3.2 Core Problem Types and Solution Workflows

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

3.2 Core Problem Types and Solution Workflows

Key Takeaways Explain This Topic AI

Percent change uses (new − old) ÷ old; percent increase then decrease does NOT cancel out.

Distance-rate-time problems all reduce to d = r × t; solve for the variable the stem omits.

Work-rate problems add rates, not times: combined rate = 1/a + 1/b, then invert for total time.

Weighted averages weight each value by its count or frequency, not by a simple mean of the values.

Last updated: June 2026

3.2 Core Problem Types and Solution Workflows

Most AR items belong to a handful of families. Recognizing the family in the first 15 seconds tells you which formula to write down, which collapses a word problem into a fill-in-the-blank.

Percent and percent change

The master relationship is part = percent × whole . For change problems use percent change = (new − old) ÷ old × 100 .

"Of" means multiply: 18% of 250 = 0.18 × 250 = 45.

Percent increase: new = old × (1 + rate). A $40 item up 15% = 40 × 1.15 = $46.

Percent decrease: new = old × (1 − rate). $40 down 15% = 40 × 0.85 = $34.

Reverse percent trap: a price raised 20% then cut 20% does not return to the start. $100 → $120 → $96. The two percents are taken from different bases.

Distance, rate, and time

Every DRT problem is d = r × t . Identify which of the three the stem leaves blank, then solve.

Given Find Rearrange
rate, time distance d = r × t
distance, time rate r = d ÷ t
distance, rate time t = d ÷ r

For average speed over a round trip, do not average the two speeds — use total distance ÷ total time. Driving 60 mi out at 60 mph (1 hr) and back at 30 mph (2 hr) gives 120 mi ÷ 3 hr = 40 mph , not 45.

Work-rate problems

When two workers or machines combine, add their rates, not their times . If A finishes a job in a hours and B in b hours, the combined rate is 1/a + 1/b, and total time is the reciprocal of that sum. Pump A fills a tank in 4 hr (rate 1/4) and pump B in 6 hr (rate 1/6); combined rate = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 tank per hour, so total time = 12/5 = 2.4 hours . The trap answer 5 hours comes from averaging the two times.

Interest: simple vs. compound

Simple interest is I = P × r × t — interest only on the original principal. $1,000 at 5% for 3 years = 1000 × 0.05 × 3 = $150 interest. Compound interest earns interest on interest: A = P(1 + r)ᵗ . The same $1,000 at 5% compounded annually for 3 years = 1000 × 1.05³ ≈ $1,157.63, so about $157.63 interest. On a 29-minute, no-calculator subtest, AR favors simple interest or short compounding (2–3 periods you can multiply by hand).

Ratios, proportions, and unit rates

Set up a proportion and cross-multiply : if 3 filters cost $12, then 7 filters cost x, so 3/12 = 7/x → 3x = 84 → x = $28. A unit rate reduces a quantity to "per one" — 360 miles on 12 gallons = 30 miles per gallon — which makes comparison and scaling trivial.

Averages and weighted averages

Simple average = sum ÷ count. A weighted average multiplies each value by its weight (count or frequency) before summing. If 4 airmen score 90 and 6 score 80, the average is not 85; it is (4×90 + 6×80) ÷ 10 = (360 + 480) ÷ 10 = 84 . Weighting by the larger group pulls the mean toward 80.

Problem family Core formula First move
Percent change (new − old) ÷ old identify the base (old value)
Distance-rate-time d = r × t match units (mph with hours)
Work rate 1/a + 1/b add rates, invert for time
Simple interest P × r × t convert rate to a decimal
Weighted average Σ(value × weight) ÷ Σweight never average the averages

The workflow is identical across families: (1) name the family, (2) write its formula, (3) substitute with unit-checked numbers, (4) solve, (5) confirm the answer matches the quantity asked. Skipping step 5 is the most common reason a confident calculation lands on a distractor.

Two more families worth pre-loading

Mixture problems combine quantities at different concentrations or prices, and they reduce to a weighted total. To mix a 10% saline solution with a 30% solution to get 20 liters of 25%, set up total solute: 0.10x + 0.30(20 − x) = 0.25 × 20. Solve: 0.10x + 6 − 0.30x = 5 → −0.20x = −1 → x = 5 liters of the 10% solution and 15 liters of the 30%. The same setup handles blended coffee prices or alloy compositions.

Basic probability appears as "what is the chance" stems: probability = favorable outcomes ÷ total outcomes. Drawing one defective part from a bin of 3 defective and 17 good is 3 ÷ 20 = 0.15, or 15%. For two independent events both occurring, multiply the probabilities; for either-or with no overlap, add them.

Choosing the formula fast

Stem keyword Family it signals
"% more / % less / discount" percent change
"miles per hour / how long" distance-rate-time
"working together / fills in" work rate
"interest / invested at" simple/compound interest
"average / mean / per" average or weighted average
"mixture / solution / alloy" mixture
"chance / probability / odds" probability

Keep these seven families and their first moves on a single index card. On test day you cannot bring it, but the act of rebuilding the card from memory each morning during prep cements the formulas so that recognition — the slowest step for most candidates — becomes automatic and the 70-second clock stops being the enemy.