Lesson Test: Translating ASVAB Word Problems

Answer: C

Correct answer: 90 crates. The same amount, 18 crates, is repeated for 5 days, so the setup is

crates.

• A: Adding 18 and 5 combines a rate with a count of days instead of repeating the daily amount.
• B: Subtracting 5 from 18 has no meaning in this story; nothing is being removed.
• C (correct): Five days of 18 crates each is equal groups, so multiply: 18 times 5 = 90.
• D: Dividing 18 by 5 splits the daily amount instead of building a total from repeated groups.

Answer: C

Correct answer: 172 miles. Name the unknown as the remaining distance x. Then

• A: Adding 300 and 128 treats the distance already covered as extra distance beyond the whole trip.
• B: This is the length of the whole trip, not the part that is left.
• C (correct): The remaining distance is the missing part of a known total: 300 - 128 = 172.
• D: This comes from a borrowing slip in 300 - 128; checking 182 + 128 gives 310, not 300.

Answer: A

Correct answer: 32. \"Nine less than a number\" means start with the number and take 9 away:

Add 9 to both sides to get

Check:

• A (correct): Writing the sentence as x - 9 = 23 and adding 9 to both sides gives x = 32.
• B: This comes from reversing the order and writing 9 - x = 23.
• C: Subtracting 9 from 23 runs the story backward; 14 - 9 is 5, not 23.
• D: Multiplying 9 by 23 uses an operation the sentence never describes.

Answer: D

Correct answer: 27 drivers. Comparing two amounts calls for subtraction:

more drivers at Site A. Check:

• A: This is a borrowing slip in 86 - 59; adding 37 + 59 gives 96, not 86.
• B: This is the Site B count from the story, not the difference between the sites.
• C: Adding the two counts gives a combined total, but the question asks for a comparison.
• D (correct): A "how many more" comparison asks for the difference: 86 - 59 = 27.

Answer: D

Correct answer:

\"The sum of a number and 9\" is $x+9$. \"Twice\" that sum doubles the whole group, so use parentheses:

• A: This doubles the 9 instead of doubling the whole sum of the number and 9.
• B: This doubles only the number and then adds 9, but the words say to form the sum first.
• C: "Twice" means multiply by 2, not add 2.
• D (correct): The sum of the number and 9 is formed first inside parentheses, and then that whole sum is doubled.

Answer: A

Correct answer: $40. Cost:

Change:

• A (correct): The purchase costs 3 x 14 + 2 x 9 = 60 dollars, and 100 - 60 leaves 40 dollars in change.
• B: This subtracts the shirts (42 dollars) but forgets to include the cost of the caps.
• C: This is the cost of the purchase, not the change the question asks for.
• D: This subtracts only one shirt and one cap (14 + 9 = 23) instead of the full quantities bought.

Answer: C

Correct answer: 132 miles. Convert the time first:

so the time is 2.75 hours. Distance = rate x time =

• A: This rounds the trip up to 3 hours, which adds 15 minutes of driving that never happened.
• B: This uses only the 2 full hours and ignores the extra 45 minutes.
• C (correct): Since 45 minutes is 0.75 hour, the time is 2.75 hours and 48 x 2.75 = 132 miles.
• D: This treats 2 hours 45 minutes as 2.45 hours, but minutes are sixtieths of an hour, not hundredths.

Answer: D

Correct answer: 91 soldiers. \"35 percent of 260\" means multiply after converting the percent:

soldiers.

• A: This is the 65 percent who did not qualify as experts, the other part of the group.
• B: This subtracts 35 from 260 as if the percent were a number of soldiers.
• C: This multiplies by 35 instead of 0.35, forgetting to change the percent to a decimal.
• D (correct): Change 35 percent to 0.35 and multiply: 0.35 x 260 = 91.

