Build the methods behind the answers. Choose a lesson, study its worked examples, then check your understanding one question at a time.
Word problems slow you down? Start with percentages, ratios, or rates. Symbols or diagrams? Choose equations or geometry.
Suggested session: 10 minutes learning · 10–15 minutes practicing · 5 minutes reviewing. Split the lesson across two sessions when needed.
Find a part, recover the original whole, and handle discounts or successive changes.
Open lesson · 4 worked methods + guided practice →Keep ratio order straight, split totals into shares, and scale quantities with units.
Open lesson · 4 worked methods + guided practice →Use compatible units, combine work rates, and calculate average speed from totals.
Open lesson · 4 worked methods + guided practice →Translate a story, undo operations, handle both sides, and preserve inequality meaning.
Open lesson · 4 worked methods + guided practice →Choose between length, area, and volume; use perpendicular height and right-triangle relationships.
Open lesson · 4 worked methods + guided practice →These lessons support both Arithmetic Reasoning word problems and Mathematics Knowledge procedures. Use paper to write a setup and check your result.
Know the methods already? Use this mixed set to find what needs attention. Start with four questions, review your setups, and continue when you are ready. It samples the lesson sets and does not estimate an official ASVAB score.
Work through one question at a time. Explain your approach, check the worked answer, then move on. Use scratch paper for calculations.
0 of 12 checked · 0 correct.
Progress is saved in this browser. These original study questions do not produce an official AFQT score.
Answer: C. 30
Red-capped bottles make up the remaining 60%. If 60% of the total is 18, the total is 18 ÷ 0.60 = 30. Dividing by 40% gives 45, but 18 counts the red group, not the blue group. Twelve is the number with blue caps.
Answer: A. $40
Undo the last change first: $56 − $6 = $50. That $50 is 125% of the original price, so the original is $50 ÷ 1.25 = $40. Subtracting 25% from $56 uses the wrong base and fails to remove the separate fee correctly.
Answer: A. 12
There are 80 × 0.60 = 48 manually checked forms. One quarter of that group is 48 ÷ 4 = 12. The 20 choice applies one quarter to all 80 forms, but the error fraction applies only to the manual subgroup.
Answer: B. 6 liters
Two ratio parts of peat equal 12 liters, so one part equals 6 liters. The compost confirms the scale because 3 × 6 = 18 liters. Grit accounts for one part, so add 6 liters. Taking one sixth of the compost alone would give 3 liters, but the six total ratio parts describe the entire mixture.
Answer: C. 36
The original red excess is two ratio parts, and removing 12 eliminates that excess. One part is therefore 12 ÷ 2 = 6 tokens. The 3 white parts contain 18 tokens; 18 red tokens remain as well. The remaining total is 36. Forty-eight is the original total before removal.
Answer: A. 3 liters
Using all 10% solution would supply 0.10 × 12 = 1.2 units of salt, but the target needs 0.15 × 12 = 1.8. Each liter replaced by 30% solution adds 0.30 − 0.10 = 0.20 unit of salt. The required amount is (1.8 − 1.2) ÷ 0.20 = 3 liters. Nine liters is the amount of the 10% solution.
Answer: B. 180 seconds
Three laps cover 3 × 240 = 720 meters. Time equals distance divided by speed, so 720 ÷ 4 = 180 seconds. The 720-second choice uses the distance as a time without dividing by speed; 120 seconds accounts for only two laps.
Answer: D. 30 seconds
The front must travel the bridge length plus the train length before the rear clears the far end: 420 + 180 = 600 meters. At 20 meters per second, that takes 600 ÷ 20 = 30 seconds. The 21-second choice covers only the front’s trip across the bridge.
Answer: B. −2
The filled endpoint includes −2, whereas the open endpoint excludes 3. The shaded set is −2≤x<3. Of the four choices, only −2 is in that set; −3 and 4 lie outside it.
Answer: C. −2
Distribute to get −6x + 8 ≤ 20, then subtract 8: −6x ≤ 12. Dividing by −6 reverses the inequality, giving x ≥ −2. Therefore −2 is the least permitted integer. Two also satisfies the inequality but is not the least, while −3 and −4 do not satisfy it.
Answer: C. 54 square units
The full rectangle has area 10 × 6 = 60 square units. The removed right triangle has area (1/2) × 4 × 3 = 6. The remaining area is 60 − 6 = 54. Subtracting 4 × 3 without halving treats the cutout as a rectangle and gives the incorrect 48.
Answer: B. 48 square units
Each corner is a right triangle whose legs are half the rectangle’s side lengths: 6 units and 4 units. Each has area (1/2) × 6 × 4 = 12 square units. The four corners total 4 × 12 = 48 square units. The full rectangle has area 96; 24 counts only two of the four congruent corner triangles.
For each missed question, record one error type: interpreting the prompt, setting up the relationship, arithmetic, or checking the answer. Then write one correction you can use next time. “I divided by the ending value” is more useful than “I need to study percentages.” Rework that question tomorrow without looking at the explanation.
The lesson sequence uses worked examples, independent attempts and later review, approaches recommended in the Institute of Education Sciences study guide.