GRE Algebra Word Problems

By Muntasir Jul 29, 2026 9 min read

TL;DR

GRE word problems fall under the Algebra content area inside GRE Quantitative Reasoning, alongside Arithmetic, Geometry and Data Analysis. The skill tested is not harder math, it is turning a sentence into an equation. Read the problem, name the unknown with a variable, translate keywords such as sum, product and is into symbols, then solve and check the result against the original sentence. The official GRE Math Review builds this skill through average, mixture, rate, work, system-of-equations and interest examples. It does not include a named age-problem example, so treat age and comparison questions as the same translation skill applied to a different story. The setup step is where wrong answers start, so check your result against the original sentences.

Word problems show up across the GRE Algebra content area, one of the four content areas inside GRE Quantitative Reasoning alongside Arithmetic, Geometry and Data Analysis. The official ETS Math Review devotes its Applications section to exactly this skill: turning a sentence into a solvable equation. The section runs through averages, mixtures, rates, work, two-variable systems and interest, all written as short stories instead of bare equations. Every one of them asks you to do the same thing first: decide what the unknown is and write a relationship for it.

The math itself, once set up, is rarely hard. The setup step is where wrong answers start: a misread word flips a plus into a minus, or two quantities swap places. A translation error survives every algebra step after it, so the arithmetic stays clean while the answer stays wrong. This guide breaks the process into a repeatable method, covers the problem types ETS names explicitly, and lists the misreads behind wrong setups.

How to Translate a Word Problem into an Equation

Every GRE word problem hides one or more unknown quantities inside plain sentences. Your first job is to name each unknown with a variable before you write anything else. Naming forces you to state the question in your own words, and the equation follows from the naming. Write the definition down, for example "x is the number of liters added", so the meaning of your variable stays fixed while you solve.

Keywords Mapping to Math Operations

ETS writes these problems in ordinary English, so specific words signal specific operations. Learn this mapping and you convert sentences into symbols without hesitation.

Word or phrase	Operation	Example phrase
Sum, total, increased by, more than	Addition	a number increased by 7
Difference, less than, decreased by, fewer	Subtraction	5 less than a number
Product, times, of, twice	Multiplication	twice a number
Quotient, per, divided by, ratio of	Division	a number divided by 4
Is, was, equals, results in	Equals sign	the total is 40

A Repeatable Translation Process

Apply the same sequence to every problem instead of guessing at a setup. The order matters most under time pressure, when skipping the first read is tempting.

Read the full problem once before writing anything.
Identify what question is being asked and name the unknown with a variable.
Underline or note every number and every keyword from the table above.
Write one equation per sentence or per relationship described.
Solve the equation using standard algebra steps.
Check the solved value against the original sentence, not only the equation.

Once your equation is written, solving it is a matter of standard algebra: isolating the variable, combining like terms and handling any inequalities or exponents. Keep the two stages separate in your head, because a setup error and an algebra error need different fixes. Our guide to GRE equations, inequalities and functions covers the manipulation stage in depth. Return to translation work once the manipulation feels automatic.

Rate, Work and Mixture Problem Setups

The ETS Math Review names average, mixture, rate and work problems as a distinct group inside the Applications section, with worked examples covering an exam-score average, a vinegar-and-oil mixture, a driving-rate scenario and a machine work-rate scenario. Each type has its own core equation, and knowing the equation before you read the story cuts your setup time. Read the story once to decide the type, then fill the known values into the matching formula. The subsections below give the formula and an original worked example for each.

Rate and Distance Problems

Rate problems connect distance, rate and time with one formula. The variations come from how many moving objects the story describes.

Distance equals rate multiplied by time: d = rt.
When two objects move toward each other, add their rates to find the combined closing rate.
When one object chases another, subtract the slower rate from the faster rate.

Original example: a train leaves a station traveling at 60 miles per hour. A second train leaves the same station one hour later on the same track at 75 miles per hour. Set t as the time the second train travels, and the first train has traveled t + 1 hours by the time it is caught. The trains meet when 60(t + 1) = 75t, so 60t + 60 = 75t, giving t = 4 hours.

Work Problems

Work problems use rate of work, not rate of travel. A worker or machine finishing a job in n hours completes 1/n of the job per hour. Add the individual rates to get the combined rate, then take the reciprocal of the combined rate to get the total time. The frequent error here is adding the times instead of the rates, which produces a total longer than either worker takes alone.