Answer: B

Correct answer: 21 quarts. Keep matching units in matching positions:

Each vehicle needs

• A: This multiplies 6 quarts by 14 vehicles, treating 6 quarts as the amount for a single vehicle.
• B (correct): The proportion 6/4 = x/14 keeps quarts on top on both sides, giving x = 21.
• C: This flips one ratio, putting vehicles over quarts on one side and quarts over vehicles on the other.
• D: This adds 10 quarts because the vehicle count rose by 10, but a rate scales by multiplying, not adding.

Answer: C

Correct answer: 528 rations. The truck's weight is extra information. Boxes left:

Rations left:

• A: This is the number of rations unloaded, not the number still on the truck.
• B: This is the starting load of 25 boxes; it forgets that 3 boxes were unloaded.
• C (correct): After unloading, 25 - 3 = 22 boxes remain, and 22 x 24 = 528 rations.
• D: This subtracts 3 rations instead of 3 boxes of 24 rations each.

Answer: B

Correct answer: 25 percent. Missed questions:

Percent = part / whole:

which is 25 percent.

• A: This uses the number of missed questions as if it were already a percent.
• B (correct): She missed 72 - 54 = 18 questions, and 18 / 72 = 0.25, or 25 percent.
• C: This is the percent she answered correctly (54 out of 72), not the percent she missed.
• D: This divides 18 by 54, comparing missed to correct instead of missed to the whole test.

Answer: A

Correct answer: $45.00. After a 20 percent increase, the new price is 120 percent of the original:

Divide:

Check: 20 percent of 45 is 9, and

• A (correct): The new price is 120 percent of the old price, so 1.20x = 54 and x = 45.
• B: This raises the new price by another 20 percent, moving in the wrong direction.
• C: This subtracts 20 dollars, treating the percent as a dollar amount.
• D: This subtracts 20 percent of the new price, but the 20 percent was figured on the old price.

Answer: A

Correct answer: 63 trailers. A 4:7 ratio splits the total into

equal parts. Each part is

vehicles, so there are

trailers (and 36 trucks, for 99 in all).

• A (correct): The ratio has 4 + 7 = 11 parts, each worth 99 / 11 = 9, so trailers are 7 x 9 = 63.
• B: This is the number of trucks (4 parts of 9), not the number of trailers.
• C: This divides 99 by 7 and multiplies by 4, treating 7 as the total number of parts.
• D: This is how many more trailers there are than trucks (3 parts), not the trailer count.

Answer: D

Correct answer: $736. Fencing follows the edge, so this is a perimeter question. Fenced length:

Cost:

• A: This multiplies the area, 1,050 square feet, by the price; fencing is a length, not an area.
• B: This fences the full perimeter of 134 feet, including the side along the building.
• C: This leaves out a 25-foot side instead of the 42-foot side along the wall.
• D (correct): The three sides measure 42 + 25 + 25 = 92 feet, and 92 x 8 = 736 dollars.

Answer: B

Correct answer: 4.5 hours. Time = amount / rate:

Convert to hours:

• A: This is the time in minutes; the question asks for hours.
• B (correct): The tank takes 4,860 / 18 = 270 minutes, and 270 / 60 = 4.5 hours.
• C: This divides 270 minutes by 100 instead of by 60 minutes per hour.
• D: This reads 4 hours 30 minutes as 4.3 hours, but 30 minutes is half an hour.

Answer: B

Correct answer: 12. Build four times the number first, then add 5:

Subtract 5 to get

then divide by 4:

Check:

• A: This comes from 4x - 5 = 53, which subtracts 5 instead of adding it.
• B (correct): Writing the sentence as 4x + 5 = 53 gives 4x = 48, so x = 12.
• C: This comes from 4(x + 5) = 53, which adds 5 before multiplying even though the words build four times the number first.
• D: This divides 53 by 4 and ignores the 5 that was added.

