seasoned workers from slips

The main idea is that checklists shield seasoned workers from slips. The manual calls a checklist a safeguard rather than a sign of incompetence, notes that experienced operators skip steps when distracted or fatigued, and observes that the most skilled professionals are the most disciplined about using them. That rules out the claim that checklists distract expert workers from tasks, and it contradicts the idea that checklists excuse untrained workers from care. Sparing competent workers from blame is never offered as the purpose.

Correct answer: He rated crew safety above survey progress

The captain rated crew safety above survey progress. He turned back rather than race the weather and said incomplete data gathered safely was worth more than complete data gathered at the cost of the ship and crew. He had adjusted course each morning on the forecasts, so he rated crew doubts above storm forecasts is unsupported, and expecting calm weather is ruled out by his retreat. Port comfort above survey results misreads him, because he still valued the data, just not at that price.

Correct answer: The enormous expense of durable structures

The obstacle the passage names is the enormous expense of durable structures: works that withstand constant saltwater corrosion and powerful currents remain costly, and tidal power stays a minor contributor until those costs fall. The uncertain rhythm of seasonal movements is the reverse of what the text says, since tides are called extraordinarily predictable and a generator can forecast its output years ahead. A limited choice of sheltered structures and endless protest of coastal communities are never raised.

Correct answer: Overlap in dates does not prove causation

The supervisor's point is that overlap in dates does not prove causation. She stresses that the decline merely coincided with the competitor's advertisement, that a seasonal slowdown or a pricing change had not been ruled out, and that a responsible conclusion acknowledges the correlation without claiming proof. She never argues that weakness in data does not permit analysis, nor that rivalry in adverts does not damage income, and she keeps a slowdown in trade alive as an explanation rather than dismissing it.

Correct answer: A downhill conduit from upland brooks

The shortage was solved by a downhill conduit from upland brooks. A surveyor traced an underground stream at a higher elevation and proposed a simple gravity-fed channel to bring its water down, and within a season the new supply ended the rationing. A pumped delivery from distant rivers is not what the text describes, a stricter ration from existing wells was the failing stopgap rather than the remedy, and a planned exodus from crowded hamlets never occurred, since the population grew.

Correct answer: A warning compels prompt reaction

A warning compels prompt reaction, and that is what separates it from a caution. The checklist defines a warning as signaling an immediate threat demanding instant action, while a caution flags a condition that allows time to respond methodically. So a warning permits leisurely study reverses the two, a warning suggests milder trouble makes it the lesser signal when it is the graver one, and a warning deserves little concern is exactly the mistake the passage calls a risk of disaster.

Correct answer: Reach, not content, decided the collection's worth

The remark suggests that reach, not content, decided the collection's worth: the director says the value multiplied not because the collection changed but because access to it did. Experts, not staff, decided the collection's worth is the expectation the passage overturns, since ordinary citizens drove the surge in use. Rewrites, not care, decided the collection's worth is wrong because nothing was rewritten, and budgets, not scans, decided the collection's worth is never claimed anywhere in the text.

Correct answer: Matches what the passage establishes

A statement is supported when it matches what the passage establishes, whether the passage says so outright or provides facts from which it reasonably follows. Duplicates what the passage supplies describes a verbatim restatement, which the text says is not required for support. Overtakes what the passage justifies is the case the text rules out, since statements going beyond the evidence are unsupported however logical they sound, and disputes what the passage guarantees contradicts the text instead of following it.

Correct answer: The notebook solved a breakdown the machines missed

Attitudes shifted because the notebook solved a breakdown the machines missed: a decade-old entry pointed to the answer when the computer diagnostics could not explain a pump failure. The notebook earned a deference the chief commanded is wrong because the change came from a result, not an order. The notebook replaced a program the sailors trusted reverses the story, since the digital logs stayed in use, and the notebook silenced a sensor the engineers valued describes something the passage never reports.

Correct answer: Predicting it means comparing air and water temperatures

Predicting it means comparing air and water temperatures. The passage says sea fog depends on the temperature difference between air and water, and that mariners anticipate it by watching for warm air moving across cool currents. Predicting it means counting rainfall and water averages is ruled out, because the text states the process does not depend on rainfall. Watching air and cloudy disturbances and timing sunrise and temperature peaks name signals the passage never ties to fog at all.

Correct answer: The survival of a craft carried through bloodlines

The central concern is the survival of a craft carried through bloodlines. The passage says outright that the harbor and the fisherman serve a larger purpose, to illustrate a way of life passed from parent to child across many years. The routine of a repairer learned through practice and the stillness of a harbor spotted through daybreak are the supporting details the text explicitly sets aside, and the collapse of a fishery squeezed through markets describes a decline the passage never mentions.

Correct answer: The report withheld its verdict through the pages

The analyst's criticism is that the report withheld its verdict through the pages: the recommendation sat in a single paragraph near the end, and a clearer report would have stated its conclusion at the outset and used the body to defend it. The report compressed its claim through the pages is wrong because the document ran to ninety pages. The report omitted its protests through the pages is also wrong, since the body presented arguments on every side, and no factual error is alleged, so the report misstated its totals through the pages has no support.

Correct answer: The compass heading of one object from another

As the passage uses it, bearing is the compass heading of one object from another, measured as an angle from a reference such as north. The regular spacing of one object from another is distance, which the text explicitly separates from bearing by saying a bearing states which way to look rather than how near a contact lies. The partial masking of one object from another and the gradual parting of one object from another are neither direction nor distance, and the passage defines neither.

Correct answer: To build the recruit's unaided judgment

The goal of mentorship is to build the recruit's unaided judgment. The designers say a mentor's role is not to decide for the recruit but to help the recruit learn to make sound decisions independently, and that success means needing the mentor less over time. To remove the recruit's daily decisions is precisely the misunderstanding they warn against, to feed the recruit's constant reliance produces the dependence they call a failure, and to shrink the recruit's annual workload is never mentioned as an aim.

Correct answer: Graded charges that climbed with wasteful usage

Consumption fell under graded charges that climbed with wasteful usage. The council member's third path kept basic use affordable while charging steeply for excess, and within a month the reservoir stabilized. Blanket curbs that arrived with official orders describes the mandatory restrictions the public resented and the bans residents feared, which were avoided. Gentle appeals that spread with printed posters had produced little change, and deeper wells that opened with seasonal rainfall appear nowhere in the passage.

Correct answer: Mapping the framework and central claim early

The strategy recommended is mapping the framework and central claim early, then returning for details only as the questions require. The passage says storing the phrasing and precise detail early backfires, because holding isolated facts in mind leaves little attention for grasping how they relate. Dodging the passage and reading queries early is never suggested, and scanning the ending and working upwards early is not the organization-first approach the text describes.

