GRE Quantitative: GRE Quantitative: Word Problems Practice Questions
Test yourself on GRE Quantitative: Word Problems with 10 original GRE practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of GRE.
advertisement
Answer the questions below — you get instant feedback and a full explanation for each.
1. A store sells pens at $3 each and notebooks at $5 each. If a customer buys a total of 12 items for $46, how many notebooks did the customer buy?
Explanation. Let n = notebooks, p = pens. Then n + p = 12 and 5n + 3p = 46. Substitute p = 12 - n: 5n + 3(12 - n) = 46, so 5n + 36 - 3n = 46, 2n = 10, n = 5.
2. A car travels from town A to town B at 60 mph and returns along the same route at 40 mph. What is the average speed for the entire round trip?
Explanation. Average speed = total distance / total time. For distance d each way: time = d/60 + d/40 = (2d+3d)/120 = 5d/120 = d/24. Total distance = 2d, so average = 2d / (d/24) = 48 mph. Note it is NOT the simple average (50).
3. A mixture contains 40 liters of a solution that is 25% acid. How many liters of pure acid must be added to make the solution 40% acid?
Explanation. Initial acid = 0.25(40) = 10 L. Add x liters pure acid: acid = 10 + x, total = 40 + x. Set (10+x)/(40+x) = 0.40, so 10 + x = 16 + 0.4x, 0.6x = 6, x = 10.
4. Working alone, machine X completes a job in 6 hours and machine Y in 3 hours. Working together, how long do they take?
Explanation. Rates: X = 1/6, Y = 1/3 = 2/6 jobs per hour. Combined = 3/6 = 1/2 job per hour. Time = 1 / (1/2) = 2 hours.
5. The sum of three consecutive even integers is 90. What is the largest of the three integers?
Explanation. Let the integers be n, n+2, n+4. Sum = 3n + 6 = 90, so 3n = 84, n = 28. The integers are 28, 30, 32; the largest is 32.
6. A jacket is marked up 50% above cost, then sold at a 20% discount off the marked price. If the cost is $80, what is the final selling price?
7. In a class, the ratio of boys to girls is 3:5. If there are 24 boys, how many students are in the class total?
Explanation. 3 parts = 24 boys, so 1 part = 8. Girls = 5 × 8 = 40. Total = 24 + 40 = 64. (Or 8 parts × 8 = 64.)
8. Five years ago, Ann was twice as old as Beth. In 5 years, Ann will be 1.5 times as old as Beth. How old is Ann now?
Explanation. Let Ann = a, Beth = b now. (a-5) = 2(b-5) → a = 2b - 5. (a+5) = 1.5(b+5) → a = 1.5b + 2.5. Set equal: 2b - 5 = 1.5b + 2.5, 0.5b = 7.5, b = 15, a = 2(15) - 5 = 25.
9. A bank account earns 5% annual simple interest. If $2,000 is deposited, what is the total balance after 3 years?
Explanation. Simple interest = principal × rate × time = 2000 × 0.05 × 3 = $300. Total = 2000 + 300 = $2,300. (The $2,331.50 reflects compound interest, which is not used here.)
10. A tank can be filled by pipe A in 4 hours and drained by pipe B in 6 hours. If both pipes are open and the tank starts empty, how long to fill it?
Explanation. Net rate = 1/4 (fill) − 1/6 (drain) = 3/12 − 2/12 = 1/12 tank per hour. Time = 1 / (1/12) = 12 hours.
📘 Want a full structured course and official-style practice tests? Browse top-rated GRE prep books and courses. Some links are affiliate links; we may earn a commission at no cost to you.
advertisement
FAQ
What is the best general strategy for GRE word problems?
Translate words into equations or expressions step by step. Define variables clearly, identify what is asked, set up the relationship (rate, ratio, percent, mixture), and solve. For multiple-choice, plugging in the answer choices or picking smart numbers can be faster than algebra.
Which word-problem types appear most often on the GRE?
Common categories include rate/work problems, distance-speed-time, percents and mixtures, ratios and proportions, ages, and simple/compound interest. Recognizing the category quickly helps you apply the right formula.
How do I avoid the 'average speed' trap?
Average speed is total distance divided by total time, not the average of the two speeds. When equal distances are traveled at two speeds, the average is the harmonic mean, which is always less than the simple arithmetic average.