Answer: A

Correct answer: $9. First find the cost:

Then find the change:

• A (correct): The purchase costs 5 x $3 + 2 x $28 = $15 + $56 = $71, and $80 - $71 = $9.
• B: This is the cost of the purchase, an in-between number, not the change asked for.
• C: This counts only one roll of wire: $15 + $28 = $43, and $80 - $43 = $37.
• D: This adds one of each price ($3 + $28 = $31) instead of multiplying by the quantities.

Answer: A

Correct answer: 23 gallons. Find the rate first:

per gallon.

Then divide the new distance by the rate:

• A (correct): The van gets 378 / 14 = 27 miles per gallon, and 621 / 27 = 23 gallons.
• B: This is the mileage rate in miles per gallon, an in-between step rather than the fuel needed.
• C: This covers only the extra 243 miles beyond the first trip (243 / 27 = 9), not the whole 621-mile trip.
• D: This adds the first trip's 14 gallons to the 23 gallons the new trip needs.

Answer: C

Correct answer: 7.5 cups. Keep cups on top in both ratios:

Cross-multiply:

• A: This is 50 / 20, the scale factor, without multiplying it by the 3 cups in the recipe.
• B: This simply doubles the recipe, which makes 40 pancakes, not 50.
• C (correct): Setting 3/20 = x/50 gives x = 3 x 50 / 20 = 7.5 cups.
• D: This adds the 30 extra pancakes to the 3 cups, mixing pancakes with cups.

Answer: D

Correct answer: $680. A 25 percent discount leaves 75 percent of the original price, so

Divide:

Check: 25 percent of 680 is 170, and

• A: This adds 25 percent of the sale price to $510, but the discount was taken from the larger original price.
• B: This takes another 25 percent off the sale price, which moves in the wrong direction.
• C: This divides by 0.25, the discount, instead of by 0.75, the part of the price that remains.
• D (correct): After a 25 percent discount, 75 percent of the price remains, so 0.75x = 510 and x = $680.

Answer: B

Correct answer: 168 muffins. Equal groups call for multiplication:

muffins.

• A: This adds 24 and 7, but the story describes equal groups, which calls for multiplication.
• B (correct): Seven equal groups of 24 is 24 x 7 = 168.
• C: This subtracts 7 from 24, which does not match anything happening in the story.
• D: This is 24 x 6, one tray short of the 7 trays filled.

Answer: A

Correct answer: 3x - 6. Build "three times a number" first as $3x$. "6 fewer than" that amount means take 6 away from it, giving $3x-6$.

• A (correct): Start with three times the number, 3x, and take 6 away from it.
• B: This reverses the order; "6 fewer than" means 6 is subtracted from the other quantity.
• C: This subtracts 6 before multiplying, but the words build three times the number first.
• D: "Fewer than" means subtract, not add.

Answer: C

Correct answer: 28 nurses. Keep nurses on top in both ratios:

Since

each ratio part stands for 4 people, so nurses

• A: This is the total number of nurses and doctors, 28 + 8, not the number of nurses.
• B: This adds the difference of 5 between the ratio numbers to 8, but ratios scale by multiplying, not adding.
• C (correct): Since 8 = 2 x 4, each ratio part is 4 people, so there are 7 x 4 = 28 nurses.
• D: This multiplies 8 by 2, using the doctors' ratio number instead of the nurses'.

Answer: A

Correct answer: 5 gallons. Paint covers a surface, so find area. One side is

and both sides are

Gallons:

Since 4 gallons would fall short, the crew must buy 5 gallons.

• A (correct): Both sides cover 2 x 120 x 6 = 1,440 square feet; 1,440 / 350 is about 4.1, so 5 whole gallons are needed.
• B: This rounds 4.1 down, which leaves part of the fence unpainted.
• C: This paints only one side: 720 / 350 is about 2.1, rounded up to 3.
• D: This paints only one side and also rounds down.

