GMAT Word Problems: Types, Strategies & 10 Worked Examples

Word problems make up a large share of GMAT Quant, and most of them test translation, not hard math. The arithmetic behind a typical rate, percent or mixture question is middle-school level. What costs points is turning a paragraph of business-style text into the right equation, fast, without a calculator.

This guide covers the word problem types you will meet on the GMAT, a repeatable method for solving any of them, the shortcuts top scorers use, and ten worked examples with full solutions.

Where word problems fit in GMAT Quant

The Quantitative Reasoning section gives you 21 questions in 45 minutes, just over two minutes per question. Every question is Problem Solving with five answer choices, and no calculator is allowed. For the full exam structure, see the GMAT exam pattern and question format.

Two changes from the old GMAT matter here:

• Geometry is gone. Quant now covers arithmetic and algebra only, so word problems carry even more weight.
• Data Sufficiency moved to Data Insights. Word problems still appear there in DS form, so the skills in this guide pay off in two sections. The Data Insights guide covers the DS format.

The section is computer-adaptive at the question level. Getting the medium word problems right, quickly, is what unlocks the harder questions that drive a high Quant score. To see how your Quant score combines with the other sections, try the GMAT score calculator.

The 10 types of GMAT word problems

Almost every GMAT word problem falls into one of ten families. Recognize the family in the first read and you already know which formula or setup to reach for.

Most real questions are hybrids. A profit question may hide a ratio, and a probability question may need an overlapping-sets table first.

A 5-step method for any word problem

The same five steps work for every type. They feel slow at first, but they stop the two biggest leaks: solving for the wrong quantity and setting up the wrong equation.

1. Read the question stem first. Find exactly what is asked: the number of girls, not the number of students; the percent change, not the final price. Write it down.
2. Identify the type. Rate, work, percent, mixture and so on. This tells you the core relationship.
3. Define variables and units. Use letters that mean something (b for boys, t for time). Convert units now: minutes to hours, cents to dollars.
4. Translate, then pick a method. Turn each sentence into math. Then decide: solve algebraically, pick numbers, backsolve from the choices, or estimate.
5. Check against the question. Does your answer match what was asked, in the right units? Is it plausible?

Translating English into math

Four strategies that save time

Algebra always works, but it is not always the fastest route. Strong test-takers choose the method after reading the answer choices.

Picking numbers. Use it when the answer choices contain variables or when the problem gives only percents or fractions. Choose simple values (100 for a price, 10 for a count), compute the target, then test each choice. If two choices match, pick new numbers and test only those two.

Backsolving. Use it when the choices are plain numbers and the question asks for one specific value. Start with the middle choice (C). If it is too big, move to the smaller choices; if too small, move up. You rarely need more than two tries.

Estimation. Use it when the choices are spread far apart. Round 49.6% to 50% and 1,987 to 2,000, and eliminate anything clearly out of range. With no calculator, this is often the biggest time saver in the section.

Alligation (the balance method). Use it for any mixture or weighted-average question. The final average sits closer to the larger group, and the distances to each value are in inverse ratio to the group sizes. Example 6 below shows it in action.

10 worked examples with solutions

Try each question before reading the solution. Time yourself: aim for under 2 minutes each.

Example 1: Average speed (rates)

A car travels from Town A to Town B at 40 miles per hour and returns along the same road at 60 miles per hour. What is the average speed for the whole round trip, in miles per hour?

(A) 45 (B) 48 (C) 50 (D) 52 (E) 55

Solution. Average speed is total distance divided by total time, not the average of the two speeds. Pick a convenient distance: 120 miles each way. The trip out takes 120 / 40 = 3 hours, the trip back takes 120 / 60 = 2 hours. Total: 240 miles in 5 hours, so 48 mph.

Answer: (B). Choice (C), 50, is the trap: it averages the speeds and ignores that the car spends more time at the slower speed.

Example 2: Combined work

Machine A can complete a job in 6 hours and Machine B can complete the same job in 4 hours. Both machines start working together, but after 1 hour Machine A breaks down. How long will Machine B need to finish the job alone?

(A) 1 hour 40 minutes (B) 2 hours (C) 2 hours 20 minutes (D) 2 hours 30 minutes (E) 3 hours

Solution. Work with rates, in jobs per hour. A does 1/6, B does 1/4, together 1/6 + 1/4 = 5/12. After 1 hour, 5/12 of the job is done and 7/12 remains. B alone needs (7/12) ÷ (1/4) = 7/3 hours = 2 hours 20 minutes.

Answer: (C). Rates add; times never do.

Example 3: Successive percent changes

A store raises the price of a jacket by 25%. During a sale, it discounts the new price by x%, and the sale price ends up 10% above the original price. What is x?

(A) 10 (B) 12 (C) 15 (D) 20 (E) 25

Solution. Pick an original price of $100. After the increase, it is $125. The sale price is $110. The discount is $15 on a base of $125: 15 / 125 = 12%.

Answer: (B). The trap is (C), 15, which treats the $15 as a percent of the original $100. Always divide by the price the discount applies to.

Example 4: Changing ratio

In a class, the ratio of boys to girls is 3 to 5. After 6 more boys join the class, the ratio becomes 3 to 4. How many girls are in the class?

(A) 24 (B) 32 (C) 40 (D) 48 (E) 56

Solution. Let boys = 3k and girls = 5k. After the change: (3k + 6) / 5k = 3/4. Cross-multiply: 12k + 24 = 15k, so k = 8. Girls = 5 × 8 = 40. Check: 24 + 6 = 30 boys, and 30 : 40 = 3 : 4.

