GRE Word Problems: Rates, Ratios, Percent, Mixtures, and Work Problems

As of January 2026, the GRE General Test is the shorter format introduced in 2023. You’ll still see the same Quant question types, including many word problems inside Arithmetic, Algebra, Geometry, and Data Analysis. Quant now appears in two timed sections (12 questions in 21 minutes, then 15 in 26 minutes), and an on‑screen calculator is available for Quant only. Word problems remain central to scoring—so a fast, repeatable setup process is essential.

Use this three-step loop: 1) Map: Underline the goal, circle given numbers and units, and list unknowns. Build a tiny table of quantities so you can see relationships at a glance. 2) Model: Write one equation per relationship using standard templates (below). Keep symbols simple and consistent. 3) Check: Verify units, test an extreme case, and ask whether your answer size makes sense before you move on. The goal isn’t elegance; it’s clarity you can execute in under a minute.

Run this quick mental checklist on every word problem:

• Units consistent? Convert early (minutes to hours, inches to feet).
• Quantity conserved? Totals for people, liters, dollars, or pure substance should balance.
• Base identified for percents? “Of what?” decides the base.
• Average defined correctly? Average speed is total distance over total time.
• Work rates added or subtracted? Helpers add; leaks subtract.
• Proportions scaled by a single multiplier? Ratios scale by one k.
• Magnitude check: Try an easy extreme—does the direction of change match intuition?

Setup: Use a Rate–Time–Quantity table. For motion, Q is distance; for production, Q is items; for flow, Q is volume. Core relations: Q = r × t; if two movers head toward each other, gap closed per unit time is r1 + r2; if one chases another, relative rate is |r1 − r2|. Average speed is total distance ÷ total time, not the average of speeds. Example: A car travels 60 miles at 30 mph and then 60 miles at 60 mph. Time = 2 h + 1 h = 3 h; distance = 120 miles; average speed = 120 ÷ 3 = 40 mph. Unit check confirms mph.

Setup: Make a Ratio→Actual table with one multiplier k. If you have two ratios sharing a category, scale them to the same middle term using the least common multiple. Convert part:part to part:whole when needed. Example: The ratio of cats to dogs is 3:5. After adding 8 dogs, the ratio becomes 3:7. Let cats = 3k and dogs = 5k; then 3k : (5k + 8) = 3 : 7 → 21k = 15k + 24 → k = 4 → cats = 12. Sanity: Adding dogs should reduce the cats share; result fits.

Setup: Base × Rate = Amount. For change problems, New = Old × (1 ± r). Successive changes multiply; they do not add. Be precise about language: “x% more than” means multiply by (1 + x%), while “x percentage points more than” shifts a rate by x points. Example: A price rises 25% then drops 20%. Net factor = 1.25 × 0.80 = 1.00 → no net change. Quick check: increase then smaller decrease on a larger base can cancel only if factors multiply to 1.

Setup: Use a three-column table: Volume (or mass), Concentration, Pure amount. Pure = Volume × Concentration. Totals conserve pure substance and volume. Weighted average = total pure ÷ total volume. Example: Make 200 mL of 42% acid by mixing 30% and 50%. Let x be 30% volume; then pure acid is 0.30x + 0.50(200 − x) = 84 → −0.20x = −16 → x = 80 mL. Mix 80 mL of 30% with 120 mL of 50%. Unit and conservation checks both pass.

Setup: Think in jobs per hour. If A alone takes TA hours, then rA = 1/TA jobs per hour. Together, rates add: rTotal = rA + rB + ...; with leaks or interruptions, subtract the opposing rate. Time to finish = 1 ÷ rTotal. Example: A can do a job in 6 h; B in 4 h. rA + rB = 1/6 + 1/4 = 5/12 job per hour, so together they finish in 12/5 = 2.4 hours. Sanity: Faster than either alone but less than 4 hours.

The on‑screen calculator is allowed in Quant, but it’s best for long division, roots, and unwieldy decimals. Prefer mental math or scratch work when you can cancel units, factor common terms, or estimate. Every calculator keystroke has a time cost and error risk. Aim to simplify symbolically first, then compute. If a result should be an integer or a clean fraction, try to spot cancellations before reaching for the calculator.

1. Units sprint: Convert 2.4 hours to minutes; convert 150 inches to feet. 2) Relative-rate reflex: Two walkers 3 mph and 4 mph head toward each other from 10 miles apart; time to meet? 3) Ratio scale: If a:b = 4:7 and b:c = 3:5, what is a:c? 4) Percent base check: Quantity Q is 15% greater than R; express Q in terms of R. 5) Mixture quickie: How many liters of 20% solution to add to 10 L of 50% to get 40%? Keep a 2–3 line scratch structure for each.

• Averaging speeds: Don’t average mph values unless times are equal; use total distance ÷ total time.
• Wrong percent base: “15% of what?” Decide before computing.
• Ratio drift: Changing only one part changes the part:whole ratio; recompute the whole.
• Work rate mis-addition: Never average times; add rates and invert.
• Hidden unit mismatch: Minutes with hours, ounces with liters—convert in the setup so equations stay dimensionally consistent.
• Weighted average misfire: The result must sit between the inputs unless you add negative or zero concentration, which you won’t on the GRE.

Use benchmarks: in Quant Section 1 (21 minutes for 12 questions), check the clock after question 6; you should be near 10–11 minutes. In Section 2 (26 minutes for 15 questions), peek after question 8; aim to be near 13–14 minutes. If you’re 90 seconds behind, guess strategically on the gnarliest Data Interpretation or algebraic grind and re-sync. Finishing every question is better than perfect accuracy on too few.

Start with the diagnostic so the platform flags which word-problem families cost you most time. In Learn, study the short lessons that introduce the tables and templates above. In Solve Together, walk through guided GRE‑style problems where the AI tutor nudges you to name the base, pick the right template (e.g., Rate–Time–Quantity), and run unit checks before solving. In Test Yourself, do timed mini-sets that mirror the 12‑then‑15 question pacing, with or without the on‑screen calculator. As you improve, Exambank adjusts difficulty, regenerates fresh variants of your weak types (say, mixture replacements or catch‑up rates), and builds personalized review sets so the framework becomes automatic.

Days 1–2: Learn and summarize the five templates; create your personal one-page checklist. Days 3–6: Two 20‑minute Quant sprints per day—one on rates/work, one on ratios/percent; end with a 10‑minute error log. Days 7–8: Mixtures focus plus mixed review; one timed 12‑question set. Days 9–12: Full mixed sets in 21 and 26‑minute blocks; practice quick calculator use only when unavoidable. Days 13–14: Two full Quant sections back‑to‑back; review all misses by tagging which checklist item you skipped (units, base, conservation, or template choice). Exambank can schedule and generate each block to the right difficulty and track accuracy by template.

Word problems reward structure, not heroics. If you can map, model, and check in a minute, you’ll convert more questions under the shorter timing. Keep the tables small, the units honest, and the sanity checks constant. When you’re ready to turn these steps into a habit with adaptive practice and guided walkthroughs, Exambank makes it easy to drill exactly what moves your score.