5.3 Worked Problem Walkthroughs

AFOQT Study Guide Exam

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1 Chapter 1: AFOQT Orientation and Exam Strategy

1.1 Current AFOQT Exam Facts 1.2 Eligibility, Application, and Scheduling 1.3 Blueprint Domains and Weighting 1.4 Question Style and Score Report Thinking 1.5 Study Calendar and Practice Plan

2 Chapter 2: Verbal Analogies

2.1 Verbal Analogies Overview 2.2 Core Workflows and Decision Points 2.3 Scenario Practice for Verbal Analogies 2.4 Common Traps in Verbal Analogies 2.5 Practice Drills and Readiness Markers

3 Chapter 3: Arithmetic Reasoning

3.1 Arithmetic Reasoning Overview 3.2 Core Problem Types and Solution Workflows 3.3 Scenario Practice and Translation Method 3.4 Common Traps in Arithmetic Reasoning 3.5 Practice Drills and Readiness Markers

4 Chapter 4: Word Knowledge

4.1 Word Knowledge Overview 4.2 Decoding Words: Roots, Prefixes, and Suffixes 4.3 Working a Synonym Question Step by Step 4.4 Common Traps in Word Knowledge 4.5 Practice Drills and Readiness Markers

5 Chapter 5: Math Knowledge

5.1 Math Knowledge Overview 5.2 Core Algebra and Geometry Workflows 5.3 Worked Problem Walkthroughs 5.4 Common Traps in Math Knowledge 5.5 Practice Drills and Readiness Markers

6 Chapter 6: Instrument Comprehension

6.1 Instrument Comprehension Overview 6.2 Reading the Attitude Indicator and Compass 6.3 Matching the Dials to the Silhouette Airplanes 6.4 Common Traps in Instrument Comprehension 6.5 Practice Drills and Readiness Markers

7 Chapter 7: Block Counting

7.1 Block Counting Overview 7.2 Core Workflows and Decision Points 7.3 Scenario Practice for Block Counting 7.4 Common Traps in Block Counting 7.5 Practice Drills and Readiness Markers

8 Chapter 8: Table Reading

8.1 Table Reading Overview 8.2 Core Lookup Workflow and Speed Technique 8.3 Reading the Grid: Worked Lookups 8.4 Common Traps in Table Reading 8.5 Practice Drills and Readiness Markers

9 Chapter 9: Aviation Information

9.1 Aviation Information Overview 9.2 Aerodynamics and Flight Controls 9.3 Aircraft Structure, Engines, and Instruments 9.4 Airport Operations, Markings, and Common Traps 9.5 Practice Drills and Readiness Markers

10 Chapter 10: General Science

10.1 Physical Science Overview 10.2 Core Concepts: Forces, Energy, and Simple Machines 10.3 Waves, Heat, and the Electromagnetic Spectrum 10.4 Chemistry and Electricity Essentials 10.5 Earth/Space Science and Practice Drills

11 Chapter 11: Situational Judgment

11.1 Situational Judgment Overview 11.2 Core Workflows and Decision Points 11.3 Scenario Practice for Situational Judgment 11.4 Common Traps in Situational Judgment 11.5 Practice Drills and Readiness Markers

12 Chapter 12: Reading Comprehension

12.1 Reading Comprehension Overview 12.2 Core Reading Methods and Question Types 12.3 Scenario Practice for Reading Comprehension 12.4 Common Traps in Reading Comprehension 12.5 Practice Drills and Readiness Markers

13 Chapter 13: Self-Description Inventory

13.1 Self-Description Inventory Overview 13.2 The Big Five and Response Strategy 13.3 Scenario Practice: Reading SDI Statements 13.4 Common Traps in the Self-Description Inventory 13.5 Practice Drills and Readiness Markers

14 Chapter 14: Final Review and Test Day

14.1 Timed Practice Strategy 14.2 Last-Week Review Map 14.3 Exam-Day Checklist 14.4 After the Exam and Next Steps

5.3 Worked Problem Walkthroughs

Key Takeaways Explain This Topic AI

Translate every word into an operation before computing: 'of' means multiply, 'per' means divide, 'is' means equals.

For percent problems, convert to decimals (45% = 0.45) and use part = whole × rate.

Estimate first to eliminate impossible answer choices, then compute the survivors precisely.

Keep units consistent — convert everything to the same unit before applying a formula.

Last updated: September 2026

5.3 Worked Problem Walkthroughs

Speed on MK comes from rehearsing complete solutions until the steps are automatic. Work each example below by hand, then check against the explanation.

Percentages

Problem: What is 35% of 80? Convert the percent to a decimal: 35% = 0.35. Multiply: 0.35 × 80 = 28 . The template is part = whole × rate .