Answer: (C). A 10-second shortcut: girls = 5k, so the answer must be a multiple of 5, and 40 is the only choice that is.

Example 5: Averages

The average score of 8 students on a test is 75. When a ninth student takes the test, the average for all 9 students rises to 77. What did the ninth student score?

(A) 77 (B) 85 (C) 89 (D) 93 (E) 95

Solution. Use sums, not averages. The first 8 scores total 8 × 75 = 600. All 9 total 9 × 77 = 693. The new score is 693 − 600 = 93.

Shortcut: the new student must cover their own 77 plus lift each of the other 8 students by 2 points: 77 + 8 × 2 = 93.

Answer: (D).

Example 6: Mixtures

Solution A is 20% alcohol and Solution B is 50% alcohol. How many liters of Solution B must be added to 30 liters of Solution A to produce a mixture that is 30% alcohol?

(A) 10 (B) 12 (C) 15 (D) 20 (E) 25

Solution (algebra). Alcohol in equals alcohol out: 0.2 × 30 + 0.5x = 0.3(30 + x). So 6 + 0.5x = 9 + 0.3x, which gives 0.2x = 3 and x = 15.

Solution (alligation). The target of 30% is 10 points from A and 20 points from B. The amounts are in the inverse ratio: A : B = 20 : 10 = 2 : 1. With 30 liters of A, you need 15 liters of B.

Answer: (C).

Example 7: Overlapping sets

A company has 120 employees. Of these, 70 speak English, 45 speak French, and 20 speak neither language. How many employees speak both English and French?

(A) 5 (B) 10 (C) 15 (D) 20 (E) 25

Solution. Use the two-set formula: Total = Group 1 + Group 2 − Both + Neither. So 120 = 70 + 45 − Both + 20, which gives Both = 15.

Answer: (C). For harder versions, draw a 2×2 table (English / not English vs French / not French) and fill the cells; the missing one usually falls out.

Example 8: Simple vs compound interest

An investor deposits $5,000 for one year at an annual interest rate of 10%. How much more will the investment earn if interest is compounded semiannually rather than calculated as simple interest?

(A) $0 (B) $12.50 (C) $25 (D) $50 (E) $125

Solution. Simple interest: 5,000 × 0.10 = $500. Semiannual compounding means 5% every six months. After 6 months: $5,250. After 12 months: 5,250 × 1.05 = $5,512.50, so $512.50 of interest. Difference: $12.50.

Shortcut: the only extra money is interest on the first $250 of interest: 250 × 0.05 = $12.50.

Answer: (B).

Example 9: Probability with "at least one"

A committee of 3 people is chosen at random from 5 men and 4 women. What is the probability that the committee includes at least one woman?

(A) 5/42 (B) 10/21 (C) 37/42 (D) 5/6 (E) 41/42

Solution. "At least one" means use the complement: 1 − P(no women). Total committees: C(9,3) = 84. All-male committees: C(5,3) = 10. So P = 1 − 10/84 = 74/84 = 37/42.

Answer: (C). Counting the 1-, 2- and 3-woman cases directly also works, but it takes three calculations instead of one.

Example 10: Variables in the answers (picking numbers)

Jane buys x pencils at y cents each and pays with a $10 bill. How much change, in dollars, should she receive?

(A) 10 − xy (B) 10 − 100xy (C) (1,000 − xy) / 100 (D) 1,000 − xy (E) 10 − xy/10

Solution. Pick x = 10 and y = 50. Ten pencils at 50 cents cost 500 cents, or $5, so the change is $5. Now test the choices: only (C) gives (1,000 − 500) / 100 = 5.

Answer: (C). Algebraically, xy cents is xy/100 dollars, and 10 − xy/100 = (1,000 − xy) / 100. Picking numbers avoids the unit-conversion slip that leads to (A).

Common traps and timing advice

GMAT wrong answers are not random. Each one is built from a predictable mistake, and these six cause most of them:

• Answering a different question. You find the number of boys when the question asks for girls. Re-read the stem before you click.
• Averaging rates. Average speed and combined work never come from a simple average of the two rates (Examples 1 and 2).
• The wrong percent base. A percent change is always measured from the starting value of that step (Example 3).
• Unit mismatches. Minutes vs hours, cents vs dollars, percent vs decimal. Convert in step 3 of the method, not at the end.
• Order flips. "5 less than x" is x − 5, not 5 − x.
• Overcounting overlaps. In sets questions, people in both groups get counted twice unless you subtract them once.

On timing, you have just over two minutes per question. If you have no setup after 60 seconds, eliminate what you can, make an educated guess and move on. A single 5-minute question costs you more than one wrong answer, because it steals time from questions you could have solved.

Formula cheat sheet

These formulas cover the core of every type above. Memorize them so your time goes into setup, not recall.

Frequently asked questions

How many word problems are on GMAT Quant?

There is no fixed number, and the mix depends on the adaptive path. In practice, a large share of the 21 questions are word problems; the rest are pure algebra and arithmetic.

Can I use a calculator?

No. The Quant section has no calculator, which is why estimation and clean arithmetic setups matter so much. An on-screen calculator is available only in Data Insights.

Are word problems easier than pure algebra?

The math is usually simpler, but the reading load is higher. Most errors come from setup, not calculation, so practice translating as much as solving.

What is the best way to practice?

Drill one type at a time until the setup feels automatic, then switch to mixed, timed sets of 10 to 20 questions. After each set, review every miss and label the cause: wrong type, wrong setup, arithmetic slip or time. The labels show you what to fix next. Our Quantitative Reasoning guide covers the other Quant topics, and how to measure your GMAT prep progress explains how to track these labels over time.

Practice word problems on Examero

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