Correct answer: Comparison exposes the gauge that has faltered

He cross-checks because comparison exposes the gauge that has faltered. The passage says that by checking several independent sources he can catch the moment one of them begins to lie, since a satellite system can lose signal, a gyrocompass can drift and a chart can go out of date. Isolation exposes the gauge that has slackened is the opposite of his practice, and he rejects neither new nor old equipment, so advancement exposes the gauge that has drifted and obsolescence exposes the gauge that has failed both misstate him.

Correct answer: Spare parts repay the room they fill, because a breakdown grounds a ship

The passage argues that spare parts repay the room they fill, because a breakdown grounds a ship. The quartermaster grants that extra crates take up space, then answers that one missing component can hold a vessel for weeks far from any help, so the apparent saving disappears at the worst moment. The claim that spare parts crowd the hold a lean ship travels with is the objection the passage answers, not the point it reaches. The ship crew and its talk never appear, and the rows the two sides spark are only the setting for the argument rather than its substance. Nothing limits the case to the brief runs a ship serves while it stays nearby; the argument is strongest on the long deployments the passage describes.

Correct answer: Bees kept in a pasture meet heavier chemical loads than city bees do

The passage supports the inference that bees kept in a pasture meet heavier chemical loads than city bees do. It reports that bees in some cities do better than their countryside counterparts, where pesticide-heavy monocultures dominate, which points to the sprayed farmland as the harder place to live. Nothing in it says a city bee must travel wider daily circuits than a country bee; flight distance is never measured or compared. The passage calls urban honey more varied in flavor rather than sweeter or darker, so the claim that a city hive can produce honey to beat an upland one is not supported. It never mentions legal barriers of any kind, stricter or otherwise, and it lists a garden as one of the many places city flowers grow rather than a site where bees are kept under special rules.

Correct answer: A remarkable achievement

In this passage the word means a remarkable achievement. The bat's flight is called precise and navigational, and the paragraph goes on to praise an animal that can pick out prey the width of a hair while weaving through branches at speed, which is admiration for a difficult act well done. A persistent misjudgment reverses that praise into failure. A continuous disturbance treats the word as a kind of noise, borrowing from the sounds the bat emits rather than from the sentence. A convenient measurement reads the word as the unit of length that sounds the same, which the sentence structure does not allow.

Correct answer: They were given a fair chance to master the shaky basics

They improved because they were given a fair chance to master the shaky basics. The passage says beginners went back over fundamentals and that recruits who had lagged kept pace once they were no longer pushed past material they had not yet learned. It never says anyone was handed a lighter drill load or asked to finish less by the end of the week, so the workload claim is unsupported. The officer split the beginners away from the advanced recruits rather than placing them beside a faster squad to match its pace. And nobody was offered a shorter course to save idle time, because the length of the course is never mentioned.

Correct answer: To show the many gifts a wetland gives and the peril ahead

The author writes to show the many gifts a wetland gives and the peril ahead. Three sentences set out how the tangled roots hold sediment, blunt waves, shelter young fish and lock away carbon, and the closing sentence warns that clearing has already wiped out huge areas. The passage treats a shrimp farm as a cause of that destruction, so it cannot be urging its case or the ground such ponds would have gained. It says these forests match or beat tropical rainforests at storing carbon, which is the reverse of rating a mangrove forest a poor carbon store or a risk. It never sets out to trace the taste a mangrove fish has, nor the appeal of any meal made from one; fish appear only as an example of what the roots shelter.

Correct answer: Slackened in force

In this passage the word means slackened in force. Everything reported after it describes a fall: the pitching seas settle into a steady swell, the wind drops to a moderate breeze, and the watch officer judges the deck safe enough for routine duties again. Stiffened in force is the reverse of what those details show. Wandered in course describes a change of direction, while the sentence is about how hard the weather blew rather than which way. Persisted in force would mean nothing changed, which contradicts the return to normal work on deck.

Correct answer: Goldfish stick to a lesson and recall a drill long afterward

The author's point is that goldfish stick to a lesson and recall a drill long afterward. The passage cites controlled work in which the animals learned to push a lever for food and still had the trick months later, and adds that they run mazes and tell one piece of music from another. That same evidence shows goldfish adapt well rather than poorly to drills, and that they hold a task far longer than the hours such a claim would allow. Goldfish that listen to a melody are showing memory, not choosing a tune over a generous plate of food. And the closing sentence attacks the bare bowl as an excuse the myth props up, so it does not claim goldfish come to little harm or flourish inside one.

Correct answer: The bright preface promised a lift the tests denied

The passage best supports the statement that the bright preface promised a lift the tests denied. Its opening summary calls the improvement consistent, while the buried data show gains under laboratory conditions and almost nothing outside them, which is the gap a careful reader would notice. That buried data is where the meaningful detail sits, so it did not give a careful reader little to work with. Outside the lab the effects were negligible, so the additive never lifted real engine output beyond a lab bench. And because the lab result and the road result differed sharply, they cannot have matched almost exactly.

Correct answer: The roads bear the daily loads of a full twenty long centuries

Durability is shown by the detail that the roads bear the daily loads of a full twenty long centuries. Traffic still running over a surface laid two thousand years ago is direct proof that the construction has lasted. That the roads crossed the whole span of a ten thousand mile empire measures reach, not endurance, and says nothing about how long any stretch survived. That they needed the packed bed of a sturdy gray stone footing, and that they carried a paved top that drained rain away like a channel, describe how the roads were built; a method on its own does not show the result held up. Only continued use after so long does that.

Correct answer: Because a tense moment leaves the sharpest mind unsure

The checklist exists because a tense moment leaves the sharpest mind unsure. The final sentence gives that as the reason directly, saying the discipline is there precisely because recall fails when someone is under strain. No rules a pilot obeys are said to demand written records, and the passage treats the inspection as a real safeguard rather than a filing exercise. It never suggests the daily routine gives a pilot quiet pleasure either; it warns instead against rushing through it. The fuel cap is one example of a small item that can matter, not a part that outweighs a single plane airframe.

Correct answer: Intrigued by what the soundscape revealed

The tone is best described as intrigued by what the soundscape revealed. The passage calls the chorus unexpected, the whale songs eerie, and the harbor a thriving acoustic community, which is the language of fascination. The author is not dismayed by what the instruments revealed, since the finding is presented as a gain rather than a loss; not annoyed by what the measurements revealed, since industrial noise is never criticized; and the detailed, wondering description rules out being unimpressed by what the research revealed.

Correct answer: Job type governs ideal workplace choice

The main idea is that job type governs ideal workplace choice. The passage rejects a single right answer and argues that concentration work may flourish at home while collaborative work may suffer outside a shared room. It does not hold that remote desks outrank crowded open space, since it grants that some projects fare worse away from colleagues. It does not hold that team projects need daily office contact, only that some benefit from proximity. And it directly rejects the notion that uniform policy suits modern staff needs.

