This lesson test puts the Ratios and Proportions lesson under pressure with 15 original ASVAB-style questions. You will see part-to-part and part-to-whole setups, equivalent ratios, proportions solved by scaling or cross-multiplication, unit rates, ratio totals, map scales and mixture problems.
A training platoon has 14 sergeants and 35 privates. What is the ratio of privates to sergeants in simplest form?
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Answer: B
Correct answer: 5:2. Write the terms in the order named: privates to sergeants is 35:14.
The greatest common factor is 7, so the ratio simplifies to 5:2.
A: This compares privates with the whole platoon of 49, a part-to-whole ratio.
B (correct): 35:14 divided by the common factor 7 gives 5:2, with privates named first.
C: This compares sergeants with the whole platoon of 49.
D: This is sergeants to privates, the reverse of the order the question asks for.
Question 2 of 15 · easy
A carpenter compares a board 3 feet long with a shim 9 inches long. What is the ratio of the board's length to the shim's length in simplest form?
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Answer: D
Correct answer: 4:1. Convert to the same unit first: 3 feet = 36 inches.
The ratio is 36:9, and dividing both terms by 9 gives 4:1.
A: This has the right numbers but reverses the order, putting the shim first.
B: This compares 3 with 9 without converting feet to inches.
C: This mixes up the conversion; the board is longer than the shim, so the first term must be larger.
D (correct): 3 feet is 36 inches, and 36:9 simplifies to 4:1.
Question 3 of 15 · easy
Solve for x in the proportion
8x=2415
What is the value of x?
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Answer: D
Correct answer: 5. Multiply diagonally:
24 × x = 15 × 8 = 120
Divide by 24: x = 5. Check: 5/8 and 15/24 both equal 0.625.
A: This finds only the factor between 8 and 24 and never uses the 15.
B: This multiplies 15 by 24 and divides by 8, which sets the products up incorrectly.
C: This uses subtraction: 24 is 16 more than 8, so 15 minus 16. Proportions scale by multiplying, not adding.
D (correct): Cross-multiplying gives 24x = 120, so x = 5.
Question 4 of 15 · easy
A technician was paid $93.50 for 11 hours of work. What is the technician's hourly rate of pay?
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Answer: A
Correct answer: $8.50 per hour. A unit rate divides the first quantity by the second: $93.50 ÷ 11 hours.
The rate is $8.50 per hour. Check:
11 × $8.50 = $93.50
A (correct): Dividing dollars by hours gives $93.50 divided by 11, which is $8.50.
B: This subtracts the hours from the pay instead of dividing.
C: The decimal point is misplaced; 11 hours at $85 would pay over $900.
D: This divides hours by dollars, which gives hours per dollar, not dollars per hour.
Question 5 of 15 · easy
On a map, 1 centimeter represents 15 kilometers. Two towns are 4.2 centimeters apart on the map. What is the actual distance between the towns?
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Answer: D
Correct answer: 63 km. Multiply the map distance by the kilometers each centimeter represents.
4.2 × 15 = 63 km
A: This divides the map length by the scale instead of multiplying.
B: This adds the map length to the scale instead of multiplying.
C: The decimal point is misplaced; about 4 centimeters is about 60 km.
D (correct): Each centimeter stands for 15 km, so 4.2 times 15 is 63 km.
Question 6 of 15 · medium
Two partners split a $360 bonus in the ratio 4:5. How much does the partner with the larger share receive?
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Answer: B
Correct answer: $200. Add the ratio terms:
4 + 5 = 9
parts. One part is
$360 ÷ 9 = $40
The larger share is
5 × $40 = $200
A: This divides $360 by 4, treating one ratio term as the whole number of parts.
B (correct): There are 9 parts worth $40 each, and the larger share is 5 parts, or $200.
C: This is the smaller share, 4 parts of $40.
D: This divides $360 by 5, treating one ratio term as the whole number of parts.
Question 7 of 15 · medium
In a parking garage, the ratio of trucks to cars is 3:8. There are 24 trucks. How many vehicles are in the garage altogether?
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Answer: B
Correct answer: 88. The 24 trucks are 3 parts, so one part is
24 ÷ 3 = 8
vehicles.
The total is
3 + 8 = 11
parts:
11 × 8 = 88
vehicles.
A: This adds the ratio terms to the truck count, treating the ratio terms as actual counts.
