What This Episode Covers
Episode 31 of Real GMAT® Problems works through three Official Guide problems that look straightforward on the surface but carry surprisingly high miss rates. The thread connecting them: each question punishes people who rush past the setup and jump straight into computation. Percent calculations, exponent rules, repeating decimals, and fraction optimization all make appearances — and on every problem, the biggest trap is not a content gap but a process gap.
The episode also explores when it is worth practicing multiple solution approaches on the same problem versus just picking one reliable method. The general guidance: if you are aiming below 645, one solid approach per question type is enough. Above that, practicing pivots between approaches on the same problem builds the flexibility needed for harder questions.
Problems Covered
Problem 1 — Warm-Up: 500 Workers, 15% Women, Hire 50 More A factory has 500 workers, 15% of whom are women. If 50 additional workers are hired and all present workers remain, how many must be women to raise the percentage to 20%? The step-by-step logical approach: 15% of 500 = 75 women now. After hiring, there will be 550 workers total, and 20% of 550 = 110. So 110 − 75 = 35 additional women needed. Answer: E. No major trap answer — most errors come from computation mistakes. The episode emphasizes doing percent calculations as fractions (e.g., 15/100 × 500) to reduce decimal errors.
Problem 2 — Mid-Level: (10⁴ − 10²) × 0.0012̄ A bar over "12" means the digits repeat indefinitely: 0.001212121212... About 25% of test-takers miss this one. The critical trap: 12% pick B because they incorrectly simplify 10⁴ − 10² as 10². The rule: never use exponent shortcut rules (adding/subtracting exponents) when the operation between the terms is addition or subtraction. Those rules only apply to multiplication and division. 10⁴ − 10² = 10,000 − 100 = 9,900, not 100. The correct path: distribute the repeating decimal into the parentheses. 10⁴ × 0.0012̄ = 12.1212... and 10² × 0.0012̄ = 0.1212... Subtract to get 12. Answer: E.
Problem 3 — Harder: Cindy's Miles Per Gallon with Rounding Cindy drove 290 miles (rounded to nearest 10) and used 12 gallons (rounded to nearest gallon). The actual miles per gallon must be between which values? 30% miss this one. The key insight: to find the true range of a fraction with rounded values, minimum fraction = minimum numerator ÷ maximum denominator and maximum fraction = maximum numerator ÷ minimum denominator. The trap (15% pick E) is dividing maximum distance by maximum gallons — that gives a middle value, not an endpoint. Also important: "between" on the GMAT® excludes the endpoints, so the boundaries are 285 and 295 for miles, 11.5 and 12.5 for gallons. Answer: D (285/12.5 to 295/11.5).
Key Takeaways
- Do percent calculations as fractions. Writing 15/100 × 500 instead of 0.15 × 500 lets you cancel visually and reduces decimal arithmetic errors.
- Never use exponent shortcuts on addition or subtraction. 10⁴ − 10² ≠ 10². Just compute the actual values. Reserve rules like "same base, add exponents" for multiplication and division only.
- "Between" on the GMAT® excludes endpoints. If a problem says "between 290 and 295," neither 290 nor 295 is included. Watch for "inclusive" as the exception.
- To find the range of a fraction with rounded inputs: min fraction = min numerator ÷ max denominator; max fraction = max numerator ÷ min denominator. Do not divide max by max — that gives a middle value.
- Practice multiple approaches on problems that support them. Especially above 645 target scores, the ability to pivot mid-problem is what separates the 80th percentile from the 85th+ in quant.
- Simple-looking problems deserve full vigilance. The easiest-looking problem in this set (Problem 3) has the highest miss rate at 30%.
Related Reading
- Real GMAT® Problems - Ep. 35 - Plugging In Answers — another episode focused on using answer choices strategically
- Real GMAT® Problems — Ep. 36 — Percent Word Problems — builds directly on the percent computation foundations from this episode