GRE Quiz: Fractions Decimals Percents

19 questions · exam conditions

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Fractions Decimals PercentsQuestion 1 of 19

A price is increased from $80$ to $92$ . The increase is what percent of the original price?

12\%

13\%

15\%

20\%

23\%

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GRE Quiz

GRE Quiz: Fractions Decimals Percents

Practice Fractions Decimals Percents in GRE with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Fractions Decimals Percents, giving you a quick way to practice the rules, question types, and explanations that matter most for GRE.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A price is increased from $80$ to $92$ . The increase is what percent of the original price?

$12\%$
$13\%$
$15\%$ (correct answer)
$20\%$
$23\%$

Explanation: This question tests percent increase calculations. The appropriate strategy is to find the increase and divide by the original price, then convert to percent. The increase is 92 - 80 = 12; 12/80 = 0.15. Thus, 0.15 × 100 = 15%. The increase is 15% of the original. A common incorrect choice is 13%, which might result from dividing by the new price (12/92 ≈ 0.13) instead of the original. Another error could be 12%, confusing the dollar increase with the percent.

Question 2

Which of the following is closest to $0.18$ expressed as a fraction in simplest form?

$\frac{9}{50}$ (correct answer)
$\frac{18}{10}$
$\frac{1}{18}$
$\frac{2}{11}$
$\frac{11}{50}$

Explanation: This question tests approximation of decimals to fractions. The appropriate strategy is to convert each fraction to a decimal and compare to 0.18. 9/50 = 0.18 exactly; 2/11 ≈ 0.1818 is close but not exact. Other options like 1/18 ≈ 0.0556 are farther. The closest is 9/50. A common incorrect choice is 2/11, tempting because it's slightly higher but not as exact as 9/50. Another error could be 11/50 = 0.22, which is an overestimate.

Question 3

A class has $30$ students. Of these, $\dfrac{2}{5}$ are juniors, and $25\%$ of the juniors are in the math club. How many juniors are in the math club?

$2$
$3$ (correct answer)
$5$
$6$
$12$

Explanation: This question tests calculating with fractions and percents in a multi-step problem. First, find the number of juniors: 30 × (2/5) = 12 juniors. Then find 25% of the juniors who are in math club: 12 × 0.25 = 3 students. Therefore, 3 juniors are in the math club. A common error is calculating 25% of all 30 students (giving 7.5) or finding 2/5 of 25% of 30 (giving 3 by coincidence but with wrong reasoning).

Question 4

Which of the following is greatest?

$0.62$
$\frac{5}{8}$ (correct answer)
$61\%$
$0.615$
$\frac{3}{5}$

Explanation: This question tests comparison of decimals, fractions, and percents. The appropriate strategy is to convert all to decimals for comparison. 5/8 = 0.625; 61% = 0.61; 3/5 = 0.6; others are 0.62, 0.615. The greatest is 0.625. A common incorrect choice is 0.62, close but less than 0.625. Another tempting error is 0.615, perhaps from underestimating 5/8.

Question 5

A tank is $\frac{2}{5}$ full. After $30\%$ of the water currently in the tank is drained, what fraction of the tank is full?

$\frac{7}{25}$ (correct answer)
$\frac{1}{4}$
$\frac{3}{25}$
$\frac{14}{25}$
$\frac{2}{7}$

Explanation: This question tests combining fractions with percents. The tank starts 2/5 full, and we need to find what fraction remains after draining 30% of the current water. First, we calculate 30% of 2/5: 0.30 × 2/5 = 6/50 = 3/25. This is the amount drained. The amount remaining is 2/5 - 3/25. To subtract these fractions, we need a common denominator: 2/5 = 10/25, so 10/25 - 3/25 = 7/25. A common error would be to calculate 30% of the full tank capacity rather than 30% of the water currently in the tank.

Question 6

A tank is $\frac{3}{5}$ full. After $20\%$ of the water currently in the tank is drained out, what fraction of the tank is full?

$\frac{12}{25}$ (correct answer)
$\frac{3}{4}$
$\frac{2}{5}$
$\frac{9}{25}$
$\frac{1}{2}$

Explanation: This question tests fractions and percents in the context of proportions. The appropriate strategy is to represent the initial fraction and apply the percentage drain to the current amount. The tank is 3/5 full; draining 20% of that means removing 1/5 of the current water, leaving 4/5 of the original amount. Thus, (4/5) × (3/5) = 12/25 of the tank is full. The result is 12/25. A common incorrect choice is 2/5, which might tempt if forgetting to apply the drain to the current amount and subtracting percentages directly. Another error could be 9/25, perhaps from miscalculating the remaining fraction as 3/5 minus 20% of the whole tank instead.