B (correct): One part is 24 divided by 3, or 8, so cars number 64 and the total is 24 + 64 = 88.
C: This is the number of cars only; the question asks for all vehicles.
D: This multiplies 24 by 3 instead of dividing to find the value of one part.
Question 8 of 15 · medium
A bin holds 12 red markers, 18 blue markers, and 10 green markers. What fraction of all the markers are blue?
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Answer: A
Correct answer: 9/20. The whole is the sum of the parts:
12 + 18 + 10 = 40
markers.
Blue out of all is 18/40, which simplifies to 9/20.
A (correct): There are 40 markers in all, and 18/40 simplifies to 9/20.
B: This compares blue markers with green markers only.
C: This compares blue markers with red markers only.
D: This compares blue markers with the 22 markers that are not blue, a part-to-part ratio.
Question 9 of 15 · medium
Five gallons of paint cover 1,750 square feet. At the same rate, how many gallons are needed to cover 4,200 square feet?
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Answer: C
Correct answer: 12 gallons. Keep the units matched: gallons over square feet on both sides,
5/1,750 = x/4,200
One gallon covers
1,750 ÷ 5 = 350 square feet
so
x = 4,200 ÷ 350 = 12 gallons
A: This divides the area by 5 gallons, which gives square feet per gallon for the wrong pairing.
B: This sets up the proportion upside down, matching gallons with the wrong area.
C (correct): The paint covers 350 square feet per gallon, and 4,200 divided by 350 is 12.
D: This is 4,200 divided by 1,750, the scale factor between areas, without multiplying it by 5 gallons.
Question 10 of 15 · medium
A rectangular sign measures 6 inches by 4 inches. It is enlarged by a scale factor of 1.5. What is the area of the enlarged sign?
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Answer: A
Correct answer: 54 square inches. Multiply each side by 1.5:
6 × 1.5 = 9 inches
and
4 × 1.5 = 6 inches
New area:
9 × 6 = 54 square inches
which equals the original 24 square inches times
1.52=2.25
A (correct): The new sides are 9 and 6 inches, so the area is 54 square inches, which is 24 times 1.5 squared.
B: This adds the scale factor to the area instead of multiplying.
C: This multiplies the area by 3, doubling the scale factor instead of squaring it.
D: This multiplies the area by the scale factor once, but area changes by the square of the factor.
Question 11 of 15 · medium
A cleaning solution is made of concentrate, alcohol, and water in the ratio 1:3:8. How many liters of water are in 60 liters of the solution?
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Answer: C
Correct answer: 40 liters. Add the ratio terms:
1 + 3 + 8 = 12
parts. One part is
60 ÷ 12 = 5 liters
Water is 8 parts:
8 × 5 = 40 liters
A: This divides 60 by 8, treating the water term as the total number of parts.
B: This is the amount of alcohol, 3 parts, not water.
C (correct): There are 12 parts worth 5 liters each, and water is 8 parts, or 40 liters.
D: This is the size of one part, which is the amount of concentrate.
Question 12 of 15 · hard
A supply room stocks flashlights and lanterns in the ratio 5:2. There are 45 more flashlights than lanterns. How many flashlights and lanterns are there in all?
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Answer: D
Correct answer: 105. The ratio 5:2 differs by 3 parts, and that difference is 45 items, so one part is
45 ÷ 3 = 15
Flashlights:
5 × 15 = 75
Lanterns:
2 × 15 = 30
Total:
75 + 30 = 105
A: This multiplies the difference by 7 parts without first dividing it by the 3-part difference.
B: This treats 45 as the number of flashlights, but 45 is the difference between the groups.
C: This is the number of flashlights only, not the total.
D (correct): The difference is 3 parts, so one part is 15; there are 75 flashlights and 30 lanterns, for 105 in all.
Question 13 of 15 · hard
A store sells coffee in four bag sizes: 2 pounds for $5.10, 3 pounds for $7.47, 5 pounds for $11.95, and 8 pounds for $19.60. Which bag has the lowest price per pound?
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Answer: A
Correct answer: The 5-pound bag. Divide each price by its weight:
$5.10 ÷ 2 = $2.55
$7.47 ÷ 3 = $2.49
$11.95 ÷ 5 = $2.39
and
$19.60 ÷ 8 = $2.45
The 5-pound bag has the lowest unit price, $2.39 per pound.
A (correct): Its unit price is $11.95 divided by 5, or $2.39 per pound, the lowest of the four.