Percent change: A price rises from $40 to $50. Change = (50 − 40)/40 = 10/40 = 0.25 = 25% increase . Always divide by the original value, not the new one.

Ratios and proportions

Problem: A recipe uses flour and sugar in a 3:2 ratio. If 12 cups of flour are used, how much sugar? Set up 3/2 = 12/x, cross-multiply → 3x = 24 → x = 8 cups . Cross-multiplication turns any proportion into a one-step linear equation.

Fractions

Problem: Compute 2/3 + 1/4. Find the least common denominator (12): 8/12 + 3/12 = 11/12 . For division, multiply by the reciprocal: (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8 .

Exponents in context

Problem: Simplify (x⁵)/(x²) · x. Subtract exponents for the division (x³), then add for the multiplication (x³ · x¹ = x⁴) → x⁴ .

Geometry

Problem: A right triangle has legs of 6 and 8. Find the hypotenuse. Apply a² + b² = c²: 36 + 64 = 100, c = √100 = 10 (a scaled 3-4-5 triple).

Problem: A circle has radius 5. Find its area. πr² = π(25) = 25π (≈ 78.5).

Translation cheat sheet

Word/phrase Operation
of multiply (×)
per, out of divide (÷)
is, equals, gives =
more than, sum, increased by add (+)
less than, difference, decreased by subtract (−)
product multiply (×)
quotient divide (÷)
Estimation as a filter

Before exact arithmetic, estimate to eliminate choices. If 35% of 80 must be 'a bit more than a third of 80,' any answer above 40 or below 20 is impossible — you may answer correctly without finishing the computation when the survivors are far apart. Reserve precise calculation for close choices.

Averages and weighted averages

The mean is the sum divided by the count. If three test scores are 80, 90, and 100, the mean is 270/3 = 90 . Watch for the reverse question: 'A student needs a 90 average over four tests and has 85, 88, and 92 — what is needed on the fourth?' Required sum = 90 × 4 = 360; current sum = 265; needed = 95 . The trick is realizing the average tells you the total, then subtracting what you already have.

Unit conversions and rates

Keep units consistent before computing. 90 minutes is 1.5 hours; 2 feet is 24 inches. For rate problems, rate = quantity ÷ time . A car covering 150 miles in 3 hours averages 50 mph. MK rarely buries rate in a story (that is Arithmetic Reasoning), but a clean rate computation can appear.

Roots and fractional exponents in context

Problem: Simplify √72. Factor out the largest perfect square: 72 = 36 × 2, so √72 = 6√2. Problem: Evaluate 8^(2/3). Read the denominator as a root and the numerator as a power: take the cube root of 8 (= 2), then square it → 4 . Fractional exponents combine the root and power rules, and reading them in the right order — root first, then power — keeps the arithmetic small.

A worked multi-step example

Problem: If 2(x + 3) − 4 = 10, find x². Solve the linear equation first: distribute → 2x + 6 − 4 = 10 → 2x + 2 = 10 → 2x = 8 → x = 4. The question asks for x², so the answer is 16 , not 4. This illustrates Trap 4 from the next section: the stem asked for a transformation of the solution, not the solution itself. Solve fully, then re-read what was requested before bubbling.

Mixture and combination thinking

Problem: A class has 12 boys and 18 girls. What fraction of the class is boys? Total = 30; boys = 12; fraction = 12/30 = 2/5 . Reduce fractions to lowest terms before checking the answer list, because the test almost always lists the reduced form. Problem: If 3 pencils cost $0.45, what does one pencil cost? Divide: 0.45/3 = $0.15 . Unit-rate questions reduce to a single division once you identify the per-unit quantity.

Geometry composites

Problem: A square has the same area as a circle of radius 4. Find the square's side length. Circle area = π(16) = 16π ≈ 50.27; side = √50.27 ≈ 7.1 . When a problem links two shapes, set their shared quantity (area, perimeter) equal and solve. Problem: Find the area of an L-shaped region by splitting it into two rectangles and adding the parts — decomposition turns an unfamiliar figure into familiar ones.

Practicing the read-then-solve habit

The single biggest accuracy gain on MK comes from a one-second pause to ask 'what exactly is being requested?' before computing. Is it x, x², the sum of roots, the perimeter, or the area? Many MK items deliberately solve cleanly to a value that is not the final answer, then require one more step. Build the habit now: underline the demand, solve, then return to the underline before you choose. In timed practice, tag any miss caused by answering the wrong quantity so you can see how often this single habit would have saved points.

Self-test prompts

After each worked set, quiz yourself with these prompts: Can I name the procedure this item tested? Can I solve a structurally identical item with new numbers? Can I explain why each of the three wrong choices is wrong? If you cannot do all three, the topic is not yet exam-ready and needs another pass of focused, untimed practice before you fold it back into timed sets.