Original example: one printer finishes a print run in 6 hours working alone, and a second printer finishes the same run in 3 hours working alone. Convert each one to a rate: 1/6 of the run per hour and 1/3 of the run per hour. Working together, their combined rate is 1/6 + 1/3 = 1/2 of the job per hour, so the job takes 2 hours. The total lands below the faster printer's own time, which is the sanity check for every work problem.

Mixture Problems

Mixture problems combine two quantities with different concentrations into one blend. Multiply each quantity by its percent concentration, add the results, then set the sum equal to the concentration of the final mixture times its total amount. The total amount of the blend is the sum of the two starting amounts, so the variable appears on both sides of the equation. Writing the final side as a single product keeps the whole setup to one unknown.

Original example: how many liters of a 40 percent salt solution must be added to 10 liters of a 10 percent salt solution to produce a 25 percent solution? Let x be the liters of the 40 percent solution. Then 0.40x + 0.10(10) = 0.25(x + 10), which solves to x = 10 liters.

Systems of Equations and Interest Problems

The same Applications section also covers two-variable systems and interest formulas. A classic setup gives the total count of two items and their combined cost, then asks for the price or quantity of each. Two unknowns need two equations, one for the counts and one for the money, solved together by substitution or elimination. Label both variables in writing before you build either equation.

For interest word problems, ETS gives two formulas directly: simple interest as V = P(1 + rt/100) and compound interest as V = P(1 + r/100)^t, where P is the principal, r is the annual percent rate and t is time in years. Scan the problem for the word compound before choosing between them. Percent-based setups like these overlap with our guide to GRE percents, ratios and proportions.

Age and Comparison Word Problems

Age and comparison problems describe two or more quantities at different points in time or in relation to each other, then ask you to solve for one of them. The official Math Review does not include a named age-problem example, and ETS states directly its review is not all-inclusive, so treat these as the same translation skill from the sections above applied to a different story. Anchor every age to one moment, usually the present, and write past and future ages as the anchor plus or minus a number of years. A quick grid with one row per person and one column per time point keeps the bookkeeping straight.

Original example: a parent is currently three times as old as their child. In 10 years, the parent will be twice as old as the child. Let c stand for the child's current age. The parent's current age is 3c, so in 10 years: 3c + 10 = 2(c + 10). Solving gives c = 10, so the child is 10 and the parent is 30.

Comparison problems follow the same pattern with relation in place of time. Assign a variable to one quantity, write the second quantity in terms of the first, then use the stated relationship to build the equation. Pick the smaller or simpler quantity as your variable, because the other side then reads as a multiple or a sum instead of a fraction. Once solved, map the value back to the named quantity the question asked about.

Common Misreads Behind Wrong Setups

Wrong setups come from a short list of repeated misreads. Learn the five below and check your equation against them before you solve.

Misread	What goes wrong	Fix
"Less than" reversed	"5 less than x" gets written as 5 - x instead of x - 5	Rewrite the phrase in x = form before translating
Wrong reference point for age	Adding years to only one person's age, not both	Apply the same time shift to every person in the problem
Percent of a changed amount	Applying a percent to the original amount instead of the new one	Identify which amount the percent is applied to before writing the equation
Rate units mismatched	Mixing hours and minutes, or miles and feet, in one equation	Convert every quantity to the same unit first
Total confused with one part	Setting a partial quantity equal to the stated total	Re-read what the final sentence asks for

Checking Your Answer Against the Original Problem

A solved equation is not the same as a correct answer. Check your result against the question the problem asked, not against the equation you wrote. Answer choices often include the value produced by a common misread, so seeing your number in the list is no confirmation of a correct setup. Run the same short review every time before you select a choice.

Substitute your answer back into the original sentence, not the equation, and confirm it makes sense in context.
Check units: an age, a distance and a percent each need to land on a sensible value.
Check the question again. Some problems solve for a variable other than the value being asked for.
Estimate before you solve. If your answer is far from a rough estimate, recheck the setup.

Practice builds the pattern recognition this section rewards. We offer three difficulty levels of free algebra word-problem drills, easy, medium and hard, each with instant explanations and no signup required. For full-length timed practice, visit our GRE exam page.