B: The largest bag is $2.45 per pound, which is more than the 5-pound bag; bigger is not always cheaper.
C: This bag works out to $2.49 per pound, higher than the 5-pound bag.
D: This bag has the lowest total price but costs $2.55 per pound, the highest unit price.
Question 14 of 15 · hard
A cookie recipe uses 2.5 cups of sugar to make 40 cookies. How many cups of sugar are needed to make 9 dozen cookies?
A motor pool has jeeps, trucks, and vans in the ratio 7:4:2. There are 30 more jeeps than vans. How many trucks are in the motor pool?
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Answer: D
Correct answer: 24. The difference between jeeps and vans is
7 - 2 = 5
parts, and that difference is 30 vehicles, so one part is
30 ÷ 5 = 6
Trucks are 4 parts:
4 × 6 = 24
A: This is the number of jeeps (7 × 6), not trucks.
B: This is the number of vans (2 × 6), not trucks.
C: This is the total of all three vehicle types, 42 + 24 + 12, not the trucks alone.
D (correct): Jeeps exceed vans by 7 - 2 = 5 parts, so one part is 30 ÷ 5 = 6 and trucks are 4 × 6 = 24.
Practice 2 of 35 · easy
A fire station has 9 engines and 6 ambulances. What is the ratio of ambulances to engines in simplest form?
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Answer: A
Correct answer: 2:3. Write the quantities in the order named: ambulances to engines is 6:9. The greatest common factor is 3, so the ratio simplifies to 2:3.
A (correct): Ambulances to engines is 6:9; dividing both terms by 3 gives 2:3.
B: This is engines to ambulances, the reverse of the order the question names.
C: This compares ambulances with all 15 vehicles, a part-to-whole ratio.
D: This compares engines with all 15 vehicles, which is neither the right order nor part-to-part.
Practice 3 of 35 · medium
A tool crib holds 15 drills and 25 saws and nothing else. What is the ratio of drills to all the tools in the crib, in simplest form?
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Answer: A
Correct answer: 3:8. "To all the tools" signals a part-to-whole ratio. The whole is
15 + 25 = 40
so drills to total is 15:40. Dividing both terms by 5 gives 3:8.
A (correct): The whole is 15 + 25 = 40 tools, and 15:40 simplifies to 3:8.
B: This is drills to saws (15:25), a part-to-part ratio, not drills to the total.
C: This is saws to all tools, 25:40, not drills to all tools.
D: This is all tools to drills, the reverse of the order asked.
Practice 4 of 35 · hard
Four workers can paint a fence in 6 hours. Working at the same rate per worker, how long would it take 3 workers to paint the same fence?
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Answer: D
Correct answer: 8 hours. Workers and time are not in direct proportion: fewer workers take longer. Find the total work first: 4 workers × 6 hours = 24 worker-hours.
With 3 workers, the time is
24 ÷ 3 = 8 hours
A: This treats workers and time as directly proportional (6 × 3/4), but fewer workers need more time, not less.
B: This assumes one fewer worker means one fewer hour, which has the relationship backward.
C: This adds one hour per missing worker instead of finding the total work in worker-hours.
D (correct): The job takes 4 × 6 = 24 worker-hours, and 24 ÷ 3 = 8 hours.
Practice 5 of 35 · medium
Solve the proportion
x6=4015
What is the value of x?
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Answer: A
Correct answer: 16. Multiply along the diagonals:
15×x=6×40
so 15x = 240.
Divide both sides by 15: x = 16. Check:
6/16 = 0.375
and
15/40 = 0.375
A (correct): Cross products give 15x = 6 × 40 = 240, so x = 16.
B: This multiplies 6 by 15/40 instead of cross-multiplying, which solves a different equation.
C: This sets 6x = 15 × 40, pairing the wrong terms across the diagonal.
D: This adds the difference 40 - 15 = 25 to 6, but proportions work by multiplying, not adding.
Practice 6 of 35 · medium
A PX sells batteries in a pack of 8 for $6.00 and a pack of 12 for $8.40. How much less per battery does the 12-pack cost?
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Answer: C
Correct answer: $0.05. Find each unit rate:
$6.00 ÷ 8 = $0.75
per battery and
$8.40 ÷ 12 = $0.70
per battery.
The savings per battery is
$0.75 - $0.70 = $0.05
A: This is the price of one battery in the 12-pack, not the savings per battery.