Correct answer: A pivotal juncture

In context the phrase names a pivotal juncture. The passage defines it as a moment after which things are never the same, and the image of rain diverging on either side of a ridge shows one event sending the future in a wholly new direction. A torrential storm reads the word as weather and a watershed survey reads it as geography, both taking a figure of speech literally. A slight roadblock is far too small, since the passage stresses a wholly new direction rather than a brief obstacle.

Correct answer: Smaller outlay for the firm, added strain for the buyers

The outcome is smaller outlay for the firm, added strain for the buyers. Fuel cost per item dropped sharply and trucks came off the road, while customers had to hold larger inventories because orders arrived less often. There were not genuine savings for the firm, plain gains for the buyers, since one side plainly absorbed a new cost. Costlier fuel for the firm, steady prices for the buyers reverses the passage, which says the per-item fuel cost fell. And slight upside for the firm, strong relief for the buyers inverts who came out ahead.

Correct answer: Sailors trusted its luck; biologists admire its efficiency

The two views differ in that sailors trusted its luck; biologists admire its efficiency. The passage says sailors prized the bird as a sign of safe passage, while modern biologists, less concerned with omens, marvel at hours of gliding on almost no effort. Sailors dreaded its omen; biologists respect its instincts reverses the sailors' attitude, since they prized rather than feared the bird. Sailors mapped its routes; biologists compute its headwind wrongly credits both groups with studying the flight. And sailors tracked its ranges; biologists credit its fortunes hands the superstition to the wrong group.

Correct answer: Measured judgment built crew trust

It can be inferred that measured judgment built crew trust. The crew, sensing that her decisions now rested on understanding rather than reflex, grew more willing to bring her early warnings of trouble. Silence replaced crew orders fully overstates the change, since she still decided and still directed. Quick reflexes suited crew members contradicts the passage, which shows the crew responding better to the newer and slower style. And slow inquiry delayed crew progress inverts the text, which says pausing to gather information often led to faster solutions.

Correct answer: To sharpen the eventual blow

The filmmakers opened with untouched beauty to sharpen the eventual blow. The passage states that by first making viewers fall in love with the place, they ensured the later revelation of danger would land with greater force. The shots were not there to pad the sluggish preamble, since they are described as a deliberate strategy. They were not there to promote the local tourism, a purpose the passage never raises. And they were not there to excuse the mining hazards, since the film exposes rather than defends the project.

Correct answer: Amassed adenosine surges when the caffeine fades

A crash follows because amassed adenosine surges when the caffeine fades. The passage explains that caffeine only blocks the receptors while the chemical keeps building, so the whole backlog registers at once afterwards. Ruined adenosine departs when the caffeine lands is wrong because nothing is destroyed, and the passage says the chemical is still present. Latent adenosine idles when the caffeine ignites is wrong because the drug masks fatigue rather than supplying energy. And fresh adenosine ceases when the caffeine arrives is wrong because production continues throughout.

Correct answer: Prolonged jams would sap the marketplace

The council paid more because prolonged jams would sap the marketplace. The passage says the members reasoned that a year of gridlock would itself impose hidden costs on the local economy. Parallel spans would undercut the prices is wrong because the parallel bridge was the far more expensive of the two proposals. Broader decks would defeat the engineers is wrong because widening was presented as a workable and cheaper option. And new crossings would avoid the earthworks is wrong because the second bridge still had to be built, only without halting traffic.

Correct answer: Timely quiet strengthens leader impact

The central message is that timely quiet strengthens leader impact. The essay says a leader comfortable with silence invites quieter members to speak, and that the most persuasive voice sometimes belongs to the one who knows when not to use it. Endless talk signals leader confidence is the very position the essay rejects, since filling every pause makes a leader miss what others are trying to say. Sheer volume decides leader persuasion misreads an argument about restraint. And withdrawn staff waste leader attention reverses the essay's respect for quieter contributors.

Correct answer: Grinding fatigue left mere subsistence

The shrinking entries suggest that grinding fatigue left mere subsistence. The passage says the late entries recorded only distances marched, rations remaining and weather endured, and that this conveyed how exhaustion stripped the journey down. Sagging interest ended idle authorship is wrong because the change tracks physical strain rather than a lapsed hobby. Dulling scenery halted lavish accounts is wrong because nothing suggests the country grew less remarkable. And dwindling paper forced cramped entries invents a shortage the passage never mentions.

Correct answer: Completing HCP training in the first 30 days

The passage says each newly reporting member shall complete HCP training within 30 days of check-in, and shall is mandatory wording, so completing HCP training in the first 30 days is required. Completing HCP refresher training once a year is the most tempting choice, but the passage says members should do it, which is advisory. Holding the refresher at a stand-down is something division officers may do, and a transfer with a recent baseline is expressly not required to repeat the audiogram.

Correct answer: The senior department head, who acts for the XO

A change after approval needs XO concurrence, and when the XO is absent the senior department head acts for the XO, so the senior department head, who acts for the XO, must concur. The CO is the tempting choice because the CO's approval cannot be delegated, but that rule covers approving the POD, not concurring with later changes. The OOD only announces the change, and OPS is the officer asking for it.

Correct answer: Swapping each broken tool for a new one

Turning in damaged tools is the one practice the passage words with should, so swapping each broken tool for a new one is recommended rather than required. Inventorying containers at the end of every shift, etching every tool with the work center code, and reporting a missing tool to Maintenance Control all carry shall. Readers often pick the end-of-shift count because it is reworded, but the passage requires an inventory at the start and at the end of each shift.

Correct answer: The pilot shows both hands clear of the controls

Rebuilt in order, the sequence is: fire-fighting equipment manned, the plane captain's signal, the pilot setting the brake and showing hands clear, the grounding cable attached, the nozzle connected, and then the supervisor's confirmation before fuel flows. So the step just before grounding is that the pilot shows both hands clear of the controls. The plane captain's signal is the tempting choice because the passage describes it next to the pilot's action, but it comes one step earlier, and the supervisor's confirmation comes after both the cable and the nozzle.

Correct answer: The CO, rather than the CDO who has the duty

Under FPCON Charlie or higher, no one other than the commanding officer may grant an exception, so the answer is the CO, rather than the CDO who has the duty. The CDO, once a qualified relief is assigned, is the tempting choice because it meets both of the CDO's normal conditions, but the FPCON sentence takes that authority away from the CDO. Saying FPCON Charlie bars all exceptions misreads the sentence, which still lets the CO grant one.

Correct answer: Mishaps peak in the same hours junior maintainers are assigned to tow

The passage puts most ground mishaps in the first two hours of the night shift and says that is when the most junior maintainers are assigned to towing, so mishaps peak in the same hours junior maintainers are assigned to tow. The passage never says what the maintainers were doing when the mishaps happened, so neither the most nor the all version about towing is supported. Saying inexperience caused the mishaps turns a timing overlap into a cause the passage does not establish.

