GMAT Quantitative: GMAT Quantitative: Problem Solving Practice Questions
Test yourself on GMAT Quantitative: Problem Solving with 12 original GMAT 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 GMAT.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. If 3x − 7 = 2x + 5, what is the value of x?
Explanation. Subtract 2x from both sides: x − 7 = 5. Add 7: x = 12. A common error is forgetting to move the 7, giving x = 2.
2. A shirt is marked up 25% above cost and then sold at a 20% discount off the marked price. What is the percent profit or loss on cost?
Explanation. Let cost = 100. Marked price = 125. Selling price = 125 × 0.80 = 100. Equals cost, so break even (0%).
3. If the average (arithmetic mean) of 5 numbers is 18, and one number is removed leaving an average of 20 for the remaining 4, what was the removed number?
Explanation. Sum of 5 = 5×18 = 90. Sum of 4 = 4×20 = 80. Removed = 90 − 80 = 10.
4. A train travels 240 miles at 60 mph and returns the same distance at 40 mph. What is the average speed for the round trip?
Explanation. Average speed = total distance / total time. Time out = 240/60 = 4 h; time back = 240/40 = 6 h. Total = 480 miles / 10 h = 48 mph. Note it is not the simple average of 50.
5. If 2^x = 32, what is the value of 2^(x+2)?
Explanation. 2^x = 32 = 2^5, so x = 5. Then 2^(x+2) = 2^7 = 128. Alternatively, 2^(x+2) = 4·2^x = 4·32 = 128.
6. Working alone, pump A fills a tank in 6 hours and pump B in 12 hours. How long to fill it together?
Explanation. Rates add: 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 tank per hour. Time = 4 hours.
7. A group of 8 people includes 3 women. How many ways can a committee of 2 be chosen that includes at least one woman?
Explanation. Total committees C(8,2)=28. Committees with no women (both men): C(5,2)=10. At least one woman = 28 − 10 = 18.
8. If x is a positive integer and x² + 6x = 27, what is x?
Explanation. x² + 6x − 27 = 0 factors as (x+9)(x−3)=0, so x = 3 or x = −9. Since x is positive, x = 3.
9. What is the units digit of 7^45?
Explanation. Units digits of powers of 7 cycle: 7,9,3,1 (period 4). 45 mod 4 = 1, so the units digit matches 7^1 = 7.
10. A mixture is 40% acid. How many liters of pure water must be added to 20 liters of this mixture to make it 25% acid?
Explanation. Acid amount = 0.40×20 = 8 L (constant). New total = 8/0.25 = 32 L. Water added = 32 − 20 = 12 L.
11. If the ratio of boys to girls in a class is 3:5 and there are 24 boys, how many students are in the class?
Explanation. 3 parts = 24 boys, so 1 part = 8. Girls = 5×8 = 40. Total = 24 + 40 = 64.
12. A square and a circle have equal areas. If the square has side 6, what is the approximate radius of the circle? (Use π ≈ 3.14)
Explanation. Square area = 36 = πr². So r² = 36/3.14 ≈ 11.46, r ≈ √11.46 ≈ 3.4.
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FAQ
How should I approach Problem Solving questions efficiently?
Read the question fully, identify what is asked, and decide between algebra, picking smart numbers, or back-solving from answer choices. For percent and rate problems, choosing convenient numbers (like 100) often speeds things up. Always check that your answer matches what's actually being asked.
What topics appear most often in GMAT Problem Solving?
Arithmetic (percents, ratios, fractions), algebra (linear/quadratic equations, exponents), word problems (rates, work, mixtures, averages), number properties (units digits, divisibility), and geometry. Mastering percents, rates, and number properties yields the highest return.
How can I avoid careless errors under time pressure?
Write down what each variable represents, watch for 'trap' answers (like the simple average in a round-trip speed problem), and re-read for qualifiers such as 'positive integer' or 'at least.' Estimate first when possible to rule out implausible choices.