GMAT Quantitative: GMAT Quantitative: Word Problems Practice Questions
Test yourself on GMAT Quantitative: Word Problems with 10 original GMAT practice questions. Pick an answer to see instant feedback and a full explanation.
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1. A train travels 240 miles at a constant speed. If the speed had been 10 mph faster, the trip would have taken 1 hour less. What was the original speed?
Explanation. Let original speed = r. Time = 240/r. At r+10, time = 240/(r+10) = 240/r − 1. Multiply: 240/(r+10) = (240−r)/r. Cross-multiply: 240r = (240−r)(r+10) = 240r + 2400 − r² − 10r. So 0 = 2400 − r² − 10r, giving r² + 10r − 2400 = 0, (r+50)(r−40)=0, r=40.
2. A mixture of 40 liters contains alcohol and water in the ratio 3:1. How much water must be added to make the ratio 3:2?
Explanation. Original: alcohol = 30 L, water = 10 L. Alcohol stays 30. New ratio 3:2 means water = (2/3)(30) = 20 L. Water added = 20 − 10 = 10 L.
3. Working together, pumps A and B fill a tank in 4 hours. Pump A alone takes 6 hours. How long does pump B alone take?
Explanation. Combined rate = 1/4 per hour. A's rate = 1/6. B's rate = 1/4 − 1/6 = 3/12 − 2/12 = 1/12. So B takes 12 hours.
4. A store marks up an item by 50% over cost, then offers a 20% discount on the marked price. What is the store's profit as a percent of cost?
Explanation. Let cost = 100. Marked price = 150. After 20% discount: 150 × 0.8 = 120. Profit = 120 − 100 = 20, so 20% of cost.
5. The average of 5 numbers is 30. If one number is removed, the average of the remaining 4 becomes 28. What was the removed number?
Explanation. Sum of 5 = 150. Sum of 4 = 112. Removed = 150 − 112 = 38.
6. Tom invests $5,000 at 8% simple annual interest and $3,000 at 6% simple annual interest. What is his total interest after one year?
7. A boat travels 36 miles downstream in 3 hours and the same distance upstream in 4 hours. What is the speed of the current?
Explanation. Downstream speed = 36/3 = 12 mph = b + c. Upstream = 36/4 = 9 mph = b − c. Subtract: 2c = 3, c = 1.5 mph.
8. In a group of 60 people, 35 like tea, 40 like coffee, and 10 like neither. How many like both tea and coffee?
Explanation. People liking at least one = 60 − 10 = 50. By inclusion-exclusion: 35 + 40 − both = 50, so both = 75 − 50 = 25.
9. A car's value depreciates 20% each year. If it is worth $16,000 now, what was its value 2 years ago?
Explanation. Value now = original × 0.8². So original = 16000 / 0.64 = 25000.
10. A father is currently 4 times as old as his son. In 12 years, he will be twice as old. How old is the son now?
Explanation. Let son = s, father = 4s. In 12 years: 4s + 12 = 2(s + 12) = 2s + 24. So 2s = 12, s = 6.
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FAQ
What types of word problems appear most on the GMAT Quant section?
Common categories include rate/time/distance, work rate, mixtures, percents and profit/loss, averages, interest, ratios, age problems, and set/overlapping-group problems. Mastering setup of variables and standard formulas (like distance = rate × time and combined work = sum of rates) covers most cases.
How should I approach translating word problems into equations?
Read carefully, define variables explicitly for each unknown, write one equation per relationship described, and check units. For ratio and percent problems, picking convenient base numbers (like 100) often speeds up the work. Always verify your answer satisfies all conditions in the original statement.
When is it better to plug in answer choices instead of solving algebraically?
Backsolving (testing answer choices) works well when the algebra is messy or when choices are simple numbers, especially for age, rate, and integer problems. Start with the middle value to quickly determine direction. For clean linear setups, direct algebra is usually faster.