GMAT Quantitative Reasoning
GMAT word problems practice questions
Word problems turn up in the Quantitative section of the GMAT in many disguises, but most reduce to a few relationships: distance equals speed times time, work equals rate times time, and interest follows a fixed rule. The skill is translating the story into an equation without missing a condition.
Key ideas
- Add rates for work done together: 1/12 + 1/18 is the combined rate of two workers.
- Average speed over equal distances is total distance divided by total time, not the average of two speeds.
- Relative speed adds when objects move toward each other and subtracts when they move the same way.
- Alligation finds a mixture ratio from three prices.
Common traps
- Averaging speeds over equal distances.
- Forgetting that a draining pipe subtracts from the filling rate.
- Using simple interest where the question says compound.
Practice questions with solutions
Try each question first, then open the solution. Aim for about two minutes per question.
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A can finish a job in 12 days and B can finish it in 18 days. Working together, how many days do they take?
- A 7.2
- B 15
- C 7.5
- D 8
- E 6
Show answer and solution
Answer: A. 7.2
Their combined rate is 1/12 + 1/18 = 5/36 of the job a day. The time is 36/5 = 7.2 days.
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A train travels 360 km at 60 km/h and returns the same distance at 90 km/h. What is its average speed for the whole trip?
- A 70 km/h
- B 80 km/h
- C 72 km/h
- D 65 km/h
- E 75 km/h
Show answer and solution
Answer: C. 72 km/h
The trip takes 6 + 4 = 10 hours for 720 km, so the average speed is 72 km/h. It is not 75, which is the simple average of the two speeds.
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What is the simple interest on 8,000 at 6% per year for 3 years?
- A 1,800
- B 1,280
- C 1,620
- D 1,440
- E 1,500
Show answer and solution
Answer: D. 1,440
Simple interest = 8,000 x 6 x 3 / 100 = 1,440.
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What is the compound interest on 10,000 at 10% per year, compounded annually, for 2 years?
- A 2,310
- B 2,200
- C 2,100
- D 2,000
- E 1,900
Show answer and solution
Answer: C. 2,100
After 2 years the amount is 10,000 x 1.1 x 1.1 = 12,100. The interest is 2,100.
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Two trains of lengths 150 m and 100 m run in opposite directions on parallel tracks at 54 km/h and 36 km/h. How many seconds do they take to cross each other?
- A 12
- B 8
- C 6
- D 10
- E 15
Show answer and solution
Answer: D. 10
Relative speed = 54 + 36 = 90 km/h = 25 m/s. Distance to cover = 150 + 100 = 250 m. Time = 250 / 25 = 10 seconds.
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A pipe fills a tank in 6 hours and a drain empties a full tank in 9 hours. If both are open together, how many hours does it take to fill the empty tank?
- A 12
- B 18
- C 20
- D 7.5
- E 15
Show answer and solution
Answer: B. 18
Net rate = 1/6 - 1/9 = 1/18 of the tank an hour. So it takes 18 hours.
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A boat's speed in still water is 12 km/h and the current is 3 km/h. How many hours does it take to go 45 km downstream and then return 45 km upstream?
- A 10
- B 8
- C 7
- D 9
- E 6
Show answer and solution
Answer: B. 8
Downstream speed is 15 km/h, so 45 km takes 3 hours. Upstream speed is 9 km/h, so 45 km takes 5 hours. Total 8 hours.
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Six workers build a wall in 15 days. How many days would 9 workers take at the same rate?
- A 12
- B 22.5
- C 9
- D 8
- E 10
Show answer and solution
Answer: E. 10
Total work is 6 x 15 = 90 worker days. With 9 workers it takes 90 / 9 = 10 days.
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Tea costing 300 per kg is mixed with tea costing 400 per kg to make a mixture worth 340 per kg. In what ratio, by weight, should the 300 tea and the 400 tea be mixed?
- A 4 : 3
- B 1 : 1
- C 2 : 3
- D 3 : 2
- E 5 : 3
Show answer and solution
Answer: D. 3 : 2
By alligation, the weights are in the ratio (400 - 340) : (340 - 300) = 60 : 40 = 3 : 2, with more of the cheaper tea.
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A father is 4 times as old as his son. In 6 years he will be 3 times as old as his son. What is the son's present age in years?
- A 10
- B 12
- C 14
- D 9
- E 15
Show answer and solution
Answer: B. 12
Let the son be x. Then 4x + 6 = 3(x + 6), so x = 12. Check: father 48 now, 54 in 6 years; son 18 in 6 years; 54 = 3 x 18.