What This Episode Covers
Episode 36 of Real GMAT® Problems tackles percent word problems — the single most common question type on the GMAT® quant section. The three problems build in complexity: a markup-then-discount calculation, a concentration problem where water evaporates and changes the percentage, and a reverse-percent problem where you know the result of an increase but need to find the original value.
A running theme is the value of "half math, half English" notation — writing intermediate steps that mix numbers and plain words (e.g., "500 gallons sodium chloride" as a numerator) before converting to pure equations. This intermediate step captures the logic of the problem and prevents the common trap of doing correct math on an incorrect setup.
The episode also includes a discussion on effort and fatigue management during study sessions, drawing on a Michael Jordan quote: "I can accept losing — but I can't accept not trying."
Problems Covered
Problem 1 — Warm-Up: 20% Markup, Then 10% Employee Discount A video recorder has a $200 wholesale cost. The store marks it up 20%, then an employee applies a 10% discount. How much does the employee pay? Step-by-step: 120/100 × 200 = $240 retail price. 10% of 240 = $24 discount. 240 − 24 = $216. Answer: B. No major trap answer — errors here come from decimal computation mistakes. The episode recommends doing percent calculations as fractions and memorizing times tables through 20 for speed.
Problem 2 — Mid-Level: Evaporation Changes Concentration A 10,000-gallon tank is 5% sodium chloride. 2,500 gallons of water evaporate. What percent sodium chloride is the remaining solution? About 18% miss this one. The correct approach: 5% of 10,000 = 500 gallons of sodium chloride (this does not evaporate — only water does). Remaining total: 7,500 gallons. New percentage: 500/7,500 = 1/15 ≈ 6.67%. Answer: D. The 8% trap answer is B (3.75%) — people assume the sodium chloride scales down by the same 25% as the water, which sounds clever but misreads the problem. The fix: write what is given and asked using half-math-half-English notation before doing any computation.
Problem 3 — Harder: Reverse Percent — Find the Original Value HMO enrollment increased 15% from 1991 to 1993. The 1993 enrollment was 45 million. What was the 1991 enrollment (to the nearest million)? About 26% miss this one. Setup: 115/100 × X = 45. Solve: X = 45 × 100/115 = 45 × 20/23 = 900/23. Long division gives ≈ 39.13, which rounds to 39. Answer: B. The trap: 13% pick A (38) and 9% pick C (40) — both are off-by-one errors from imprecise estimation or computation mistakes. When answer choices are only 1 apart, estimation is risky — commit to precise long division.
Key Takeaways
- Percent word problems are the most common quant question type. Invest in a reliable computation method — fractions are recommended over decimals for most people.
- Use half-math-half-English notation as an intermediate step. Write "sodium chloride / total remaining water" before converting to numbers. This captures the logic and prevents solving the wrong equation.
- Label units as you compute. Writing "500 gallons NaCl" instead of just "500" prevents losing track of what each number represents mid-problem.
- Check answer spacing before deciding to estimate. If answers are 1 apart (38, 39, 40, 41, 42), use precise computation. If answers are far apart, aggressive estimation is safe.
- A reverse percent is not the same as subtracting the percent. If something increased 15% to reach 45 million, the original is not 45 − 15% of 45. It is 45 ÷ 1.15. This is one of the most common percent traps on the exam.
- Finish strong. If you started a problem with good execution, force yourself to maintain quality all the way through — especially on the last computation step, which is where fatigue errors concentrate.
Related Reading
- Real GMAT® Problems — Ep. 37 — Divisibility Shortcuts — continues the series with divisibility rules and organized scratch work
- Real GMAT® Problems — Ep. 31 — Percents, Exponents, and Rounding — earlier episode covering percent computation foundations and exponent traps
- Real GMAT® Problems - Ep. 39 - Translating Percents — more advanced percent translation problems