What This Episode Covers
Three problems from the Official Guide, 11th Edition — each testing a different quant skill, and each with a trap that catches test takers who know the math but slip on setup.
The hit rates tell the story. Problem 107 has a 91% hit rate but the 9% who miss it concentrate on one wrong answer caused by a single transcription error. Problem 108 drops to a 70% hit rate, with 21% picking the same wrong answer because of a forgotten constraint. Problem 110 sits at 77%, with two popular wrong answers that each reveal a different setup mistake.
None of these problems require advanced math. The errors happen in transcription, constraint tracking, and formula setup — not in computation.
Key Takeaways
-
Unify the bases for exponent inequalities. When you see different bases on each side of an equation or inequality, rewrite them to match before doing anything else. Once the bases match, you can ignore them and just compare exponents.
-
"Must be true" means always true, no exceptions. If you can find a single counterexample, the statement doesn't qualify. Start with the easiest Roman numeral to evaluate, prove or disprove it, and eliminate answer choices immediately.
-
All primes greater than 2 are odd. That single fact resolves most prime number property questions on the GMAT®. The sum of two odd numbers is even. The difference of two odd numbers is even. The quotient of two different primes is never an integer.
-
The percent change formula bridges the gap between words and math. Use $\frac{\text{new} - \text{old}}{\text{old}} \times 100$. The formula forces you to identify which value is new and which is old before you do any arithmetic, which prevents the two most common errors on price reduction problems.
-
Write what's asked and all constraints before solving. The single most effective habit across all three problem types. It takes seconds and prevents the transcription errors, forgotten constraints, and misidentified quantities that cause most wrong answers.
Worked Solutions
Full step-by-step walkthroughs for each problem:
- Problem 1: "What Is the Smallest Integer N for Which 25^N Is Greater Than 5^12..." — exponent inequality with base unification
- Problem 2: "If X and Y Are Different Prime Numbers, Each Greater Than 2..." — prime number properties with Roman numeral elimination
- Problem 3: "If Candy Bars That Regularly Sell for 40 Cents Each Are on Sale at Two for 75 Cents..." — percent change formula with sale price
Strategy Article
GMAT® Quant: Three Systems for Exponents, Primes, and Percent Change — the full framework covering base unification, must-be-true elimination with systematic listing, and the percent change formula setup.