Most GMAT word problems are easy algebra hidden inside a paragraph. The skill being tested is translation: turning each sentence into an equation, keeping track of what the question actually asks, and knowing when testing the answer choices is faster than algebra. This guide covers the translation rules, a five-step method, the common problem types, five worked examples, and four practice questions.
On the GMAT Focus Edition, word problems appear in Quantitative Reasoning: 21 Problem Solving questions in 45 minutes, five answer choices each, no calculator, and no geometry. GMAC lists word problems (general algebra, profit, percentages, and interest) and ratio problems (mixtures, speed, and work rates) among the section's topics. The GMAT Quantitative Reasoning overview covers the section as a whole.
Translation works phrase by phrase. These are the phrases that carry the math.
| Words | Math | Example |
|---|---|---|
| is, was, will be, equals | = | x is 5 → x = 5 |
| of (with a fraction or percent) | × | 1/3 of x → x/3; 20% of y → 0.2y |
| what, a number, how many | a variable | what number → n |
| more than, greater than, increased by | + | 5 more than x → x + 5 |
| less than, fewer than | − (order reverses) | 3 less than x → x − 3, not 3 − x |
| times, twice, triple | × | twice b → 2b |
| per, for each, ratio of a to b | ÷ | 60 miles per hour → 60 miles / 1 hour; a to b is 3:4 → a/b = 3/4 |
| x percent greater than z | z(1 + x/100) | 30% greater than z → 1.3z |
| x percent less than z | z(1 − x/100) | 25% less than z → 0.75z |
| a exceeds b by c | a − b = c | Maria's age exceeds Leo's by 4 → M − L = 4 |
Steps 3 and 5 take a few seconds and catch many avoidable errors, because GMAT wrong answers are often the right value for the wrong quantity.
| Type | Key relationship | Watch for |
|---|---|---|
| Age | Everyone ages by the same number of years | "In 6 years" adds 6 to every person |
| Percent change | new = old × (1 ± rate) | Successive changes multiply; they don't add |
| Profit | profit = revenue − cost; markup is a percent of cost | Percent of cost vs percent of selling price |
| Mixture | amount of ingredient = concentration × total amount | Add up the ingredient, not the percentages |
| Rate (distance) | distance = rate × time | Average speed = total distance ÷ total time |
| Work | combined rate = sum of individual rates (jobs per hour) | Add rates, never times |
| Averages | sum = average × number of items | Work with sums, then divide |
| Interest | simple interest: I = P × r × t; compound amount: P(1 + r)^t | Compounding periods per year; interest vs total amount |
Percent and profit questions are covered in depth in GMAT arithmetic and percentages, and distance and work questions in the GMAT rate and work problems guide.
Backsolving means plugging the answer choices into the problem. It works best when the choices are specific numbers and the equation would be awkward to set up. GMAT numeric choices are listed in increasing order, so start with the middle choice (C). If it gives a result that is too small, move to the larger choices; if too large, move to the smaller ones. You'll usually finish in one or two tries.
If the choices contain variables or percentages instead of values, pick numbers. Use 100 for percent questions. For variable questions, choose small numbers that satisfy the conditions (and avoid 0 and 1, which make different expressions look equal), compute the target, then test each choice with the same numbers.
| Situation | Usually fastest |
|---|---|
| Specific numeric choices, awkward setup | Backsolve, starting with (C) |
| One unknown, clear translation | Direct algebra |
| Two unknowns, two facts | System of equations (substitution) |
| Percent questions with no starting value | Pick 100 |
| Variables in the answer choices | Pick numbers, test every choice |
Each example is in the Focus Quant format: Problem Solving with five answer choices. Try it before you read the solution.
Worked Example 1 — Age (translation)
Maria is 4 years older than twice her son's age. In 6 years, the sum of their ages will be 58. How old is Maria now?
Solution
Worked Example 2 — Successive percent changes
The price of a product was increased by 20 percent and later decreased by 20 percent. The final price is what percent of the original price?
Solution
Worked Example 3 — Mixture
How many liters of a 40 percent salt solution must be added to 30 liters of a 10 percent salt solution to produce a 20 percent salt solution?
Solution
Worked Example 4 — Work (combined rates)
Pump A can fill a tank in 4 hours, and pump B can fill the same tank in 6 hours. Working together at their constant rates, how long will the two pumps take to fill the empty tank?
Solution
Worked Example 5 — Backsolving
A store sells pens for $3 each and notebooks for $5 each. Lena bought 14 items and paid $54 in total. How many notebooks did she buy?
Solution
Choose an answer, then check it. For more questions across every Quant topic, use the GMAT quantitative practice questions; the formulas behind these problems are collected in the GMAT math formulas cheat sheet.
Name each unknown with a letter and its units, then translate one sentence at a time: "is" becomes =, "of" becomes ×, "more than" adds, "less than" subtracts in reverse order ("3 less than x" is x − 3), and "per" divides. Before solving, write down exactly what the question asks for, because it is often not the variable you defined.
Backsolving means testing the answer choices in the problem instead of writing the algebra. GMAT numeric choices are listed in increasing order, so start with the middle choice (C): if it is too small or too large, you know which direction to move and can often finish in two tries. It works best when the choices are specific numbers and the setup is awkward to write as an equation.
Yes. GMAC lists word problems (general algebra, profit, percentages, and interest) and ratio problems (mixtures, speed, and work rates) among the Quantitative Reasoning topics. All 21 Quant questions are Problem Solving with five answer choices, there is no geometry, and no calculator is allowed. GMAC does not publish how many questions are word problems.
Pick numbers when the answer choices contain variables or percentages rather than specific values. Use 100 for percent questions and small, easy numbers that satisfy the conditions for variable questions, then test each answer choice with the same numbers.