Answer: B

Correct answer: 203 books. The unknown is the starting count. The story is start minus lent equals left:

Add 47 to both sides:

Check:

• A: This subtracts 47 from 156, running the story backward because of the word "left."
• B (correct): Start minus lent equals left, so x - 47 = 156 and x = 156 + 47 = 203.
• C: This is an addition slip; 156 + 47 is 203, not 193.
• D: This is the number left after lending, not the starting number.

Answer: C

Correct answer: $59.50. Convert the percent to a decimal: 30 percent is 0.30. The discount is

Sale price:

Equivalently,

• A: This is the amount of the discount, not the price after the discount.
• B: This subtracts 30 dollars instead of 30 percent of the price.
• C (correct): The discount is 0.30 x $85 = $25.50, and $85 - $25.50 = $59.50.
• D: This subtracts 0.30 dollars, treating 30 percent as 30 cents.

Answer: B

Correct answer: 432 pages. Pages per minute times minutes leaves pages:

pages.

• A: This adds the rate and the time instead of multiplying them.
• B (correct): A rate times time gives a total: 36 x 12 = 432 pages.
• C: This divides 36 by 12, which would split a total, not build one from a rate.
• D: This subtracts 12 from 36, which has no meaning in this story.

Answer: D

Correct answer: 108 bottles. "A dozen" means 12, and the trailer length is extra information. Nine equal boxes of 12 give

bottles.

• A: This adds 12 and 9 instead of multiplying for equal groups.
• B: This multiplies the 9 boxes by the trailer length, a number that has nothing to do with the bottles.
• C: This multiplies a dozen by the trailer length, which is an extra fact.
• D (correct): A dozen is 12, and 9 boxes of 12 is 9 x 12 = 108 bottles.

Answer: C

Correct answer: 3.75 hours. Minutes are sixtieths of an hour:

So 3 hours 45 minutes is

• A: This treats the minutes as hundredths of an hour, but minutes are sixtieths of an hour.
• B: This divides 60 by 45 instead of 45 by 60.
• C (correct): Since 45 minutes is 45/60 = 0.75 hour, the shift is 3.75 hours.
• D: This finds 225 total minutes but then divides by 100 instead of 60.

Answer: C

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

Multiply by 100 to get 80 percent.

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

Answer: D

Correct answer: 18 mph. Convert the time: 10 minutes is

so the time is

Speed is distance divided by time:

per hour.

• A: This treats 2 hours 10 minutes as 2.10 hours, reading minutes as a decimal.
• B: This ignores the 10 minutes and divides by 2 hours only.
• C: This multiplies distance by time instead of dividing distance by time.
• D (correct): 2 hours 10 minutes is 2 1/6 hours, and 39 / (13/6) = 18 miles per hour.

Answer: C

Correct answer: 18. The ratio 5:3 has

parts, so each part is

people.

Adults:

Teenagers:

Difference:

which is also $(5-3)\times 9$.

• A: This is the number of adults, an in-between value rather than the difference asked for.
• B: This is the number of teenagers, not how many more adults there are.
• C (correct): The ratio has 8 parts, so each part is 72 / 8 = 9 people; adults are 45, teenagers are 27, and 45 - 27 = 18.
• D: This subtracts the ratio numbers, 5 - 3, without scaling them to the actual group size.

Answer: C

Correct answer: 8 sections. Edging goes around the border, so find perimeter:

Sections:

Seven sections cover only 56 feet, so 8 sections are needed.

• A: This rounds 7.25 down, which leaves 2 feet of the border without edging.
• B: This uses the area, 198 square feet, but edging runs along the border, which is a perimeter.
• C (correct): The perimeter is 2(18 + 11) = 58 feet; 58 / 8 = 7.25, so 8 whole sections are needed.
• D: This uses only one length and one width, 29 feet, which is half the perimeter.

