GMAT Quant practice at home: percentages, ratios and rates

For GMAT Quant practice at home, the aim is to understand arithmetic well enough to work without a calculator. An AI explanation can help you investigate a mistake after an attempt, but it should not replace the unaided practice the exam demands.

The exercises below are original illustrations of useful arithmetic methods. They are not official GMAT questions, a complete preparation course or a prediction of your score. Use official GMAT preparation resources alongside topic practice.

Can you use a calculator in the GMAT?

No calculator is available in the Quantitative or Verbal sections. Data Insights provides an on-screen calculator. Personal calculators and calculator-enabled devices are not permitted during the GMAT unless specifically approved by GMAC’s Accommodations team.

The GC-1 is therefore for study outside the exam, not for use in a GMAT test-centre or online exam. Check the current official GMAT calculator and note-taking policy. Complete timed Quant practice without AI or a calculator.

Use explanations after you have attempted a question

1. Write down what the question asks and try a manual method.
2. Estimate the answer before doing exact arithmetic. This gives you a way to detect an unreasonable result.
3. If you get stuck, ask AI about a specific step: “Why does a percentage decrease use the new value as its base?” or “Show this calculation with fractions.”
4. Check the explanation against the original wording and your own arithmetic. AI can misread a photo or make a mathematical error.
5. Close the explanation and solve a fresh version without assistance.

Track the reasoning mistake, not just the final answer. A correct answer obtained from an explanation is not yet evidence that you can reproduce the method under time pressure.

Example 1: successive percentage changes

Question: A price of 100 increases by 20%, then the new price decreases by 20%. What is the final price and the overall percentage change?

The increase gives 100 × 1.20 = 120. The decrease is calculated from 120: 120 × 0.80 = 96. Compared with the original 100, the overall change is a 4% decrease.

For a manual method, 20% of 100 is 20, and 20% of 120 is 24. So the two changes are +20 and −24, leaving 96.

Common mistake: assuming equal percentage increases and decreases cancel. They use different base values.

Check: multiply the two change factors: 1.20 × 0.80 = 0.96. The final price is 96% of its original value.

Useful AI prompt: “Explain the difference between the original base and the new base, then verify the result using fractions.”

Retry unaided: a price of 250 rises by 10% and then falls by 10%. Find the final price and the overall percentage change.

Example 2: ratios after adding one component

Question: A 25-litre mixture contains juice and water in the ratio 2:3. Five litres of water are added. What is the new juice-to-water ratio?

There are 2 + 3 = 5 ratio parts. Each is 25 ÷ 5 = 5 litres. Initially there are 10 litres of juice and 15 litres of water. Adding 5 litres of water leaves 10 litres of juice and 20 litres of water. The new ratio is 10:20, which simplifies to 1:2.

Common mistake: adding 5 to the “3” in the original ratio. Ratio parts are not necessarily one litre each; first convert them into quantities.

Check: the new total is 30 litres, and the juice is 10/30 = 1/3 of the mixture. A 1:2 ratio also assigns one of three parts to juice.

Useful AI prompt: “Label the units at every step and explain why adding water changes only one quantity.”

Retry unaided: a 20-litre mixture has juice and water in the ratio 3:2. Add 4 litres of water. Find the new ratio.

Example 3: combine work rates

Question: Machine A completes one job in 6 hours and machine B completes the same job in 3 hours. How long do they take together, assuming constant independent rates with no interference?

Machine A completes 1/6 of a job each hour. Machine B completes 1/3, or 2/6, of a job each hour. Together they complete 3/6 = 1/2 of a job per hour. Time equals work divided by rate: 1 ÷ (1/2) = 2 hours.

Common mistake: averaging the completion times. Add the work rates, not the hours.

Check: in 2 hours, A completes 2/6 = 1/3 of the job and B completes 2/3. Their combined work is exactly one job. Two machines should also finish sooner than either alone under the stated assumptions.

Useful AI prompt: “Explain the units in jobs per hour and verify the result by calculating each machine’s contribution.”

Retry unaided: A takes 4 hours for a job and B takes 12 hours. Under the same assumptions, how long do they take together?

Retry answer key

• Percentages: 247.50, a 1% decrease. The increase produces 275; 10% of 275 is 27.50.
• Ratio: 1:1. The original quantities are 12 litres of juice and 8 litres of water; the addition brings water to 12 litres.
• Rates: 3 hours. The combined rate is 1/4 + 1/12 = 1/3 of a job per hour.

Make the next session an independent check

After studying an explanation, use new numbers and put the help away. Keep a mistake log with the topic, the incorrect assumption and the check that exposed it. Review percentages, ratios and rates separately, then mix them so you must identify the method yourself. These examples cover only a small part of Quant preparation.

Choosing an AI tool for home study

If you want a dedicated device for explanation-led home practice, read our guide to choosing an AI scientific calculator and how camera-based AI explanations should be checked. Verify the actual learning workflow against your needs rather than relying on a promise of better scores.

AI Plus costs and promotional access

3 months of AI Plus are included only with pre-orders placed from 15 November 2026 through 31 December 2026, starting at first activation. Standard purchases from 1 January 2027 exclude AI Plus unless an advertised promotion includes it.

No paid subscription starts automatically when the included months end. Choose a paid AI Plus plan to continue camera solving and AI access. Without a paid plan, the offline scientific functions continue to work.

AI Plus costs €24/month or €216/year in the EU, or £21/month or £189/year in the UK, including VAT. A chosen paid plan renews each billing period until cancelled through your website account. Cancellation stops renewal; access continues until the end of the paid period. Camera solving and AI also require a compatible nano SIM and mobile data plan, supplied by you.

The GC-1 product page explains its development status, mobile-data requirement, AI Plus access and current dispatch estimate. You can join the free waitlist without placing an order or reserving a device. For another exam’s practice routine, see SAT maths practice at home.

GeniCalc is not affiliated with or endorsed by GMAC. GMAT is a trademark of GMAC. Calculator-policy source checked on 1 October 2026.