Correct answer: A Sailor whose one failure is followed by a pass leaves FEP

FEP enrollment lasts until the Sailor passes the next official PFA, so a Sailor whose one failure is followed by a pass leaves FEP. The tempting choice reverses the conditions: advancement is blocked only after two consecutive failures, and a Sailor can be in FEP after a single failure. The passage never mentions separation, and a Sailor who fails twice was already placed in FEP after the first failure. A waived cycle counts as neither a pass nor a failure.

Correct answer: The lapses came while the escorts themselves were at a brief

Both incidents happened during the noon brief, which the escorts were attending, so the lapses came while the escorts themselves were at a brief. Saying visitors are most often left unescorted during the noon brief turns two incidents in one month into a general pattern. The visitors were found near the catapults, not in the landing area. The passage requires an escort at all times, so attending the brief never lets a visitor move about unescorted.

Correct answer: A documented search can allow an aircraft's release even if the tool is never found

The release rule has two exits, the tool being found or a completed and documented search, so a documented search can allow an aircraft's release even if the tool is never found. The tempting claim that the aircraft cannot be released until the tool is recovered drops the second half of that either-or condition. The passage says most tools turn up within the hour but never says the sign-out record is why, and the hold applies only to the aircraft the borrower last worked on, not every aircraft in the squadron.

Correct answer: The review does not show whether the course itself produced the lower mishap rate

Because the course takers were mostly experienced senior drivers and the review did not compare drivers of similar experience, the review does not show whether the course itself produced the lower mishap rate. Claiming the course produced it treats a correlation as a cause, and claiming the drivers' experience produced it makes the same leap in the other direction, since experience was never tested either. The safety office only recommended making the course mandatory; no decision is reported.

Correct answer: Water in a single aircraft's sample does not on its own lead to the truck's quarantine

Quarantine requires contamination in two or more aircraft fueled from the same truck, so water in a single aircraft's sample does not on its own lead to the truck's quarantine. The aircraft is not downed immediately either; sampling continues and the down status follows only after three failed attempts. One contaminated sample does not show the truck is the source, and the sampling described happens before the first flight of the day, not before every flight.

Correct answer: The shorter syllabus did not raise first-year error rates in the air wing that tested it

Error rates that were no higher than under the standard syllabus mean the shorter syllabus did not raise first-year error rates in the air wing that tested it. Saying it lowered them reads 'no higher' as 'lower', which the passage does not claim. The result comes from one air wing, so a three-week gain in every air wing is a scope shift, and the report only cautions that supervisors were unusually experienced; it does not say they caused the faster qualification.

Correct answer: No, since sustained winds must go above 35 knots

The passage defines a high-wind event as sustained winds above 35 knots, and a sustained 35 knots is not above 35, so no additional walkdown is required. The gust option is the most tempting, but the definition counts only sustained winds, not gusts. The 40-knot option reaches the right answer with a threshold the passage never states.

Correct answer: Chloride deposits that salt spray leaves on bare metal

The passage states that the reaction begins when salt spray leaves chloride deposits on exposed metal, so chloride deposits that salt spray leaves on bare metal is correct. Hangar-bay heat and humidity is the most tempting choice, but the instruction says those conditions only speed up a reaction they do not start. Paint chips merely expose metal, and the 14-day rinse is a preventive rule, not the cause.

Correct answer: A single annual threshold shift does not by itself change duty status

The passage says the program does not change anyone's duty status on the basis of a single result, so a single annual threshold shift does not by itself change duty status is supported. The retest option is the most tempting, but the passage says most shifts seen on the annual test are temporary, not those that show up on the retest. Annual results are compared with the baseline, not the prior year, and a retest follows only a significant shift.

Correct answer: A markedly longer distance from the pivot

A seesaw balances when weight multiplied by distance matches on both sides, so the lighter child needs a markedly longer distance from the pivot to build the same moment as the heavier one. A slightly shorter stretch from the pivot shrinks the lighter child's moment and tips the board even further. A wholly negligible offset from the pivot leaves almost no moment arm, so the lighter child contributes almost nothing. A totally arbitrary spread from the pivot cannot balance the board, because only one separation satisfies the moment equation.

Correct answer: Precisely dividing the effort and the load

A first-class lever carries its pivot precisely dividing the effort and the load, so that one arm falls on either side of it, as in a seesaw or a pair of scissors. Resting underneath the effort and the load would leave the two arms no separation along the bar, so pressing down could raise nothing. Overhanging beyond the effort and the load puts the pivot off the bar altogether, which matches no lever class. Standing alongside the effort and the load shrinks the load arm to nothing, so the bar would simply lift as one rigid piece.

Correct answer: A wheel and axle unit

Turning a doorknob rotates a large outer knob that drives a much narrower inner spindle, and that pairing of a broad turning grip with a slim shaft is a wheel and axle unit. A rope and pulley rig would need a flexible line running in a grooved sheave to redirect a pull, and the knob has no line. A beam and lever pair would need a fulcrum with effort and load set apart along a rigid bar, which the knob does not provide. A slope and wedge set works by driving a sloping face into something, and nothing inside a doorknob slopes.

Correct answer: At a plainly quicker rate

The smaller driven gear carries fewer teeth, so it must complete several revolutions for each revolution of the larger driver, and it therefore turns at a plainly quicker rate. At a markedly slower rate describes the opposite pairing, in which the driven gear is the bigger of the two. At a fully unchanged rate would require both gears to carry the same tooth count. At a wildly unsteady rate is impossible, because meshed teeth lock the two shafts into one fixed ratio.

Correct answer: 2

The mechanical advantage of a pulley block is set by how many lengths of rope actually carry the load, so a system with two supporting segments gives about 2. A value of 3 would require a third supporting length threaded through the blocks. A value of 5 would require five such lengths, and a value of 6 would require six, neither of which matches the system described.

Correct answer: Diminish the force applied along the slope

A longer ramp reaching the same height has a gentler gradient, so it will diminish the force applied along the slope while lengthening the distance traveled. Enlarge the effort exerted along the slope reverses the relationship, since a shallower incline demands less push rather than more. Steady the tension endured along the slope ignores the gradient change entirely, and a ramp's whole advantage comes from that gradient. Multiply the weight hauled along the slope confuses force with weight; the load weighs the same however long the ramp is.

Correct answer: Bright copper wire

Copper is a metal whose loosely held outer electrons drift freely through the lattice, so bright copper wire carries current far better than the other choices. Thick rubber sheet is a standard insulator, used precisely because it blocks current. Polished glass rod is also an insulator, and polishing alters only its surface, never its resistance. Seasoned oak plank conducts poorly as well, and seasoning drives out the trace moisture that might otherwise let a little current pass.

Correct answer: Climbs sharply at that point

By the continuity principle the same volume of fluid must pass every section each second, so where the pipe narrows the speed climbs sharply at that point. Eases off at that tight spot treats the constriction like a traffic jam, but the fluid must move faster to keep the flow rate up. Holds steady as flow narrows confuses a constant flow rate with a constant speed. Dips sharply as flow narrows describes what happens to pressure, not speed, under Bernoulli's principle.