Question 7

A number is increased by $10\%$ and then decreased by $10\%$ . The result is what percent of the original number?

$99\%$ (correct answer)
$100\%$
$90\%$
$110\%$
$101\%$

Explanation: This question tests percents with successive changes. The appropriate strategy is to apply the increase and decrease multipliers sequentially. Increasing by 10% multiplies by 1.1; decreasing by 10% multiplies by 0.9. The overall factor is 1.1 × 0.9 = 0.99. The result is 99% of the original. A common incorrect choice is 100%, tempting because one might think the changes cancel, but the decrease is on a larger base. Another error could be 90%, from subtracting 10% twice incorrectly.

Question 8

A salary is decreased by $10\%$ and then increased by $10\%$ . The final salary is what percent of the original salary?

$100\%$
$99\%$ (correct answer)
$101\%$
$90\%$
$110\%$

Explanation: This question tests successive percent changes applied to a salary. Starting with an original salary of 100, a 10% decrease gives us 100 × 0.90 = 90. Then, a 10% increase from 90 gives us 90 × 1.10 = 99. The final salary of 99 is 99% of the original salary of 100. This demonstrates that successive percent changes of equal magnitude but opposite signs do not cancel out. The key insight is that the increase is calculated on the smaller intermediate value (90), so it doesn't fully restore the original amount. Many students incorrectly assume the changes cancel to give 100%.

Question 9

A store advertises that an item priced at $50$ is on sale for $40\%$ off. Which of the following is the sale price?

$20$
$25$
$30$ (correct answer)
$35$
$40$

Explanation: This question tests percents in the context of discounts. The appropriate strategy is to calculate the discount amount or multiply by the remaining percentage. 40% off means paying 60% of 50. Thus, 50 × 0.6 = 30. The sale price is 30. A common incorrect choice is 20, which is the discount amount itself, not the sale price. Another error could be 40, perhaps from subtracting 10 incorrectly instead of 20.

Question 10

A quantity $Q$ is decreased by $20\%$ and then increased by $25\%$ . The final value is equal to what fraction of the original value $Q$ ?

$\frac{4}{5}$
$\frac{5}{4}$
$1$ (correct answer)
$\frac{19}{20}$
$\frac{6}{5}$

Explanation: This question tests fractions through successive percentage changes. The appropriate strategy is to apply the decrease and increase multipliers. Decreasing by 20% multiplies by 0.8; increasing by 25% multiplies by 1.25. Overall: 0.8 × 1.25 = 1. The final value is 1 times the original Q. A common incorrect choice is 4/5, which is the value after decrease only, forgetting the increase. Another tempting error is 5/4, perhaps from adding the percentages incorrectly.

Question 11

Which of the following is equal to $45\%$ of $\frac{2}{3}$ ?

$\frac{3}{10}$ (correct answer)
$\frac{1}{3}$
$\frac{9}{20}$
$\frac{2}{5}$
$\frac{1}{5}$

Explanation: This question tests percents and fractions in multiplication. The appropriate strategy is to convert the percent to a fraction or decimal and multiply by the given fraction. 45% is 45/100 = 9/20. Multiplying by 2/3 gives (9/20) × (2/3) = 18/60 = 3/10. The result is 3/10. A common incorrect choice is 9/20, which might tempt if forgetting to multiply by 2/3 and stopping at the percent fraction. Another error could be 1/3, perhaps from approximating 45% as about 1/2 and miscalculating.

Question 12

A recipe uses $0.6$ cup of sugar. If the amount of sugar is reduced by $\frac{1}{6}$ , how many cups of sugar are used in the new recipe?

$0.4$
$0.45$
$0.5$ (correct answer)
$0.55$
$0.7$

Explanation: This question tests decimals and fractions in percentage reductions. The appropriate strategy is to interpret the reduction as multiplying by (1 - 1/6) or subtracting the fraction of the original. Reducing by 1/6 means multiplying 0.6 by 5/6. Calculation: 0.6 × 5/6 = 0.5. The new amount is 0.5 cups. A common incorrect choice is 0.4, which might result from subtracting 1/6 directly from 0.6 without multiplying. Another tempting error is 0.45, perhaps from miscalculating 1/6 of 0.6 as 0.15 and subtracting.

Question 13

A recipe uses $\frac{3}{4}$ cup of sugar. If the amount of sugar is increased by $25\%$ , what is the new amount of sugar, in cups?

