Ratios & Proportions
A ratio is just a comparison by division, so 3 : 5 carries exactly the same information as the fraction 3/5 — and that single realisation makes the whole chapter easier. The GRE almost never asks a bare "simplify 12 : 18"; instead it hands you a ratio and a real total ("the ratio is 3 : 5 and there are 40 in all") and expects you to move between the two instantly. The other half of the chapter is proportion — two equal ratios — which powers scaling, unit conversion, similar triangles and every "if 4 machines make 240 parts…" question. Because a ratio has no built-in units, it is also the friendliest object on a Quantitative Comparison question: you can often decide which quantity is larger without ever finding a single real value. This chapter builds ratio fluency from the ground up — simplifying and combining ratios, splitting a total, solving proportions, and the direct-versus-inverse variation split that trips up so many test-takers.
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.
- Turn a ratio into "parts": a : b has a + b parts, so one part = total ÷ (a + b). Every share is then one multiply.
- A ratio is a fraction — a : b larger than c : d exactly when a/b > c/d. Cross-multiply (ad vs bc) to compare instantly.
- To combine a : b and b : c, scale each so the shared b matches (use its LCM), then read off a : b : c.
- Decide direct vs inverse by direction: both move the same way ⇒ direct (set ratios equal); opposite ways ⇒ inverse (set products equal).
- For inverse "men and days / speed and time" problems, the product stays constant: just solve x₁y₁ = x₂y₂.
- When only a ratio is given (no total), you can still answer Quantitative Comparison and "what fraction" questions — no real values required.
⚠️ Common mistakes & traps
GRE is designed so that careless errors here cost you marks. Internalise each trap before the exam.
- Reversing the order of a ratio — "A to B is 3 : 5" is not 5 : 3. Keep the wording’s order.
- Comparing ratios with different units without converting first (cm vs m, minutes vs hours).
- Adding ratio parts wrong when a difference (not a total) is given — the difference is (larger − smaller) parts.
- Treating an inverse-variation problem as direct (more workers should mean fewer days, not more).
- Answering the total when the question asked for one share, or vice versa — read the last line carefully.
- Forgetting that scaling both terms by the same number leaves a ratio unchanged (12 : 21 is still 4 : 7).
📈 GRE exam insight & question patterns
Quantitative Comparison — the ratio of a to b is 4 : 9. Quantity A: a/b. Quantity B: 0.5. Which is greater?
Quantity B. a/b = 4/9 ≈ 0.444 < 0.5. A ratio alone settles it — no values needed.
Word problem — $9,600 is divided in the ratio 3 : 5 : 8. What is the largest share?
Parts = 16, one part = 9600/16 = $600, largest = 8 × 600 = $4,800.
Numeric Entry — if 4 machines produce 240 parts in a shift, how many parts do 7 machines produce at the same rate?
Direct variation: 240/4 = 60 per machine, so 7 × 60 = 420 parts.
Inverse setup — 5 workers finish a job in 12 days. How many days for 6 workers?
workers × days = 60, so 6 × d = 60 ⇒ d = 10 days.
🎴 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 Ratios & Proportions 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
Ratio basics
| Ratio as a fraction | a : b = a/b (same information) |
|---|---|
| Scaling a ratio | a : b = ka : kb for any k ≠ 0 |
| Dividing a total in a : b | shares = [a/(a+b)] × T and [b/(a+b)] × T |
| Combining a : b and b : c | make the shared term equal, then read a : b : c |
Proportion & variation
| Proportion (cross-multiply) | a/b = c/d ⇔ a·d = b·c |
|---|---|
| Direct variation | y = kx ⇒ y₁/x₁ = y₂/x₂ (ratio constant) |
| Inverse variation | y = k/x ⇒ x₁y₁ = x₂y₂ (product constant) |
| Mean proportional of a and b | √(ab) |