If you've ever read a GMAT® word problem, understood the words, and then gotten the wrong answer, that makes sense.
Most word problem mistakes don't come from the math. The arithmetic is usually fine. The algebra is usually doable. What goes wrong is the step between reading the words and writing the equation — the moment your brain has to translate English into math while also trying to do the math.
That translation step is where a lot of points are lost on the GMAT® Quantitative section. And it's fixable.
This guide covers the full system: how to translate, when to use tables, when to pick numbers instead of algebra, and the trap patterns that show up across every word problem type on the GMAT® Focus Edition.
What Are Word Problems on the GMAT®
Word problems are among the most common questions on the Quantitative Reasoning section. Many Problem Solving questions present a paragraph of prose that describes a situation, followed by five answer choices.
On the GMAT® Focus Edition, the Quantitative Reasoning section has 21 Problem Solving questions in 45 minutes. There's no Data Sufficiency in this section (that's in Data Insights). You get an on-screen calculator in Data Insights but not in Quantitative Reasoning, which means word problem math has to be done by hand or in your head.
Word problems test two things at once:
- Can you translate the words into math?
- Can you execute the math correctly?
Most students focus on #2. Most points are lost on #1.
The word problem types you'll see include:
- Average and total problems
- Pricing and cost problems
- Rate, distance, and time problems
- Percent and commission problems
- Ratio and proportion problems
- Mixture problems
- Work and combined rate problems
- Consecutive integer problems
- Age and relationship problems
You don't need a separate strategy for each type. You need one translation system that works across all of them, plus a few type-specific patterns to recognize.
The Core Method: Half Math, Half English
The system that handles most word problems is an intermediate step between reading and equating. We call it "half math, half English."
Here's how it works:
After you read the problem, write down what's given and what's asked — using a mix of math notation and plain English. Not full equations. Not just English. Something in between.
For an average revenue problem, that might look like:
- 10-day average = $400
- first 6 days average = $360
- last 4 days average = ?
That's not fully math. It's not fully English. It captures the structure of the problem on the page before you try to make equations.
For a commission problem, it might look like:
- salary = $240
- commission = 5% after $800
- total earned = $450
- total sales = ?
The benefit is bandwidth. Short-term memory can hold about seven things at once. Word problems often have more than that. When you try to read, translate, and write equations all at the same time, details slip. Splitting the work into stages — read, capture, then equate — frees up bandwidth at each step.
We cover this method in detail in Episode 43 of our podcast series, and the study guide that goes with it walks through three worked examples. The same framework appears in Episode 32 of our podcast series with different problem types.
If you've been going straight from reading to equations and getting questions wrong, try adding this step. It may feel like it costs time. In practice, it saves time because you're less likely to do correct math on an incorrect setup.
Translation Patterns You Need to Know
Certain words and phrases show up across almost every word problem type. Knowing what they mean in math terms prevents the most common translation errors.
"Per" means division
When a problem says "meters per second" or "dollars per case," that's a fraction. What comes before "per" goes in the numerator. What comes after "per" goes in the denominator.
"$60 per case" becomes
"M meters per S seconds" becomes
This comes up in rate problems, pricing problems, and any situation involving units. If you're not sure how to set up a fraction from a "per" phrase, the word goes on top and the unit goes on the bottom.
"Percent" means divide by 100
"5 percent" is
"5% of total sales" becomes
"Percent change" is the difference divided by the original:
We walk through this one word at a time in our guide to translating percent word problems.
"Times as many" means multiply
"10 times as great" means multiply by 10. "Three times as many as" means multiply by 3.
The trap here is confusing "times as many" with "more than." "Three times as many as X" is 3X. "Three more than X" is X + 3. These look similar in English but produce very different equations.
"Ratio of A to B" means A/B
A ratio of 2 to 3 is
Our guide to GMAT® ratios and word problem translation covers this in more depth.