Correct answer: A sliding inclined plane

A wedge is a sliding inclined plane: rather than an object being pushed up a fixed slope, the slope itself is driven forward and forces material apart. A revolving spiral screw does its work by turning in place so that a thread draws material along, rather than by being driven bodily forward. A rolling grooved pulley redirects a line over a wheel and presents no sloping face at all. A swinging pivoted lever turns about a fulcrum, and a wedge has no fulcrum.

Correct answer: Practically half the earlier pull

Doubling the number of rope segments that support the load doubles the mechanical advantage, so the effort drops to practically half the earlier pull. Precisely double the earlier pull inverts the relationship, since adding supporting segments eases a lift rather than burdening it. Nearly quadruple the earlier pull compounds that same error. Exactly matching the earlier pull would mean the extra segments carry none of the weight, which is not how a block and tackle shares a load.

Correct answer: Roughening the mating faces

Friction depends on how strongly the microscopic high points of two surfaces catch on each other, so roughening the mating faces raises it. Enlarging the contact areas does not help, because for the same pressing force friction is largely independent of apparent area. Increasing the sliding rate leaves kinetic friction roughly unchanged. Starting the object sliding actually lowers resistance, since sliding friction is smaller than the static friction that held it in place.

Correct answer: Its weight equals the water pushed aside

A body floats when the water it shoves out of the way weighs as much as the body itself, so its weight equals the water pushed aside. Its mass undercuts the chilly salt water is false of a steel ship, whose plating is many times denser than seawater. Its cavities hold the trapped rain water describes a swamped object, which is what sinks a hull rather than what keeps it up. Its ascent shows the water lacks density is impossible, since water has a definite density and that density is precisely what generates the upward push.

Correct answer: A rotating or twisting force

Torque is a rotating or twisting force, the action that makes a body turn about an axis, and it grows with both the force applied and its distance from that axis. A settled or pressing weight acts straight downward and carries no rotational sense of its own. A straight or shoving thrust drives along a line and produces no rotation unless it is offset from an axis. A gentle or revolving motion describes how fast something already spins, which is angular speed rather than the agent that changes it.

Correct answer: Retaining the shared heading

A chain wraps the same way around both sprockets, so the driven wheel ends up retaining the shared heading of the driver, exactly as a bicycle chainwheel and rear sprocket turn together. Blocking the complete motion would require the chain to bind, which is a fault rather than normal running. Repeating the identical rate holds only when the two sprockets carry the same number of teeth. Reversing the input rotation would require the two wheels to press tooth against tooth, whereas a chain pulls both sprockets from the same side of the loop.

Correct answer: The uppermost perch

Gravitational potential energy grows with height above a reference level, so the rock at the uppermost perch holds more than the identical rock lower down. The lowermost basin is the bottom of the hill, where height and stored energy are least. The fastest descent is where the rock has the most kinetic energy, not potential energy, because the height has already been spent. The rolling descent is partway down, so it has already lost some of the height the top position holds.

Correct answer: The steady inclined plane

A screw is the steady inclined plane wound helically around a shaft, so that turning it converts rotation into slow linear travel and multiplies force. The grooved cable pulleys redirect a line over a wheel and involve no slope whatever. The pivoted wooden levers turn about a fulcrum, which a thread does not have. The broader wheeled axles trade turning distance for torque about a single shaft, but nothing in that pairing rises gradually the way a thread does.

Correct answer: Grow markedly stronger

Heating a gas makes its molecules move faster, so in a rigid sealed vessel they strike the walls harder and more often and the pressure will grow markedly stronger. Stay at the same level would hold only if the temperature were unchanged. Fall as volume expands assumes the gas can spread out, which a rigid container prevents. Rise then settle back ignores that the higher temperature persists, so the higher pressure persists with it.

Correct answer: Expand at unequal speeds

A bimetallic strip curls because its two bonded metals expand at unequal speeds for the same rise in temperature, so the faster-growing metal is forced to the outside of the curve. Melt at identical points is irrelevant, since the strip works far below either melting point. Conduct at feeble levels is false of metals, which conduct well, and poor conduction would not bend anything. Insulate at equal grades fails for the same reason: two identical behaviors could never produce the difference that makes the strip bend.

Correct answer: Pushing it up a lengthy slope

A long ramp spreads the same rise over a far greater distance, so pushing it up a lengthy slope needs the smallest force of the four, even though the box travels farther. Easing it up a steeper ascent shortens the journey but raises the required force in the same proportion. Hauling it up a sheer surface means lifting against the full weight with no mechanical advantage whatever. Throwing it up a sudden curve demands the largest force of all, delivered in a very short burst.

Correct answer: Pressure is passed evenly throughout the fluid

A pressure change in a confined liquid reaches every part of it undiminished, so pressure is passed evenly throughout the fluid and the wider face, having more area, feels a proportionally larger force. Friction is removed wholly around the pipework is false, since real systems lose a little to friction and would multiply force even without that loss. Liquid is squashed easily inside the cylinders is the reverse of the truth: hydraulics work precisely because liquid barely compresses. Weight is lessened greatly behind the cylinder confuses the moving part's own weight with the force the fluid delivers to it.

Correct answer: Accelerating because its heading turns

Velocity carries both size and direction, so a body running round a circle at a steady rate is accelerating because its heading turns from instant to instant, and that acceleration points toward the center. Untroubled because its motion persists mistakes constant speed for constant velocity. Balanced because its forces counteract is wrong, since a net inward force is exactly what bends a straight path into a circle. Decelerating because its speed shrinks contradicts the stem, which fixes the speed as constant.

Correct answer: The regular second lever class

In the regular second lever class the load sits between the fulcrum and the effort, so the effort arm is necessarily longer than the load arm and the mechanical advantage exceeds one; a wheelbarrow is the everyday example. The centered pivot lever class can give an advantage above or below one, depending on how far the pivot sits from each end of the bar. The third lever class entirely fails the test, since it puts the effort between fulcrum and load and its advantage is always below one. The overall lever class family cannot be the answer, because the three classes behave differently from one another.

Correct answer: Steady wall conduction

Energy moving from one body to another where they physically touch is conduction, so steady wall conduction is the process being named. Rapid fluid convection carries energy by the bulk movement of a liquid or gas, not by contact between solids. Thin rubber insulation names a material choice that slows the flow rather than a mode of transfer. Nearby flame radiation crosses empty space as electromagnetic waves and needs no contact whatever.

Correct answer: Store rotational energy and steady motion

A flywheel exists to store rotational energy and steady motion: its inertia soaks up energy during a power stroke and gives it back between strokes, so the shaft turns evenly. Raise unwanted friction and absorb effort describes a brake, whereas a flywheel is built to lose as little as it can. Generate electric current and drive lamps needs windings and a magnetic field, which a plain spinning mass does not have. Chill overheated cylinders and vent steam is the work of a cooling system rather than of a flywheel.