B: This is the difference in pack prices, which ignores that the packs hold different numbers of batteries.
C (correct): The 8-pack is $0.75 each and the 12-pack is $0.70 each, a difference of $0.05.
D: This divides the $2.40 price difference by the 4 extra batteries, which does not compare unit prices.
Practice 7 of 35 · hard
On a floor plan, 1 inch represents 8 feet. A rectangular room measures 2.5 inches by 3 inches on the plan. What is the actual floor area of the room?
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Answer: A
Correct answer: 480 square feet. Convert each plan length to real length first:
2.5 × 8 = 20 feet
and
3 × 8 = 24 feet
Then find the area:
20 × 24 = 480 square feet
A (correct): The room is 2.5 × 8 = 20 ft by 3 × 8 = 24 ft, and 20 × 24 = 480 square feet.
B: This finds the plan area, 7.5 square inches, and multiplies by 8 once; areas scale by 8 squared, or 64.
C: This is the perimeter of the real room, 2 × (20 + 24) feet, not its area.
D: This adds the two real side lengths, 20 + 24, instead of multiplying them.
Practice 8 of 35 · medium
A platoon divides 540 rounds of training ammunition among three squads in the ratio 2:3:4. How many rounds does the squad with the 3-part share receive?
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Answer: B
Correct answer: 180. Add the ratio terms:
2 + 3 + 4 = 9
parts. One part is
540 ÷ 9 = 60
rounds.
The 3-part share is
3 × 60 = 180
rounds.
A: This is the share of the squad with 2 parts, 2 × 60.
B (correct): There are 2 + 3 + 4 = 9 parts, each 540 ÷ 9 = 60 rounds, so 3 parts is 180.
C: This is the share of the squad with 4 parts, 4 × 60.
D: This is the value of one part, not the 3-part share.
Practice 9 of 35 · easy
A supply truck uses 18 gallons of diesel to travel 306 miles. How many miles does it travel per gallon?
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Answer: B
Correct answer: 17 miles per gallon. A unit rate is the first quantity divided by the second: 306 miles ÷ 18 gallons = 17 miles per gallon. Check:
17 × 18 = 306
A: This comes from a division slip; 15 × 18 is only 270 miles.
B (correct): Dividing miles by gallons gives 306 ÷ 18 = 17 miles per gallon.
C: This comes from a division slip; 19 × 18 is 342 miles, more than the trip.
D: This subtracts 18 from 306 instead of dividing.
Practice 10 of 35 · medium
A 4-inch by 6-inch photo is enlarged so that its 6-inch side becomes 15 inches. How long does the 4-inch side become?
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Answer: D
Correct answer: 10 inches. The scale factor is new length over original length:
k=615=2.5
Every side is multiplied by 2.5, so the 4-inch side becomes
4 × 2.5 = 10 inches
A: This adds 9 inches to each side, but an enlargement multiplies every length by the same factor.
B: This divides 4 by the scale factor 2.5 instead of multiplying.
C: This uses the upside-down factor 6/4 on the 15-inch side, mixing up the matching sides.
D (correct): The scale factor is 15 ÷ 6 = 2.5, and 4 × 2.5 = 10 inches.
Practice 11 of 35 · medium
At a base clinic, the ratio of nurses to doctors is 7:2. There are 63 nurses. How many nurses and doctors are there in all?
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Answer: C
Correct answer: 81. Use the known group to find one part: 63 nurses ÷ 7 parts = 9 people per part.
Doctors are
2 × 9 = 18
so the total is
63 + 18 = 81
A: This is the number of doctors only, not the total of nurses and doctors.
B: This adds one part (9) to the nurses instead of the two parts that represent the doctors.
C (correct): One part is 63 ÷ 7 = 9, so there are 2 × 9 = 18 doctors and 63 + 18 = 81 in all.
D: This is the difference between nurses and doctors, 63 - 18, not the total.
Practice 12 of 35 · easy
On a blueprint, 1 inch represents 6 feet. A wall is drawn 4.25 inches long. How long is the actual wall?
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Answer: D
Correct answer: 25.5 feet. Each inch on the blueprint stands for 6 feet, so multiply:
4.25 × 6 = 25.5 feet
A: This adds 6 to 4.25 instead of multiplying by the scale.
B: This uses only the whole 4 inches and drops the 0.25 inch, which is another 1.5 feet.
C: This divides 6 by 4.25, which turns the scale upside down.