"Of" usually means multiply
"Half of the students" is
"Greater than" and "less than" set up inequalities or differences
"X is 5 greater than Y" means X = Y + 5. "X is 5 less than Y" means X = Y - 5.
The order matters here. "X is 5 less than Y" puts the subtraction on Y, not on X. This is a common translation error — writing X - 5 = Y instead of X = Y - 5.
Word Problem Types on the GMAT®
Average and Total Problems
The average formula — sum divided by count equals average — comes up in more word problems than almost any other concept.
The formula works in both directions. Given any two of the three quantities, you can solve for the third.
For most average word problems, the missing piece is the sum. You're given an average and a count, and the first step is converting that into a fixed total. That total unlocks the rest of the problem.
Example setup:
- 10-day average = $400
- first 6 days average = $360
- last 4 days average = ?
From here: total revenue = 10 times $400 = $4,000. First 6 days revenue = 6 times $360 = $2,160. Last 4 days revenue = $4,000 - $2,160 = $1,840. Average = $1,840 divided by 4 = $460.
The half math, half English step is where you'd write "10-day average = $400" before jumping to "sum/10 = 400." That intermediate step prevents you from accidentally using 10 as the count for the wrong group.
Pricing Problems: Siloed vs. Tiered
Pricing problems describe a structure where the price per unit changes based on quantity. The trap is assuming the wrong structure.
In siloed pricing, an order's entire price is based on its total size. A 30-case order at $45 per case is 30 times $45. No splitting across brackets.
In tiered (or cumulative) pricing, an order is split across brackets. The first 5 cases cost $60 each, the next 15 cost $50 each, and so on.
GMAT® problems usually describe siloed pricing. But a lot of students default to the tiered interpretation because it's more familiar from real-world experience (tax brackets, utility bills).
The fix is to read the wording carefully and write down which structure the problem describes — in half math, half English — before computing. We walk through a classic example in Episode 43 of our podcast series and the bracket pricing worked solution.
Rate, Distance, and Time Problems
Rate problems use one formula: rate times time equals distance.
rate times time = distance
The most useful organizing tool is a chart with three columns — rate, time, distance — and one row per person or object. Write what you know in each cell. Put question marks where you don't.
If the rate is in meters per second but the time is in minutes, convert to a common unit before multiplying. The cleanest way is to write a fraction with the new unit on top and the unit you want to drop on the bottom:
Multiply the time by that fraction. The old unit cancels. You're left with the unit you need.
We cover this method in Episode 25 of our podcast series, which includes a cyclist distance problem with a unit conversion trap.
Percent and Commission Problems
Percent problems combine translation with algebra. The key is identifying the base — the quantity that the percent applies to.
In a commission problem, the commission might apply to all sales, or only to sales above a threshold. That threshold is the trap.
Example: "5% of total sales that exceed $800."
The commission applies to (total sales - $800), not to total sales. Writing "commission = 5% after $800" in half math, half English forces you to notice that distinction before you write the equation.
Our guide to percent word problems and the fraction system covers the computation side, and our one-word-at-a-time translation guide covers the translation side.
Ratio and Proportion Problems
Ratios give you a relationship between quantities, not the quantities themselves. The standard approach is to introduce a variable for the shared unit.
If the ratio of cats to dogs is 2 to 3 and the total is 40, write:
- cats = 2x
- dogs = 3x
- 2x + 3x = 40
Then solve for x and find each quantity.
The trap is mixing up which number goes with which side of the ratio. Writing "cats = 2x, dogs = 3x" in the half math, half English step prevents that.
Mixture Problems
Mixture problems combine two or more quantities with different concentrations (or prices, or rates) and ask about the result.
The organizing tool is a table:
| Amount | Concentration | Pure Amount | |
|---|---|---|---|
| Solution A | x | 30% | 0.30x |
| Solution B | y | 60% | 0.60y |
| Mixture | x + y | 50% | 0.50(x + y) |
The key relationship: the pure amounts add up. 0.30x + 0.60y = 0.50(x + y).
