GMAT Quant no longer tests geometry. What is left is a short list of arithmetic and algebra formulas. Here they are, with tricks to make them stick.
The Good News: The List Got Shorter
The GMAT Quantitative Reasoning section is now 21 Problem Solving questions on arithmetic and elementary algebra, with no calculator. Geometry is no longer tested, so circle, triangle and coordinate geometry formulas are off the list.
What remains is short. You need every formula below cold, so you can recall it mid-question without slowing down. The hard part of GMAT Quant is not the formulas. It is applying them quickly, without a calculator, while avoiding the traps.
Percentages
Percent change — (new − old) ÷ old × 100. Memory trick: "change over original."Successive changes — multiply the factors, never add the percentages. A 20% rise then a 20% fall is 1.2 × 0.8 = 0.96, a 4% fall overall.Reverse percentages — if a price after a 25% increase is 150, the original is 150 ÷ 1.25 = 120. Divide by the multiplier; do not subtract 25%.Interest
Simple interest — principal × rate × time.Compound interest — principal × (1 + rate)^time. For any period longer than one, compound interest is larger than simple interest, which is often enough to eliminate answer choices without calculating.Rates and Work
Distance = rate × time — remember it as D = RT, "the DIRT formula."Average speed — total distance ÷ total time. Never average the two speeds. For equal distances at speeds a and b, the average speed is 2ab ÷ (a + b).Relative speed — moving towards each other, add the speeds; moving the same way, subtract them.Combined work — add the rates, not the times: 1/T = 1/A + 1/B. Two people who take 3 and 6 hours alone take 2 hours together.Ratios and Mixtures
Weighted average — (w1 × x1 + w2 × x2) ÷ (w1 + w2). Memory trick: the average always sits closer to the bigger group.Mixtures — concentration × volume = amount of the pure substance. Track the pure substance and the question usually solves itself.Algebra
Special products — (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², and a² − b² = (a + b)(a − b).Difference of squares in disguise — 99 × 101 = (100 − 1)(100 + 1) = 10,000 − 1. Look for it whenever two numbers sit evenly around a round number.Quadratics — for ax² + bx + c = 0, the roots add to −b/a and multiply to c/a. This often answers the question without finding the roots.Arithmetic sequences — nth term = a + (n − 1)d. Sum = number of terms × (first + last) ÷ 2. Memory trick: the average of an evenly spaced list is the average of its first and last terms.Geometric sequences — nth term = a × r^(n − 1).Exponents and Roots
Exponent rules — x^a × x^b = x^(a + b), (x^a)^b = x^(ab), x^(−a) = 1 ÷ x^a, and x^0 = 1.Roots — √(ab) = √a × √b, but √(a + b) is not √a + √b. Memory trick: roots split over multiplication, never over addition.Numbers to memorise — squares to 20², cubes to 10³, powers of 2 to 2^10, and √2 ≈ 1.41, √3 ≈ 1.73. Without a calculator, these save real time.Number Properties
Number of factors — write the prime factorisation, add 1 to each exponent and multiply. 72 = 2³ × 3², so it has (3 + 1)(2 + 1) = 12 factors.LCM and GCD — for two numbers, LCM × GCD = the product of the numbers.Divisibility — a number is divisible by 3 or 9 when its digit sum is; by 4 when its last two digits are.Statistics and Counting
Mean — sum ÷ count. The useful form is usually the rearranged one: sum = mean × count.Standard deviation — you will rarely calculate it. Know the behaviour: adding the same number to every value leaves it unchanged, multiplying every value by k multiplies it by k, and spreading values out increases it.Permutations and combinations — arrangements: n! ÷ (n − r)!. Selections: n! ÷ (r! × (n − r)!). Memory trick: ask "does order matter?" If yes, it is a permutation.Probability — favourable outcomes ÷ total outcomes. Multiply for independent events. For "at least one," use 1 − P(none).Using myExamRoutine to Lock These In
The note field on every subtopic is your personal formula sheet. Add each formula to the subtopic it belongs to, in your own words, with one example you worked yourself.
Before each Quant session, reread the notes for the subtopics you are about to practise. Then log your practice in the subtopic's Practice tab, so you can see which formulas you know and which you only recognise.
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