D (correct): Multiplying drawing inches by feet per inch gives 4.25 × 6 = 25.5 feet.
Practice 13 of 35 · easy
Which ratio is equivalent to 4:7?
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Answer: C
Correct answer: 12:21. Equivalent ratios come from multiplying or dividing both terms by the same number.
4 × 3 = 12
and
7 × 3 = 21
so 12:21 matches 4:7.
A: This reverses the order, which changes the comparison.
B: This adds 4 to each term; equivalent ratios come from multiplying or dividing, not adding.
C (correct): Multiplying both terms of 4:7 by 3 gives 12:21.
D: This multiplies the first term by 3 but the second by 4, so it simplifies to 3:7.
Practice 14 of 35 · medium
A crew lays 45 feet of pipe in 3 hours. Working at the same rate, how many feet of pipe can the crew lay in 7.5 hours?
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Answer: A
Correct answer: 112.5 feet. Find the unit rate: 45 feet ÷ 3 hours = 15 feet per hour.
Scale it to 7.5 hours:
15 × 7.5 = 112.5 feet
A (correct): The rate is 45 ÷ 3 = 15 feet per hour, and 15 × 7.5 = 112.5 feet.
B: This uses 7 hours instead of 7.5, dropping the half hour.
C: This sets up the proportion upside down, computing 45 × 3 ÷ 7.5.
D: This adds 4.5 hours' worth as 4.5 feet instead of using the rate per hour.
Practice 15 of 35 · medium
A chainsaw needs a fuel mix of gasoline to oil in the ratio 40:1. How many fluid ounces of oil are needed for 2.5 gallons of gasoline? (1 gallon = 128 fluid ounces)
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Answer: D
Correct answer: 8 fluid ounces. Convert first:
2.5 × 128 = 320
fluid ounces of gasoline.
The gasoline is 40 parts, so one part is
320 ÷ 40 = 8
fluid ounces, and the oil is 1 part: 8 fluid ounces.
A: This divides 320 by 41, treating the gasoline as the whole mixture instead of the 40-part share.
B: This divides 2.5 by 40 without converting gallons to fluid ounces.
C: This is the oil for only 1 gallon of gasoline, 128 ÷ 40.
D (correct): 2.5 gallons is 320 fluid ounces, and 320 ÷ 40 = 8 fluid ounces of oil.
Practice 16 of 35 · easy
A bilge pump removes 210 gallons of water in 14 minutes. What is its pumping rate?
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Answer: A
Correct answer: 15 gallons per minute. A rate is gallons divided by minutes:
14 min210 gal=15
gal/min.
A (correct): Dividing gallons by minutes gives 210 ÷ 14 = 15 gallons per minute.
B: This subtracts 14 from 210 instead of dividing.
C: This misplaces the decimal point; 1.5 × 14 is only 21 gallons.
D: This adds 14 to 210 instead of dividing.
Practice 17 of 35 · medium
Drilling one hole takes 45 seconds, and the whole job takes 6 minutes. What is the ratio of the time for one hole to the time for the whole job, in simplest form?
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Answer: A
Correct answer: 1:8. Convert to the same units first: 6 minutes =
6 × 60 = 360 seconds
The ratio is 45:360. The greatest common factor is 45, so it simplifies to 1:8.
A (correct): 6 minutes is 360 seconds, and 45:360 simplifies to 1:8.
B: This compares 45 with 6 without converting minutes to seconds.
C: This reverses the order; the question asks for one hole to the whole job.
D: This treats 6 minutes as 600 seconds, but a minute has 60 seconds, not 100.
Practice 18 of 35 · hard
A concrete mix uses cement, sand, and gravel in the ratio 2:5:8. A crew uses 20 bags of sand. How many bags of all three materials does the batch use?
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Answer: B
Correct answer: 60. Sand is 5 parts and equals 20 bags, so one part is
20 ÷ 5 = 4
bags.
The mix has
2 + 5 + 8 = 15
parts, so the batch uses
15 × 4 = 60
bags (8 cement, 20 sand, 32 gravel).
A: This is only the gravel, 8 × 4 bags.
B (correct): One part is 20 ÷ 5 = 4 bags, and the 15 total parts make 15 × 4 = 60 bags.
C: This adds cement and gravel (8 + 32) but leaves out the 20 bags of sand.
D: This multiplies 20 by the 15 total parts, treating the 20 bags as one part instead of five.
