GRE Quantitative: GRE Quantitative: Arithmetic Practice Questions
Test yourself on GRE Quantitative: Arithmetic 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.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. What is the value of (3/4) ÷ (9/8)?
Explanation. Dividing fractions means multiplying by the reciprocal: (3/4) × (8/9) = 24/36 = 2/3. The distractor 3/2 comes from inverting the wrong fraction.
2. If a number is increased by 20% and then decreased by 20%, the net result compared to the original is:
Explanation. Multiplying by 1.20 then 0.80 gives 0.96, a 4% decrease. Successive percentage changes are multiplicative, not additive, so they don't cancel.
3. What is the greatest common divisor (GCD) of 84 and 126?
Explanation. 84 = 2²·3·7 and 126 = 2·3²·7. The GCD takes the lowest power of each common prime: 2¹·3¹·7¹ = 42.
4. A jar contains coins worth $4.50 in nickels and dimes. If there are 60 coins total, how many are dimes?
Explanation. Let d = dimes, n = nickels. n + d = 60 and 0.05n + 0.10d = 4.50. Substitute n = 60 − d: 0.05(60−d) + 0.10d = 4.50 → 3 + 0.05d = 4.50 → 0.05d = 1.50 → d = 30.
5. Which of the following is equal to 2^5 · 2^3 / 2^4?
Explanation. Add exponents when multiplying same base, subtract when dividing: 2^(5+3−4) = 2^4. The distractor 2^15 wrongly multiplies the exponents.
6. The ratio of boys to girls in a class is 3:5. If there are 40 students, how many are boys?
Explanation. Total ratio parts = 3 + 5 = 8. Each part = 40/8 = 5 students. Boys = 3 × 5 = 15.
7. What is the remainder when 7^4 is divided by 5?
8. If 0 < x < 1, which of the following is the largest?
Explanation. For a number between 0 and 1, taking a square root makes it larger (closer to 1), while raising to higher powers makes it smaller. So √x > x > x² > x³. √x is the largest of the listed power expressions.
9. A price was discounted 25%, then a coupon took 10% off the discounted price. What single percent discount equals these combined?
Explanation. Multiply factors: (1 − 0.25)(1 − 0.10) = 0.75 × 0.90 = 0.675, meaning you pay 67.5%, so the total discount is 32.5%. Adding 25% + 10% = 35% is a common mistake.
10. What is the value of |−8| − |3 − 11| + (−2)^2?
Explanation. |−8| = 8; |3 − 11| = |−8| = 8; (−2)^2 = 4. So 8 − 8 + 4 = 4. Watch order of operations and the absolute values.
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FAQ
How much arithmetic appears on the GRE Quant section?
Arithmetic is a major content area, covering integers, fractions, decimals, percents, ratios, exponents, roots, divisibility, and number properties. Mastering it underpins much of the algebra and word-problem work too.
Can I use a calculator for arithmetic questions?
Yes, the GRE provides an on-screen calculator for the Quant section. However, it's basic, so strong mental and estimation skills—especially for percent changes, fractions, and number properties—still save time and reduce entry errors.
What's the most common arithmetic trap to watch for?
Treating successive percentage changes as additive instead of multiplicative. A 20% increase followed by a 20% decrease does NOT return to the original value; always multiply the decimal factors together.