Correct answer: Firmer and tougher under load

Two identical springs side by side each carry a share of the weight, so the pair deflects only half as far as one spring would and the combination is firmer and tougher under load. Slacker and softer under load describes springs joined end to end in series, not side by side. Flimsier and unfit under load is wrong because splitting a weight between two springs raises the capacity rather than lowering it. Unchanged and flat under load ignores the second spring altogether, when in fact its stiffness adds directly to the first.

Correct answer: Pressure from the weight of the liquid

Water levels out in linked vessels because of pressure from the weight of the liquid standing above each point, and flow continues until those pressures match at every depth. Magnetism from the metals of the walls plays no part, since water levels out in glass and plastic containers just the same. Voltage from the charge of the beakers is equally irrelevant to a still column of water. Tension from the surfaces of the water shapes droplets and menisci on a small scale but is far too weak to raise or lower a whole column.

Correct answer: 4

The driver has 40 teeth and the driven gear has 10, so the ratio is four to one and the small gear makes 4 turns for each turn of the large gear. A value of 1 assumes meshed gears always turn at the same rate. A value of ¼ inverts the ratio, which is how far the large gear turns per turn of the small one. A value of 2 halves the true ratio of teeth.

Correct answer: A rocket forcing gas downward and climbing high

Newton's third law pairs equal and opposite forces acting on two different bodies, and a rocket forcing gas downward and climbing high is precisely that pair: the engine pushes the exhaust one way and the exhaust pushes the rocket the other. A puck gliding straight ahead and holding speed illustrates the first law, since a body with no net force on it keeps its velocity. A cart rolling gently onward and halting nearby illustrates the second law, with a retarding force producing an acceleration. A ball spinning ever slower and shedding motion is the same second-law case, driven by friction.

Correct answer: A larger applied push

Force equals mass times acceleration, so for the same acceleration a heavier object needs a larger applied push. An equal steady force would give the heavier object less acceleration; equal acceleration for all masses holds only in free fall. A longer steady force changes how long the push lasts, not the acceleration it produces at each moment. A higher steady speed confuses speed with acceleration, and a steady speed means no acceleration at all.

Correct answer: The local air pressure

A barometer balances the column of atmosphere standing above it, so what it reports is the local air pressure, and a falling reading is the classic sign of worsening weather. The outdoor air warmth is the business of a thermometer. The seasonal air vapor is measured by a hygrometer. The steady air current is measured by an anemometer, which counts the turns of a set of cups rather than weighing a column of air.

Correct answer: The mechanical advantage

A block and tackle multiplies the force you apply, so what is bought at the price of hauling extra rope is the mechanical advantage. The load's lifting speed falls rather than rises, because the load moves less than your hand does. The load's lifting power is never increased, since power in can at best equal power out. The total work performed is not gained either; friction means slightly more work goes in than comes out.

Correct answer: It packs force inside a slimmer strip

Pressure is force divided by the area it acts on, so a sharpened knife works because it packs force inside a slimmer strip of material, raising the pressure enough to part the fibers. It sheds weight beneath a worn handle is beside the point, since cutting depends on the edge and not on how much the tool weighs. It carries cold along a chilled blade has no bearing either; a warm sharp edge cuts just as well as a cold one. It drives drag toward a flawless zero overstates the case, because friction is never removed entirely and sharpening does not set out to remove it.

Correct answer: The plain counterclockwise spin

Directly meshed gears must move in opposite senses, because the teeth of one push sideways on the teeth of its neighbor, so a clockwise driver produces the plain counterclockwise spin in the gear beside it. The repeated clockwise rotation would need some intermediate element carrying the drive between the two wheels, which a direct mesh does not have. The completely motionless shaft would mean the teeth had jammed rather than meshed properly. The unpredictable double motion is impossible, since meshed teeth fix the sense of rotation as firmly as they fix the speed ratio.

Correct answer: Outward, away from the middle

Rotation throws objects outward, away from the middle of the circular path, which is what the correct choice states. Inward, drawn from the border names the centripetal pull that holds an object on the circle instead of the apparent outward push. Static, halted from the whirl is wrong because a spinning system keeps its contents moving. Upward, clear from the ground names a vertical lift that rotation does not supply.

Correct answer: A curved arch

The support that carries compression best is a curved arch, which channels the load down its curve into the abutments as pure compression. A woven cable carries tension only and collapses the moment it is pushed rather than pulled. A flat girder works mainly in bending and sags long before an arch of the same material would. A slotted pin is a pivot for transferring motion, not a member sized to carry a compressive load.

Correct answer: Ten pounds

Holding the weight takes ten pounds of force. A single fixed pulley changes only the direction of the pull, never its size, so the effort equals the load. Five pounds would be correct for a movable pulley, where two rope sections share the load, but this pulley is fixed. Twelve pounds assumes the pulley itself adds resistance, and the problem excludes friction. Thirty pounds treats the pulley as multiplying the required effort, which no fixed pulley does.

Correct answer: Atmospheric pressure drops

Water boils once its vapor pressure matches the pressure pressing down on it, so the reason is that atmospheric pressure drops as altitude rises and the boiling point falls with it. Circulating liquid freezes is wrong because the water's own temperature is not what altitude changes. Available oxygen increases fails twice: oxygen thins out with height and takes no part in boiling. Nearby gravity strengthens reverses reality, and gravity does not set a boiling point.

Correct answer: Convert rotation into straight travel

A cam exists to convert rotation into straight travel, driving a follower back and forth as the shaft turns. Convert pressure into visible numbers describes a gauge, which reads a value rather than moving a follower. Convert friction into cooler surfaces reverses what rubbing does, since friction raises temperature. Convert current into chemical storage describes a battery cell and has nothing to do with a shaped rotating profile.

Correct answer: Heavier contents and stronger friction

The loaded box resists because of heavier contents and stronger friction: the frictional force grows in proportion to how hard the surfaces are pressed together. Thinner materials and lighter friction describes the empty box, which is the easier one to push. Smoother surfaces and reduced friction would make the box slide more freely, not less. Narrower footprint and slight friction is wrong twice over, because contact area is identical for the two boxes and would not change the friction anyway.

Correct answer: Load lifted divided by effort applied

Mechanical advantage is load lifted divided by effort applied, the factor by which a machine multiplies the force a user supplies. Force exerted divided by weight moved inverts that ratio and would report a number below one for every helpful machine. Output motion divided by input motion is the velocity ratio, a separate quantity that compares distances rather than forces. Useful energy divided by time elapsed defines power, which says nothing about force multiplication.