$\frac{15}{16}$ (correct answer)
$\frac{3}{8}$
$\frac{9}{16}$
$1$
$\frac{4}{5}$

Explanation: This question tests increasing a fraction by a percentage. We start with 3/4 cup of sugar and need to increase it by 25%. To increase by 25%, we multiply by 1.25: (3/4) × 1.25 = (3/4) × (5/4) = 15/16. We can verify this by converting to decimals: 3/4 = 0.75, and 0.75 × 1.25 = 0.9375 = 15/16. The calculation shows that increasing 3/4 by 25% gives us 15/16 cups. A common error would be to add 25% of 1 cup to 3/4, giving 3/4 + 1/4 = 1, but we must calculate 25% of the original amount (3/4), not of 1 cup.

Question 14

A jacket is on sale for $25\%$ off its original price. The sale price is $45. What was the original price?

$33.75
$56.25
$60 (correct answer)
$70
$75

Explanation: This question tests working backwards from a discounted price to find the original price. If the jacket is 25% off, the sale price represents 75% of the original price. We can write: 0.75 × (original price) = $45. Solving for the original price: original price = $45 ÷ 0.75 = $60. We can verify: 25% of $60 is $15, and $60 - $15 = $45, confirming our answer. A common error is to add 25% of the sale price to the sale price ($ 45 + 0.25 × $45 = $56.25), but this incorrectly uses the sale price as the base for the percentage calculation.

Question 15

A jacket originally priced at $120$ is discounted by $25\%$ and then the discounted price is increased by $20\%$ . What is the final price of the jacket?

$96$
$108$ (correct answer)
$90$
$120$
$114$

Explanation: This question tests percents, specifically successive percentage changes. The appropriate strategy is to apply the discount and then the increase to the original price. Discounting 120 by 25% gives 120 × 0.75 = 90. Increasing 90 by 20% gives 90 × 1.2 = 108. The final price is 108. A common incorrect choice is 96, which might result from applying both percentages to the original and subtracting incorrectly. Another error could be 120, assuming the changes cancel out, but they do not due to different bases.

Question 16

A solution is $30\%$ salt by volume. If $\frac{1}{2}$ of the solution is removed and replaced with an equal volume of water, what percent of the resulting solution is salt?

$10\%$
$15\%$ (correct answer)
$20\%$
$30\%$
$45\%$

Explanation: This question tests percents in the context of mixtures and dilutions. The appropriate strategy is to assume a total volume and calculate the salt amount before and after the replacement. Assume 100 units of solution with 30 units of salt; removing half (50 units) removes 15 units of salt, leaving 15 units of salt in 50 units. Adding 50 units of water results in 15 units of salt in 100 units total. The resulting solution is 15% salt. A common incorrect choice is 20%, which might come from averaging 30% and 0% incorrectly instead of tracking the actual amounts. Another tempting error is 10%, perhaps from halving the original percentage directly without considering the replacement.

Question 17

A class has 24 students. If $\frac{1}{3}$ of the students are absent, what percent of the students are present?

$33\frac{1}{3}\%$
$60\%$
$66\frac{2}{3}\%$ (correct answer)
$75\%$
$80\%$

Explanation: This question tests conversion between fractions and percents. The appropriate strategy is to find the present fraction and convert to percent. With 1/3 absent, 2/3 are present. Converting 2/3 to percent: (2/3) × 100 ≈ 66.67%. The result is 66 2/3%. A common incorrect choice is 33 1/3%, which is the absent percent, confusing absence with presence. Another tempting error is 75%, perhaps from miscalculating 3/4 instead of 2/3.

Question 18

A store increases the price of an item by $20\%$ and then decreases the new price by $20\%$ . The final price is what percent of the original price?

$96\%$ (correct answer)
$100\%$
$104\%$
$80\%$
$98\%$

Explanation: This question tests understanding of successive percent changes. When calculating successive percent changes, we must apply each change to the result of the previous change, not to the original value. Starting with an original price of 100, a 20% increase gives us 100 × 1.20 = 120. Then, a 20% decrease from 120 gives us 120 × 0.80 = 96. The final price of 96 is 96% of the original price of 100. A common error is to think that a 20% increase followed by a 20% decrease returns to the original price, but this ignores that the decrease is calculated on the larger intermediate value.

Question 19

A bookstore sold $\frac{3}{10}$ of its books on Monday and $40\%$ of its books on Tuesday, with no overlap between the days. What fraction of the books were sold on Monday and Tuesday combined?

$\frac{7}{10}$ (correct answer)
$\frac{1}{10}$
$\frac{3}{4}$
$\frac{2}{5}$
$\frac{11}{25}$

Explanation: This question tests addition of fractions and percents. The appropriate strategy is to convert percent to fraction and add to the given fraction. 40% = 2/5 = 4/10; 3/10 + 4/10 = 7/10. Assuming percentages are of the total with no overlap, the combined is 7/10. The result is 7/10. A common incorrect choice is 2/5, which is Tuesday's share alone, forgetting to add Monday. Another error could be 3/4, perhaps from misadding or converting incorrectly.