Build the model before doing the arithmetic
Model percentages, rates and group totals, then use basic integer properties to calculate without a calculator.
The idea
Most arithmetic mistakes start before the calculation: a percentage is applied to the wrong base, an afternoon fraction is treated as part of the original stock, or time is confused with a rate. Name the quantity that stays fixed, write each operation with units, and only then simplify. A model also provides a reasonableness check: a drain makes filling slower; a weighted mean sits between the group means; revenue depends on both price and quantity.
A method to try
- Underline the requested quantity and its unit. Distinguish profit as a share of cost from profit as a share of revenue.
- Name the starting total. For successive percentage changes, multiply the appropriate factors instead of adding percentages that use different bases.
- Convert completion times to work per unit time. Add collaborating rates, subtract opposing rates, then divide remaining work by the net rate.
- Recover totals before combining averages. For mixtures, track the amount of concentrate separately from the total volume.
- Simplify fractions before multiplication. Estimate whether the answer should increase, decrease or lie between known bounds.
- For a remainder, write n = dq + r and substitute it into the requested expression. For powers, rewrite both sides with the same positive base other than 1 before comparing exponents.
- For a positive-divisor count, use prime factors: if N = p^a × q^b for distinct primes p and q, each divisor chooses an exponent from 0 to a and from 0 to b, so there are (a + 1)(b + 1) divisors. For example, 12 = 2² × 3 has 3 × 2 = 6 positive divisors.
- For the optional section timer, 45 minutes over 21 questions averages about 2 minutes 9 seconds each. This is a planning average, not a rule that every item deserves equal time. Review a correct-answer count alongside the reasons for your mistakes.
Follow the reasoning.
A wholesaler pays 200 currency units for a batch, marks it 40% above cost, and offers a 15% discount on the marked price. Find the profit as a percentage of cost.
- Start with the base: cost is 200. The marked price is 200 × 1.40 = 280 currency units.
- A 15% discount leaves 85% of the marked price: 280 × 0.85 = 238. One mental route is 280 − (28 + 14) = 238.
- Profit is 238 − 200 = 38. Relative to cost, the profit percentage is 38/200 × 100% = 19%.
- Check the combined multiplier: 1.40 × 0.85 = 1.19. The result is a 19% gain, not 40% − 15% = 25%. The marked price and cost are different percentage bases.
Think it through first.
Sixteen learners have a mean of 70 and a separate group of eight has a mean of 85. What is their combined mean?
Show the explanation
75.
The group totals are 16 × 70 = 1,120 and 8 × 85 = 680. Divide the total 1,800 by 24 learners to get 75. It is closer to 70 because that group is larger.
Make it your own
Before section A, choose two questions and describe the model without calculating. After your attempt, classify each error as a reading, model, arithmetic or time-management error. This practice permits free navigation and does not reproduce GMAT adaptivity or its review-and-edit limit.
This lesson is one part of a short starter pathway. It does not cover the full exam syllabus or establish a predicted score.
Official references
These provider and publisher links explain the exam or underlying concepts. Our lessons and questions are original, independent practice.
View 4 references and checked dates
- GMAC: exam structure (opens in a new tab)Checked 2026-10-06
- GMAC: exam content (opens in a new tab)Checked 2026-10-06
- GMAC: official preparation (opens in a new tab)Checked 2026-09-20
- GMAC: calculator and note-taking policies (opens in a new tab)Checked 2026-10-06