Correct answer: Their inertia

Passengers lurch forward because of their inertia, the tendency of a body to keep moving until a force changes that motion; the car stops but their bodies do not. Their g-force is a measure of the deceleration felt, not the cause of the lurch. Their impetus is the outdated medieval idea of a stored push, which modern physics replaced with inertia. Their recoil describes a reaction to a force pushing back, and nothing pushes the passengers forward.

Correct answer: Increases the applied torque

A longer handle increases the applied torque, because torque equals the force times its distance from the turning axis. Increases the output of work is wrong since no simple tool gives out more work than is put in. Reduces the resisting torque is wrong because the bolt's resistance is fixed by its threads and tightness, not by the wrench. Reduces resisting friction fails for the same reason: handle length never touches the friction in the threads.

Correct answer: In the identical direction

Each mesh reverses the sense of rotation, so two meshes restore it and the third gear runs in the identical direction as the first. In the backward revolution describes the middle gear, which is the one directly reversed. In the accelerated cadence confuses direction with speed, and an idler between two gears alters neither. In the stalled arrangement is wrong because meshed gears in a working train all turn.

Correct answer: Expands and raises pressure

Steam does work because it expands and raises pressure, occupying far more volume than the water it came from and pushing the piston along its stroke. Holds heat and moves faster describes the energy it carries but not the push that does the work. Holds heat and flows freely names properties that do nothing without pressure behind them. Weighs less and climbs fast describes buoyancy, which plays no part in driving a piston.

Correct answer: Suspended mass

The period of a simple pendulum is set by length and gravity alone, so the quantity that makes no difference is the suspended mass. Support length changes the period directly, with a longer support swinging more slowly. Gravity effect changes it too, which is why the same pendulum keeps different time on the moon. Both variables would mean length and gravity are equally irrelevant, yet both of them appear in the period formula.

Correct answer: Four hundred joules

Work equals force multiplied by the distance moved in the direction of that force, so 50 newtons over 8 meters gives four hundred joules. Exactly 6.25 joules divides the force by the distance instead of multiplying. Nearly 3,920 joules treats the 50 newtons as a mass and multiplies by gravity as well, even though the figure is already a force. Forty-two joules subtracts the distance from the force.

Correct answer: Zero joules of work

The answer is zero joules of work. Work equals force multiplied by the distance the object moves, so when the displacement is nothing the product is nothing, however large the applied force may be. Thirty joules of work simply reports the force as though newtons were joules. Sixty joules of work and ninety joules of work multiply that force by an imagined displacement, but the box never moved, so no mechanical work was performed on it.

Correct answer: Three to one

The gear ratio is three to one. The formula divides the teeth on the driven gear by the teeth on the driver gear, and 36 divided by 12 is 3, so the driver turns three times for each turn of the driven gear. One to three inverts the formula by putting the driver on top. Three to two compares the 36 driven teeth with the 24-tooth difference, and two to three compares that difference with the 36.

Correct answer: One hundred rpm

The driven gear turns at one hundred rpm. In a reduction the output speed is the input speed divided by the ratio, so three hundred divided by three is one hundred, and the larger driven gear turns more slowly while delivering more torque. Three hundred rpm leaves the input speed unchanged, nine hundred rpm multiplies by the ratio instead of dividing, and nine thousand rpm compounds that error with a decimal slip.

Correct answer: Increased torque

The gain is increased torque: a gear reduction trades rotational speed for turning effort, so the slower large gear delivers proportionally more twisting force. Increased energy is impossible, because gears cannot create energy. More shaft power is wrong, since power out at best equals power in. Lower shaft drag does not follow from changing tooth counts; friction is set by the mesh and bearings.

Correct answer: A gain of four times

The lever gives a gain of four times. Mechanical advantage is the output load force divided by the input effort force, and six hundred divided by one hundred and fifty is four, so the lever multiplies what the person applies four times over. A gain of one fourth inverts that division. A gain of seven fifty adds the two forces together instead of dividing them, and a gain of six hundred simply repeats the load force as though it were the ratio.

Correct answer: How much the machine multiplies the force

Mechanical advantage is the ratio of output force to input force, so it describes how much the machine multiplies the force. How much the machine multiplies the work is wrong because no simple machine puts out more work than it receives. How much the machine multiplies the power is wrong for the same reason, since power is work per unit time. How much input work the machine gives out describes efficiency, a separate measure.

Correct answer: Halved effort for twice the load

A movable pulley gives roughly a mechanical advantage of two, which is halved effort for twice the load. Two rope segments share the weight, so the effort needed falls to about half of it. Unaided effort for once the load describes the single fixed pulley the question compares it with, which only redirects the force. Third effort for triple the load overstates a single movable sheave, and doubled effort for half the load would be worse than lifting by hand.

Correct answer: Fixed ones steer force while movable ones lessen it

The main difference is that fixed ones steer force while movable ones lessen it: a fixed pulley is attached to a stationary support and changes only the direction of the pull, giving a mechanical advantage of about one, whereas a movable pulley travels with the load and roughly halves the effort. Fixed ones shrink force while movable ones point it reverses the two. Fixed ones divide force while movable ones split it wrongly credits both with reducing effort, and fixed ones double force while movable ones carry it credits the fixed pulley with a gain it does not give.

Correct answer: Sixty pounds of effort

The answer is sixty pounds of effort. Ignoring friction, the mechanical advantage equals the number of rope segments supporting the load, four here, so the pull is 240 divided by 4. Thirty pounds of force doubles the count to eight segments. Forty pounds of force assumes six supporting segments. Forty-eight pound pull divides by five, wrongly counting the free end the operator pulls on as a supporting segment.

Correct answer: Five feet away

The lighter child must sit five feet away. A lever balances when weight multiplied by distance matches on both sides, and sixty pounds at four feet gives two hundred and forty, so the forty-eight pound child needs two hundred and forty divided by forty-eight. Four feet off simply copies the heavier child's distance, three feet away comes from working the ratio upside down, and eight feet away overshoots the balance point, since the lighter child sits farther out but not that far.

Correct answer: Lever fulcrum

The fixed point the plank turns on is the lever fulcrum, and both the effort and load distances are measured from it. The load distance is the length from that fulcrum to the load, a measurement rather than the point. An effort moment is the effort multiplied by its distance, a turning effect. A lever moment likewise names a force times a distance, not the place the plank rests on.

Correct answer: A heavy wheelbarrow

A heavy wheelbarrow is the class 2 example. Its load sits between the wheel, which acts as the fulcrum, and the handles where the effort is applied, so it always yields a mechanical advantage above one. A playground seesaw is a class 1 lever, with the central pivot as the fulcrum sitting between the effort at one end and the load at the other. A pointed pitchfork and a galvanized shovel are class 3 levers, because the effort from the lower hand is applied between the fulcrum hand and the load at the far end.