Practice 19 of 35 · medium
On a map, 1 centimeter represents 40 kilometers. Two cities are 340 kilometers apart. How far apart are they on the map?
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Answer: B
Correct answer: 8.5 cm. Going from real distance to map distance, divide by the real length each centimeter stands for:
340 ÷ 40 = 8.5 cm
A: This multiplies by the scale, which converts map length to real length, the wrong direction.
B (correct): Dividing the real distance by kilometers per centimeter gives 340 ÷ 40 = 8.5 cm.
C: This divides 40 by 340, turning the scale upside down.
D: This subtracts 40 from 340 instead of dividing.
Practice 20 of 35 · easy
Which of these is a true proportion?
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Answer: D
Correct answer:
6/8 = 15/20
In a true proportion the cross products are equal. For 6/8 and 15/20:
6 × 20 = 120
and
8 × 15 = 120
so the ratios are equal (both reduce to 3/4).
A: Cross products are 6 × 12 = 72 and 9 × 10 = 90, which are not equal.
B: Cross products are 4 × 16 = 64 and 5 × 12 = 60, which are not equal.
C: Cross products are 3 × 14 = 42 and 7 × 9 = 63; the numerator was tripled but the denominator only doubled.
D (correct): Cross products are 6 × 20 = 120 and 8 × 15 = 120, which are equal.
Practice 21 of 35 · hard
A training class of 40 recruits has Army and Navy recruits in the ratio 3:5. How many more Army recruits must join the class for the ratio of Army to Navy recruits to become 1:1?
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Answer: B
Correct answer: 10. There are
3 + 5 = 8
parts, so one part is
40 ÷ 8 = 5
recruits: 15 Army and 25 Navy.
For a 1:1 ratio the Army count must equal the Navy count of 25, so
25 - 15 = 10
more Army recruits must join.
A: This subtracts the ratio terms, 5 - 3, treating them as actual counts.
B (correct): The class has 15 Army and 25 Navy recruits, so 10 more Army recruits make 25:25.
C: This is the current number of Army recruits, not how many must be added.
D: This is half of the 40 recruits, which is not the number of Navy recruits to be matched.
Practice 22 of 35 · medium
A model of a square helipad is enlarged by a scale factor of 4 to build the real pad. How many times the model's area is the real pad's area?
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Answer: D
Correct answer: 16 times. Each length is multiplied by k = 4. Area depends on two lengths, so it is multiplied by
k2=42=16
A: This applies the scale factor to area as if it were a length.
B: This doubles the scale factor instead of squaring it.
C: This cubes the scale factor, which is how volume changes, not area.
D (correct): Area changes by the square of the scale factor, 4 × 4 = 16.
Practice 23 of 35 · medium
A recruit runs 3 miles in 24 minutes. At the same pace, how many minutes will it take to run 5 miles?
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Answer: C
Correct answer: 40 minutes. Label the units: minutes over miles on both sides gives
324=5x
The pace is 8 minutes per mile, so
x = 8 × 5 = 40 minutes
A: This puts the proportion upside down, computing 24 × 3 ÷ 5.
B: This adds the 2 extra miles as 2 extra minutes instead of using the pace.
C (correct): The pace is 24 ÷ 3 = 8 minutes per mile, and 8 × 5 = 40 minutes.
D: This is the time for only 4 miles, 24 + 8.
Practice 24 of 35 · medium
A recipe uses 1.5 cups of rice to serve 4 people. How many cups of rice are needed to serve 14 people?
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Answer: C
Correct answer: 5.25 cups. Set up cups over people on both sides:
41.5=14x
Cross-multiply: 4x = 21, so x = 5.25 cups.
A: This adds the 10 extra people as 10 extra cups instead of scaling.
B: This is only the scale factor 14 ÷ 4, not multiplied by the 1.5 cups.
C (correct): Each person needs 1.5 ÷ 4 = 0.375 cup, and 0.375 × 14 = 5.25 cups.
D: This multiplies 1.5 cups by 14, as if 1.5 cups served one person.
Practice 25 of 35 · medium
In a motor pool, 2/7 of the vehicles are trucks and the rest are jeeps. What is the ratio of trucks to jeeps?
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Answer: B
Correct answer: 2:5. The fraction 2/7 is part-to-whole: 2 of every 7 vehicles are trucks. The other
7 - 2 = 5
are jeeps, so trucks to jeeps is 2:5.
