Word Problems & Translation
Most GRE Quant questions do not arrive as equations — they arrive as sentences, and the real skill is translation: turning words into algebra you can solve. The arithmetic is usually easy; the points are won or lost in the setup. Define your variable explicitly ("let n be the number of adult tickets"), convert each phrase into a symbol as you read, and the equation almost writes itself. A quiet but decisive habit is to name the variable for the quantity the question actually asks about, so you are not left solving for the wrong thing at the end. This chapter drills the four highest-frequency families: general word-to-algebra translation, ages and consecutive integers, interest and growth, and the discipline of setting up equations cleanly. Because the on-screen calculator is basic, the winning approach is to model carefully and keep the numbers small — and on many GRE items, plugging in the answer choices or testing smart numbers beats solving from scratch.
Topics
⚡ GRE shortcuts & speed methods
The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.
- Translate as you read: "is" → =, "of" → ×, "more than" → +, "less than" → −, "per" → ÷. Convert each phrase the moment you meet it.
- "Less than" flips the order: "5 less than x" is x − 5, never 5 − x. This single sign trap is the most common translation error.
- For an odd count of consecutive integers, the sum equals the middle term times the count — so three summing to 72 have middle term 24 with no algebra.
- Express two related unknowns with ONE variable (adult a, child = total − a) so you solve one equation instead of a system.
- Compound growth uses the multiplier (1 + r) per period; a decrease uses (1 − r). Chain it for small t rather than reaching for exponent keys.
- With numeric answer choices, back-solve: drop a choice into the original wording and check. It often beats solving forward and dodges algebra slips.
⚠️ Common mistakes & traps
GRE is designed so that careless errors here cost you marks. Internalise each trap before the exam.
- Reversing "less than" or "subtracted from" — the order of the two terms flips.
- Adjusting only one person's age for "in 5 years" instead of every age in the problem.
- Confusing the COUNT of coins with their monetary VALUE in coin problems.
- Solving for the variable but forgetting the question asked for a different expression (e.g. 2x + 1, not x).
- Using compound-interest arithmetic where the problem says simple interest, or vice versa.
- Leaving a rate as a whole number (5 instead of 0.05) inside I = P·r·t or the growth factor.
📈 GRE exam insight & question patterns
A GRE word problem gives numeric answer choices. What is the fastest reliable tactic?
Back-solve: substitute a choice into the original sentence and check whether it fits. Starting from a middle choice narrows it in one or two tries, and it sidesteps setup errors entirely.
Quantitative Comparison — $1,000 invested for 2 years at 8%. Quantity A: value under annual compounding. Quantity B: value under simple interest. Which is greater?
Compound = 1000 × 1.08² = 1166.40; simple = 1000 + 160 = 1160. Quantity A is greater — compounding beats simple beyond one period.
Numeric Entry — the sum of three consecutive integers is 84. Enter the largest.
Middle term = 84/3 = 28, so the integers are 27, 28, 29 and the largest is 29. Use the middle-term shortcut instead of solving 3n + 3 = 84.
A mixture problem asks how much of one component to add. What stays fixed and what changes?
Track the amount of the target substance and the total volume separately: adding pure acid changes both numerator and denominator; adding water changes only the total. Set the new ratio equal to the target percent.
🎴 Flashcards — instant recall
Tap a card to reveal the answer. Drill these until they are automatic.
📌 Quick revision
Chapter test
🏆 Vidaara GRE success checklist
You have truly mastered Word Problems & Translation when you can tick every box below.
- Recall every formula in this chapter without looking them up
- Solve each topic’s practice set with at least 80% accuracy
- Use the chapter shortcuts to cut your solving time in half
- Spot and avoid every common trap listed above
- Score 80%+ on the timed chapter test
📋 Chapter mastery scorecard
Track where you stand. Aim for the target before moving to the next chapter.
| Skill checkpoint | Target |
|---|---|
| Concept theory & formulas understood | 100% |
| Topic practice sets attempted (4 topics) | 4/4 |
| Best topic-test score | — → 80%+ |
| Chapter test score | — → 80%+ |
| Flashcards drilled to instant recall | 8 cards |
Formula Reference Sheet
Translation keywords
| "is" / "was" / "equals" | = |
|---|---|
| "of" (with a fraction/percent) | × |
| "more than" / "sum" / "increased by" | + |
| "less than" / "difference" / "fewer" | − |
| "per" / "for each" / "ratio" | ÷ |
Common models
| Consecutive integers | n, n + 1, n + 2, … |
|---|---|
| Consecutive even/odd | n, n + 2, n + 4, … |
| Simple interest | I = P · r · t |
| Compound growth | A = P (1 + r)ᵗ |
| Age "t years ago/from now" | (current age) ± t |