Correct answer: Forty-five newton-meters

The torque produced is forty-five newton-meters. Torque is the applied force multiplied by the perpendicular lever arm, so ninety newtons acting at half a meter gives forty-five. Ninety newton-meters reports the force alone and ignores the handle length. One eighty newton-meters divides by the half-meter instead of multiplying by it, and four fifty newton-meters treats the handle as five meters long rather than half a meter.

Correct answer: The law of inertia

The resting book illustrates the law of inertia, which is the first of Newton's three laws of motion: a body stays at rest, or keeps moving at a steady speed, until an unbalanced outside force acts on it. The law of gravity describes the pull between two masses rather than a body's resistance to any change in its state of motion, so it does not name what the book demonstrates. The law of cooling is also Newton's, but it sets the rate at which a warm object sheds heat and says nothing about rest or movement. The law of entropy belongs to thermodynamics and governs how disorder grows, which is a different subject altogether.

Correct answer: The stroke in which the burning gases drive the piston down

The crankshaft is turned by the stroke in which the burning gases drive the piston down. Ignition makes the compressed charge expand very rapidly, and that expansion is the only part of the cycle that delivers energy to the crankshaft. The stroke that lets the fresh fuel charge fill the chamber only loads the cylinder and takes energy from the crankshaft rather than adding any. The stroke in which the rising piston squeezes the fuel mix likewise absorbs energy to raise pressure before ignition. The stroke that pushes the burned gases away clears the cylinder afterward and produces no useful work.

Correct answer: 10 to 1

The mechanical advantage is 10 to 1. Pascal's principle transmits the same pressure through the confined fluid, so the force ratio equals the output area divided by the input area, and 20 divided by 2 is 10. A ratio of 40 to 1 comes from multiplying the two areas instead of dividing them. A ratio of 22 to 1 comes from adding the areas, and a ratio of 18 to 1 comes from subtracting them; neither operation yields a force ratio.

Correct answer: Pulley, lever, and inclined plane

The pulley, lever, and inclined plane are three of the six classic simple machines, along with the wheel and axle, the wedge, and the screw. Each changes the size or the direction of an applied force with no internal power source. An engine, a spring, and a battery cable are a compound assembly, an energy store, and a conductor, not simple machines. A piston, a magnet, and a flywheel gear are parts of larger mechanisms rather than machines in their own right. A rotor, a gasket, and a hydraulic pump are likewise components of complex systems.

Correct answer: Slide the bucket toward the far support

The worker should slide the bucket toward the far support. Each support carries a share of the load in proportion to the load's distance from the other support, so lengthening the bucket's arm about the far support shortens it about the near one and the near support bears less. Center the bucket atop the near support does the opposite and throws almost the whole weight onto it. Anchor the bucket nearer the plank edge leaves the weight at the same end the near support already carries. And double the bucket load beside the plank adds weight instead of moving it.

Correct answer: Raises the torque while cutting the speed

Low gear raises the torque while cutting the speed. A low gear is a large reduction, so the wheels turn more slowly than the engine but with multiplied turning force, which is exactly what a climb demands. Lifts the torque while doubling the tempo cannot happen, because a gear train trades one for the other rather than raising both. Reduces the torque while raising the pace describes high gear, the wrong choice for a hill. And blunts the torque while trimming the rate would leave the vehicle worse off in every respect.

Correct answer: Twenty-five pounds

The ideal effort is twenty-five pounds. A ramp's ideal mechanical advantage is its length divided by its rise, twelve over three, or four, and the hundred-pound load divided by four leaves twenty-five pounds. Seventy-five pounds subtracts that result from the load instead of reporting it. Four hundred pounds multiplies by the advantage instead of dividing by it. And thirty-three pounds divides by the three-foot rise alone, ignoring the length of the ramp that creates the advantage.

Correct answer: Speedier

Water in the narrow pipe is speedier: steady flow means the same volume passes every cross-section each second, so a smaller bore forces faster water. Constant confuses equal volume per second with equal speed. Steadier is wrong because both pipes carry equally steady flow; only speed differs. Slower reverses the continuity rule and would leave water piling up at the constriction.

Correct answer: The gyroscopic effect

The behavior is called the gyroscopic effect. A rapidly spinning wheel carries angular momentum that resists any change in the direction of its spin axis, the same rigidity a spinning top and a gyrocompass both rely on. The Bernoulli theorem concerns pressure in a moving fluid rather than a spinning solid. The centrifugal force is the outward tendency felt in a turn and does nothing to hold an axis steady. And the thermal expansion simply describes how materials grow when heated.

Correct answer: Extra torque on the nut

A perpendicular push produces extra torque on the nut. Torque depends on the component of force acting at right angles to the handle, so a square push uses the whole lever arm. Lower torque on the nut is backwards, because the push aimed along the handle is the weaker of the two. Equal torque on the nut ignores the angle altogether. And faint torque on the nut describes the push driven straight at the bolt, which has almost no lever arm to work with.

Correct answer: Fit a broader wheel onto a thinner axle

You should fit a broader wheel onto a thinner axle. Mechanical advantage here is the wheel's radius divided by the axle's radius, so widening the wheel and slimming the axle multiplies whatever effort you apply. Fit a small wheel onto a thickened axle drives that ratio below one and makes the lift harder. Fit a weighted wheel onto a smooth axle adds mass without touching the ratio. And fit a wooden wheel onto a polished axle only trims friction, leaving the advantage exactly where it was.

Correct answer: Box A equals box B exactly

At the bottom, box A equals box B exactly. On a frictionless ramp the speed gained depends on the vertical drop alone and not on mass, so the two boxes accelerate alike and arrive together. Box A doubles box B easily assumes that weight adds speed, which it does not. Box B outpaces box A twice assumes that lightness adds speed, which it also does not. And box A beats box B fourfold compounds the same mistake.

Correct answer: Slower than the drive pulley

The large fan pulley turns slower than the motor pulley. A belt drags the rims of both wheels along at one linear speed, so the bigger circumference swallows more belt per turn and completes fewer turns each minute. Faster than a smaller pulley reverses that relationship. Level with the driver pulley would hold only if the two wheels were the same size. And opposite to the motor pulley is wrong because an ordinary open belt drives both wheels the same way round.

Correct answer: The balls arrive dead level

Dropped in a vacuum, the balls arrive dead level. With no air to resist them, gravity accelerates every object at the same rate whatever its mass, so the solid and the hollow sphere fall side by side. The solid ball lands sooner assumes that heavier means quicker, which holds only where air resistance is in play. The hollow ball lands early makes the opposite mistake. And the balls hang frozen aloft confuses the absence of air with the absence of gravity.

Correct answer: One half of the load

The effort needed is one half of the load, about a hundred pounds. Two rope segments support the movable pulley, so they share the weight between them and the mechanical advantage is two. One third of the load would follow from counting three supporting segments instead of two. One fourth of the load counts four segments. And one eighth of the load counts eight, an advantage no single movable pulley can supply.

Correct answer: Freezes at a colder point