A: This is trucks to all vehicles, a part-to-whole ratio, not trucks to jeeps.
B (correct): If trucks are 2 parts out of 7, jeeps are 7 - 2 = 5 parts, so trucks to jeeps is 2:5.
C: This is jeeps to trucks, the reverse of the order asked.
D: This is jeeps to all vehicles, not trucks to jeeps.
Practice 26 of 35 · hard
A convoy travels 27 miles in 36 minutes. At this rate, how far will it travel in 2.5 hours?
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Answer: D
Correct answer: 112.5 miles. Match the units. The rate is 27 miles ÷ 36 minutes = 0.75 mile per minute, and 2.5 hours =
2.5 × 60 = 150 minutes
Distance =
0.75 × 150 = 112.5 miles
(Equivalently, 0.75 mile per minute is 45 mph, and
45 × 2.5 = 112.5
)
A: This treats 2.5 hours as 250 minutes; half an hour is 30 minutes, so 2.5 hours is 150 minutes.
B: This multiplies the per-minute rate by 2.5 without converting hours to minutes.
C: This multiplies 27 miles by 2.5, as if 27 miles took a full hour instead of 36 minutes.
D (correct): The rate is 27 ÷ 36 = 0.75 mile per minute, and 2.5 hours is 150 minutes, so 0.75 × 150 = 112.5 miles.
Practice 27 of 35 · easy
A depot stores 48 spare tires and 72 wheel rims. What is the ratio of tires to rims in simplest form?
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Answer: C
Correct answer: 2:3. Write tires first: 48:72. The greatest common factor of 48 and 72 is 24, so the ratio simplifies to 2:3.
A: This is rims to tires, the reverse of the order named.
B: This compares tires with the total of 120 items, a part-to-whole ratio.
C (correct): Dividing both terms of 48:72 by their greatest common factor, 24, gives 2:3.
D: This compares rims with the total of 120 items, not tires with rims.
Practice 28 of 35 · hard
A topographic map has a scale of 1:50,000, meaning 1 unit on the map equals 50,000 of the same units on the ground. Two hilltops are 7 centimeters apart on the map. What is the actual distance between them? (1 km = 100,000 cm)
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Answer: A
Correct answer: 3.5 km. Multiply the map distance by the scale: 7 cm × 50,000 = 350,000 cm on the ground.
Convert to kilometers:
350,000 ÷ 100,000 = 3.5 km
A (correct): 7 × 50,000 = 350,000 cm on the ground, and 350,000 ÷ 100,000 = 3.5 km.
B: This divides 350,000 cm by 10,000 instead of 100,000 when converting to kilometers.
C: This divides 350,000 cm by 1,000,000, slipping a decimal place in the conversion.
D: This divides by 1,000 as if converting meters to kilometers, but the ground distance is in centimeters.
Practice 29 of 35 · easy
A cook uses 3 cups of water for every 1 cup of rice. What is the ratio of rice to water?
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Answer: B
Correct answer: 1:3. Write the quantities in the order the question names them: rice first, then water. One cup of rice to 3 cups of water is 1:3.
A: This is water to rice, the reverse of the order asked.
B (correct): Rice is named first, so the ratio is 1 cup of rice to 3 cups of water, 1:3.
C: This is rice to the total of 4 cups, a part-to-whole ratio.
D: This is water to the total of 4 cups, not rice to water.
Practice 30 of 35 · easy
A 45-foot rope is cut into two pieces whose lengths are in the ratio 4:5. How long is the shorter piece?
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Answer: C
Correct answer: 20 feet. Add the ratio terms:
4 + 5 = 9
parts. One part is
45 ÷ 9 = 5 feet
The shorter piece is 4 parts:
4 × 5 = 20 feet
A: This is the longer piece, 5 parts of 5 feet.
B: This divides 45 by 5, using one ratio term instead of the 9 total parts.
C (correct): There are 4 + 5 = 9 parts of 45 ÷ 9 = 5 feet, so the shorter piece is 4 × 5 = 20 feet.
D: This multiplies 45 by 4/5, using a part-to-part ratio as if it were a fraction of the whole.
Practice 31 of 35 · hard
Machine A fills 54 bottles in 6 minutes, and Machine B fills 40 bottles in 5 minutes. Working together at these rates, how many minutes will the two machines take to fill 680 bottles?