This same structure works for price mixtures (cheap coffee + expensive coffee = blend), interest mixtures, and any problem that combines two groups with different properties.
Work and Combined Rate Problems
Work problems ask how long it takes to complete a job when multiple workers or machines work together.
The key insight: rates add. If machine A completes a job in 4 hours, its rate is
Time to complete the job together is the reciprocal of the combined rate:
The trap is averaging the times instead of averaging the rates. You can't add 4 and 6 and divide by 2. That gives 5 hours, which is wrong. Rates add — times don't.
We cover work problems in Episode 44 of our podcast series, with three worked solutions.
Consecutive Integer Problems
Consecutive integer problems ask about sets of integers that follow each other in order.
If the problem says "three consecutive integers," write:
- first = x
- second = x + 1
- third = x + 2
If it says "three consecutive even integers," write:
- first = x
- second = x + 2
- third = x + 4
The spacing depends on the type. Consecutive integers step by 1. Consecutive even (or odd) integers step by 2.
The trap is using the wrong step size. Writing it in half math, half English — "consecutive even, step = 2" — prevents that.
When to Use Tables (Rows and Columns)
When a word problem gives you data across three or more categories, a table can help.
A two-column table with categories down one side and the relevant quantity across the other is usually enough. One row per group. Question marks where the value is unknown.
Example: 30 students, some borrowed 0 books, some borrowed 1, some borrowed 2, and the rest borrowed 3 or more. The average is 2 books per student. What's the maximum any single student could have borrowed?
| Students | Books Borrowed |
|---|---|
| 2 | 0 |
| 12 | 12 |
| 10 | 20 |
| 6 | ? |
| 30 total | 60 total |
The table doesn't solve the problem. It keeps the data visible so you can see which pieces are missing and which operations need to happen. On a problem with this many moving parts, that visibility is what prevents you from finishing the math and then realizing you solved for the wrong quantity.
We walk through this exact problem in the library books worked solution from Episode 43 of our podcast series.
When to Pick Numbers Instead of Algebra
Sometimes algebra is the slower, riskier path. When the answer choices contain variables, or when the problem gives you a relationship but no actual numbers, picking numbers can be faster and less error-prone.
Here's the move: replace each variable with a specific number, compute the answer, and check which answer choice matches.
Rules for picking numbers:
- Pick easy numbers. 2, 10, 100. Not 7 or 13.
- Pick numbers that work with the fractions in the problem. If the problem mentions thirds, pick a multiple of 3.
- Pick different numbers for each variable. Don't reuse.
- Avoid 0 and 1 — they can make multiple answer choices look correct.
Picking numbers isn't a shortcut for every problem. It's a tool for problems where the algebra is abstract or the variables make the setup hard to see. We cover this in detail in our guide to when picking numbers beats algebra.
Common Traps on GMAT® Word Problems
The wrong base for a percent
"Percent of X" means the base is X. If the problem says "20% of the remaining amount," the base is the remaining amount — not the original amount. Write down what the percent applies to in the half math, half English step.
Averaging rates instead of times
In rate and work problems, rates add. Times don't. If one train takes 4 hours and another takes 6 hours, the combined time isn't 5 hours. Convert to rates, add the rates, then take the reciprocal.
Mixing up the question
You solve the whole problem, get a number, and it's not in the answer choices. Sometimes the problem asked for the remaining amount and you solved for the total. Write what's asked — with a question mark — in the half math, half English step. Circle it. Check it before you pick an answer.
Unit mismatches
The rate is in meters per second. The time is in minutes. You multiply without converting. The answer is off by a factor of 60. Check that your units match before combining quantities. Write the units in your scratch work — not just the numbers.
Solving for the wrong variable
You need the price per item. You solve for the total price. You need the time. You solve for the distance. This is the most common version of the "mixed up question" trap, and it's why writing what's asked — clearly, in a circle, with a question mark — is worth the three seconds it takes.