Answer: B

Correct answer: 196 miles. Convert minutes: 24 minutes is

and 36 minutes is

First leg:

Second leg:

Total:

• A: This reads the times as 2.24 and 1.36 hours, treating minutes as hundredths of an hour.
• B (correct): The legs are 2.4 hours and 1.6 hours, so the distance is 55 x 2.4 + 40 x 1.6 = 132 + 64 = 196 miles.
• C: This averages the two speeds to 47.5 mph over 4 hours, but the bus spent more time at the faster speed.
• D: This is only the first leg of the trip, an in-between total.

Answer: B

Correct answer: $372.60. Labor:

Tax on parts only:

Total:

• A: This charges the 8 percent tax on labor as well as parts.
• B (correct): Labor is $216, tax on parts is 0.08 x $145 = $11.60, and $216 + $145 + $11.60 = $372.60.
• C: This leaves out the sales tax and stops at the subtotal.
• D: This adds 8 dollars of tax instead of 8 percent of the parts cost.

Answer: D

Correct answer: 68 inches. Convert to one unit:

then add the extra 8 inches:

• A: This treats a foot as 10 inches instead of 12.
• B: This adds the 5 and the 8 without converting feet to inches.
• C: This converts the 5 feet but forgets to add the extra 8 inches.
• D (correct): Each foot is 12 inches, so 5 x 12 + 8 = 60 + 8 = 68 inches.

Answer: D

Correct answer: $120. Work backward from the end. Before lunch she had

After spending one-third on the jacket, two-thirds remained, so

Check: one-third of 120 is 40,

• A: This undoes the lunch but stops before undoing the jacket purchase.
• B: This undoes the steps in the wrong order, scaling $56 up first and adding $24 last.
• C: This treats the $80 as one-third of her money instead of the two-thirds left after the jacket.
• D (correct): Before lunch she had $56 + $24 = $80, which is two-thirds of her money, so she started with $80 / (2/3) = $120.

Answer: A

Correct answer: 48 pillows. The floor number does not connect to the question. Beds:

Pillows:

• A (correct): Beds: 6 x 4 = 24; pillows: 24 x 2 = 48.
• B: This is the number of beds, an in-between total, not the number of pillows.
• C: This also multiplies by 5, but the floor number is extra information.
• D: This adds 6, 4 and 2 instead of multiplying for equal groups.

Answer: C

Correct answer: $2,200. Round to friendly numbers:

The exact value,

confirms the estimate.

• A: This is ten times too small; 200 tickets at about $10 each is about $2,000.
• B: This is ten times too large, likely from a misplaced zero.
• C (correct): Rounding 198 to 200 gives 200 x $11 = $2,200, very close to the exact $2,178.
• D: This adds 198 and 11 instead of multiplying tickets by price.

Answer: B

Correct answer: 21. Translate in order: three times a number is $3x$, and subtracting 15 from it gives

Add 15:

Divide by 3:

• A: This comes from 3x + 15 = 48, which adds 15 instead of subtracting it.
• B (correct): The sentence is 3x - 15 = 48, so 3x = 63 and x = 21.
• C: This comes from 3(x - 15) = 48, which subtracts before multiplying.
• D: This divides 48 by 3 and ignores the 15 that was subtracted.

Answer: C

Correct answer: 80 tiles. Patio area:

Convert the tile side: 18 inches is 1.5 feet, so each tile covers

Tiles:

(Check by rows: 10 tiles along 15 feet and 8 along 12 feet give 80.)

• A: This divides the area by 1.5, the tile's side length, instead of by the tile's area.
• B: This divides 180 square feet by 18 without converting inches to feet or finding the tile's area.
• C (correct): Each tile is 1.5 ft by 1.5 ft = 2.25 square feet, and 180 / 2.25 = 80 tiles.
• D: This treats 18 inches as 1.8 feet, mixing up inches with tenths of a foot.

Answer: A

Correct answer: 2,400 words. Find the rate per minute:

words per minute.