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Answer: C
Correct answer: 40 minutes. Find each unit rate: Machine A makes
54 ÷ 6 = 9
bottles per minute, and Machine B makes
40 ÷ 5 = 8
bottles per minute.
Together they fill
9 + 8 = 17
bottles per minute, so 680 bottles take
680 ÷ 17 = 40 minutes
A: This divides 680 by the average rate of 8.5 per minute, which is the rate of one machine, not both together.
B: This uses only Machine A's rate, 680 ÷ 9.
C (correct): The rates are 9 and 8 bottles per minute, 17 together, and 680 ÷ 17 = 40 minutes.
D: This uses only Machine B's rate, 680 ÷ 8.
Practice 32 of 35 · medium
A road crew uses 9 bags of patching mix for every 16 feet of trench it repairs. At this rate, how many bags does it need to repair 80 feet of trench?
Show the answer
Answer: A
Correct answer: 45 bags. Set up bags over feet on both sides:
169=80x
Look for a whole-number scale factor before cross-multiplying:
80 ÷ 16 = 5
so
x = 9 × 5 = 45
bags. Check:
9 × 80 = 720
and
16 × 45 = 720
A (correct): Since 80 feet is 5 times 16 feet, the crew needs 9 × 5 = 45 bags.
B: This adds 64 (the difference 80 - 16) to 9 instead of multiplying by a scale factor.
C: This flips the ratio to feet per bag, computing about 80 × 16 ÷ 9.
D: This is the scale factor 80 ÷ 16, not the number of bags.
Practice 33 of 35 · medium
A field generator burns 3 gallons of fuel every 4 hours. How many gallons will it burn running nonstop for 3 days?
Show the answer
Answer: C
Correct answer: 54 gallons. Convert days to hours:
3 × 24 = 72 hours
The rate is 3 gallons ÷ 4 hours = 0.75 gallon per hour.
Fuel used:
0.75 × 72 = 54 gallons
A: This treats 3 days as 3 hours instead of converting days to hours.
B: This sets up the rate upside down, as hours per gallon, computing 72 × 4 ÷ 3.
C (correct): 3 days is 72 hours, and at 0.75 gallon per hour it burns 0.75 × 72 = 54 gallons.
D: This is the fuel for only one day, 0.75 × 24.
Practice 34 of 35 · medium
In a qualification course, 5 out of every 8 trainees pass on the first attempt. If 120 trainees passed on the first attempt, how many did not pass on the first attempt?
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Answer: B
Correct answer: 72. Passing trainees are 5 parts of 8, and that group is 120, so one part is
120 ÷ 5 = 24
Those who did not pass are
8 - 5 = 3
parts:
3 × 24 = 72
trainees.
A: This is the total number of trainees, 8 × 24, not the number who did not pass.
B (correct): One part is 120 ÷ 5 = 24 trainees, and 3 parts did not pass: 3 × 24 = 72.
C: This multiplies 120 by 5/8, treating 120 as the whole class instead of the passing group.
D: This subtracts 75 from 120, building on the mistake of treating 120 as the whole.
Practice 35 of 35 · hard
A storage bin holds bolts and nuts in the ratio 4:3. After 30 more nuts are added, the ratio of bolts to nuts becomes 4:5. How many bolts are in the bin?
Show the answer
Answer: B
Correct answer: 60. The number of bolts does not change and stays 4 parts in both ratios, so the parts are the same size. Nuts go from 3 parts to 5 parts, a change of 2 parts, which equals the 30 added nuts.
One part is
30 ÷ 2 = 15
so bolts =
4 × 15 = 60
Check: 60:75 = 4:5.
A: This is the original number of nuts, 3 × 15, not the bolts.
B (correct): Bolts stay at 4 parts while nuts grow from 3 to 5 parts, so 2 parts = 30, one part = 15, and bolts = 60.
C: This is the number of nuts after the 30 are added, 5 × 15.
D: This multiplies 30 by 4, treating the 30 added nuts as one part instead of two.
About this test
Every answer is explained. The explanations make the ratio setup explicit, label which quantity is the part and which is the whole, and show the shortest path to the solution. If a wrong choice looked convincing, the explanation usually names the setup error behind it.
Review your misses against the lesson outline. Errors on totals or missing groups suggest rereading ratio totals using parts; mistakes on maps point to the scale factor and scale drawing sections. Once you have patched the gaps, work through the 35 extra practice questions for this lesson. The score you see is practice accuracy, not an ASVAB result.
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