How to Practice Word Problems
The most effective practice method for word problems is slow and deliberate at first:
- Pick a word problem from the Official Guide.
- Before solving, write what's given and what's asked in half math, half English.
- Write the equations.
- Solve by hand. Use long multiplication, long division, long addition when needed.
- Check that your answer matches what was asked.
- After finishing, review: did the half math, half English step help? Did you make any translation errors? Did you make any computation errors?
Speed comes from reps. The goal at first is accuracy and habit-building. Once the habit is automatic, speed follows.
If you're looking for practice material, our guide to the best GMAT® study materials covers what's worth using. And our guide to using the Official Guide effectively covers how to get the most out of the single most important resource.
If you keep missing word problems even after building the habit, our guide to breaking through a GMAT® score plateau covers the diagnostic process.
FAQ
What is the most common mistake on GMAT® word problems?
Translation errors. The math is usually correct — the setup is wrong. This happens when students go straight from reading to equations without an intermediate step. The half math, half English method prevents this by splitting the translation and equation-writing into separate stages.
How much time should I spend on the setup vs. the math?
For most word problems, the setup should take about 30-40% of your time. That includes reading, writing what's given and what's asked, and writing the equations. The remaining 60-70% is computation and checking. If you're spending almost all your time on computation and rushing the setup, you're likely losing points to translation errors.
Should I always use algebra for word problems?
No. When the answer choices contain variables, or when the problem gives relationships but no actual numbers, picking numbers can be faster and less error-prone. The key is knowing when each method works best. Algebra is the default. Picking numbers is the alternative for abstract or variable-heavy problems.
Do I need to memorize formulas for word problems?
A few formulas come up often: the average formula (sum/count = average), the rate formula (rate times time = distance), and the work rate formula (combined rate = sum of individual rates). Beyond those, most word problems can be solved with translation and basic arithmetic. You don't need a long list of specialized formulas.
Can I use the on-screen calculator for word problems?
On the GMAT® Focus Edition, the on-screen calculator is available in Data Insights but not in Quantitative Reasoning. For word problems in the Quant section, you'll need to do computation by hand or in your head. Our math basics series covers long multiplication, long division, and long addition if you need to refresh those skills.
What if I'm running out of time on word problems?
Timing on word problems is usually a setup problem, not a speed problem. If your setup is clean — half math, half English, clear equations, labeled variables — the computation tends to go smoothly. If your setup is rushed, you'll often do correct math on the wrong equation, then have to start over. That's what takes the most time. Our guide to GMAT® timing strategy covers pacing for all three sections.
Are word problems on the GRE® too?
Yes. Both the GMAT® and GRE® test word problems in their quantitative sections. The translation system — half math, half English — works on both exams. The main difference is that the GRE® gives you an on-screen calculator for all quantitative sections, while the GMAT® doesn't give you one for Quantitative Reasoning.
Want to Learn Even More?
Listen to the full episodes that cover word problems in detail:
- Episode 43 — Word Problems (half math, half English, average formula, siloed vs. tiered pricing, rows and columns)
- Episode 32 — Word Problems (translation system, elimination method, percent word problems)
- Episode 39 — Translating Percents (one-word-at-a-time translation system)
- Episode 36 — Percent Word Problems (fraction system for percent computation)
Related guides:
- GMAT® Word Problems: Half Math, Half English — the setup system in detail
- GMAT® Word Problems: A Translation System — the full translation framework
- Translating Percent Word Problems — percent translation in depth
- When Picking Numbers Beats Algebra — the alternative approach
- GMAT® Ratios: How to Translate Word Problems — ratio translation in depth
- GMAT® Percent Word Problems: The Fraction System — percent computation in depth
- GMAT® Number Properties: A Complete Guide — the companion guide for number properties questions
- How to Study for the GMAT®: A Complete Guide — the full study system