GMAT · Section guide 2 · 4 min read
GMAT Quantitative Reasoning: problem solving
What GMAT Focus Quantitative Reasoning tests: 21 problem-solving questions in 45 minutes, arithmetic and algebra only, no calculator and no geometry.
What the section looks like
Quantitative Reasoning has 21 questions in 45 minutes, a little over two minutes per question. Every question is Problem Solving: a question with five answer choices, of which one is correct.
Three facts set the tone for this section:
- No calculator. You work by hand on your notepad or whiteboard.
- No geometry. Lines, angles, triangles, circles and coordinate geometry are no longer tested.
- No Data Sufficiency. That question type has moved to the Data Insights section.
The section is computer adaptive, so the difficulty of each question responds to your performance as you go.
What is tested
The content is high-school level, but the questions test reasoning more than recall. The two broad areas are arithmetic and algebra.
Arithmetic
- properties of integers: factors, multiples, primes, divisibility, odd and even, remainders;
- fractions, decimals and percentages, including percentage change;
- ratios and proportions;
- exponents and roots;
- descriptive statistics: mean, median, mode, range and the idea of standard deviation;
- counting methods, sets and basic probability.
Algebra
- linear and quadratic equations and inequalities;
- simultaneous equations;
- absolute value;
- functions, including unusual symbols defined in the question;
- word problems: rates, work, mixtures, interest, profit and age problems.
Many questions are set in a short business or everyday scenario, but no business knowledge is needed.
How to approach a problem
- Read the whole question and identify exactly what it asks for. Many wrong answers are the right answer to a different question, such as the value of x when the question asks for 2*x*.
- Look at the answer choices. Their form tells you a lot: are they far apart (estimate) or close together (calculate exactly)? Are they in terms of a variable (consider picking numbers)?
- Choose a method, not necessarily the textbook one.
- Check that your answer is reasonable before you confirm it.
Three methods worth mastering
Algebra. Set up equations cleanly and solve them. This is the default for most questions.
Picking numbers. When the choices contain variables or the question says "for any positive integer n", choose simple values that satisfy the conditions, work out the result, and test the choices. Avoid 0 and 1, which can make several choices look correct.
Working backward. When the choices are numbers and the question asks for a single value, plug the choices into the question. Starting with the middle value often tells you whether to go higher or lower.
An example of our own. A shop raises a price by 20% and then lowers the new price by 20%. What is the overall change? Pick 100 as the starting price: 100 becomes 120, then 120 falls by 24 to 96. The overall change is a 4% decrease, not zero.
Mental arithmetic without a calculator
Because there is no calculator, fluency matters. Practice until you can do these quickly:
| Skill | Example |
|---|---|
| Common fraction–percentage equivalents | 1/8 = 12.5%, 3/5 = 60% |
| Squares up to 15 or 20 | 13² = 169 |
| Simplifying before multiplying | Cancel common factors first |
| Estimating | 49 × 21 is close to 1,000 |
| Prime factorization | 360 = 2³ × 3² × 5 |
Common traps
- Answering for the wrong quantity.
- Forgetting that a variable could be negative or a fraction when the question does not say it is a positive integer.
- Treating percentage changes as if they add (as in the example above).
- Overlooking units, for example hours versus minutes in a rate problem.
- Spending five minutes on one question that is worth no more than any other.
Pacing in Quant
With about 2 minutes 8 seconds per question on average, some questions will take 60 seconds and a few will take three minutes. If you have spent around three minutes without a clear path, make an educated guess, bookmark the question, and move on. You can revisit it at the end if time remains, and change your answer using the review and edit feature.
Exam tip: before you start a long calculation, ask whether you can estimate. If the choices are 12, 45, 90, 180 and 400, you rarely need the exact value.
How to practice
Work through each topic untimed until your method is secure, then mix topics in timed sets of 10 or 11 questions in about 22 minutes. Keep an error log noting why you missed each question: content gap, misread, arithmetic slip or time pressure. Most improvement comes from fixing the last three.
Check yourself
- How many questions are in Quantitative Reasoning, and how long do you have?
- Name two things that are no longer tested in this section.
- When is picking numbers a good method, and which numbers should you avoid?
- If a price rises by 10% and then falls by 10%, does it return to its original value?
Find practice material and the rest of this series on the GMAT hub.