Scale to an hour:

words per hour. Or divide by 0.75 hour:

• A (correct): Her rate is 1,800 / 45 = 40 words per minute, and 40 x 60 = 2,400 words per hour.
• B: This is her rate per minute, not per hour.
• C: This treats 45 minutes as 0.45 hour; 45 minutes is 0.75 hour.
• D: This multiplies the words by the minutes instead of dividing to find a rate.

Answer: B

Correct answer: 15.25 miles. The total is known, so the third day is a missing part:

Combine:

• A: This is the total for the first two days, an in-between number.
• B (correct): The first two days total 31.75 miles, and 47 - 31.75 = 15.25 miles.
• C: This adds all three numbers, but 47 is already the total.
• D: This subtracts only the first day's distance from the total.

Answer: D

Correct answer: 40 pieces. Convert to one unit: 3 inches is

so each piece is 6.25 feet.

Pieces:

• A: This treats 6 feet 3 inches as 6.3 feet instead of 6.25 feet.
• B: This ignores the 3 inches and divides by 6 feet.
• C: This adds 6 and 3 as if both were feet, dividing by 9.
• D (correct): 6 feet 3 inches is 6.25 feet, and 250 / 6.25 = 40 pieces.

Answer: A

Correct answer: 46 workers. Convert 15 percent to 0.15. The increase is

workers.

New size:

• A (correct): The increase is 0.15 x 40 = 6 workers, so the crew has 40 + 6 = 46.
• B: This is the number of workers added, not the new crew size.
• C: This adds 15 workers instead of 15 percent of 40.
• D: This decreases the crew by 15 percent, but the crew grew.

Answer: D

Correct answer: 26. Let the sister's age be s. Marcus is $2s-4$, and the sum is

So

Marcus:

Check:

• A: This is the sister's age, an in-between value rather than Marcus's age.
• B: This doubles the sister's age but forgets the "4 years less."
• C: This simply subtracts 4 from the sum of their ages.
• D (correct): With sister = s, Marcus = 2s - 4, so s + 2s - 4 = 41 gives s = 15 and Marcus = 26.

Answer: A

Correct answer: 180 square feet. Carpet covers a surface, so find area:

• A (correct): Carpet covers a surface, so use area: 12 x 15 = 180 square feet.
• B: This is the perimeter, 2(12 + 15) = 54 feet, which measures the border, not the surface.
• C: This adds the length and width instead of multiplying them.
• D: This takes half of the area, as if the floor were a triangle.

Answer: D

Correct answer: 80 parcels. Rate times time gives each total: A ships

and B ships

"How many more" asks for a difference:

parcels.

• A: This compares only the hourly rates, ignoring that the warehouses work different numbers of hours.
• B: This adds the two totals, but "how many more" asks for a difference.
• C: This multiplies the rate difference of 45 by 8 hours, as if both worked the same time.
• D (correct): A ships 140 x 6 = 840 and B ships 95 x 8 = 760, so A ships 840 - 760 = 80 more.

Answer: A

Correct answer: 3 gallons. Area:

which is 4 sections of 1,000 square feet.

Fertilizer:

Convert:

• A (correct): The lawn is 4,000 square feet, which needs 4 x 3 = 12 quarts, and 12 / 4 = 3 gallons.
• B: This is the amount in quarts; the units were never converted to gallons.
• C: This multiplies 12 quarts by 4 instead of dividing when changing to the larger unit.
• D: This converts 3 quarts for a single 1,000-square-foot section and ignores the lawn's size.

Answer: D

Correct answer: 67.5 miles. Keep inches on top in both ratios:

Cross-multiply:

Each inch stands for 7.5 miles, and

• A: This multiplies 9 by 15 as if 1 inch, not 2 inches, stood for 15 miles.
• B: This flips one ratio, putting miles on top in one fraction and inches on top in the other.
• C: This adds 9 and 15, but a map scale is a ratio that calls for multiplying.
• D (correct): Setting 2/15 = 9/x gives 2x = 135, so x = 67.5 miles.