GRE Quantitative Quiz: Percent Change Growth

What this quiz covers

This quiz focuses on Percent Change Growth, giving you a quick way to practice the rules, question types, and explanations that matter most for GRE Quantitative.

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.

Question 1

1. 215 grams
2. 230 grams (correct answer)
3. 200 grams
4. 185 grams
5. 245 grams

Explanation: This question tests percent increase in the amount of flour for a recipe. Percent increase is defined as the increase divided by the original base amount, multiplied by 100%. The increase is 15% of 200 grams, so 0.15 × 200 = 30 grams added. The new amount is 200 + 30 = 230 grams. This is correct because the percentage is applied to the original as specified. A common incorrect choice like 215 adds only 7.5% mistakenly. Another error, such as 200, ignores the increase entirely.

Question 2

1. 14%
2. 16.8%
3. 20% (correct answer)
4. 120%
5. 24%

Explanation: This question tests calculating what percent an increase represents of the original value. Percent change is defined as (change ÷ original) × 100%, with the original score as the base. The score increases from 70 to 84, an increase of 14 points. The percent increase relative to the original score is (14 ÷ 70) × 100% = 20%. The correct answer is 20%. A common error is to calculate 14% by looking at the absolute numbers without properly dividing by the base.

Question 3

1. 75
2. 90
3. 120
4. 105 (correct answer)
5. 135

Explanation: This question tests multiple sequential percent changes with different bases. Each percent change uses the previous month's value as its base. January sales: 120 copies. February sales are 30% fewer: 120 × 0.70 = 84 copies. March sales are 25% more than February: 84 × 1.25 = 105 copies. The bookstore sold 105 copies in March. A common mistake is to apply both percentages to the January amount or to incorrectly combine the percentages.

Question 4

1. $500,010
2. $550,000
3. $600,000
4. $540,000 (correct answer)
5. $450,000

Explanation: This question tests compound percent change, where multiple percent changes are applied sequentially. When calculating percent change, each percentage is based on the value at that stage, not the original. First, revenue increases by 20% from $500,000: $500,000 × 1.20 = $600,000. Then it decreases by 10% from this new amount: $600,000 × 0.90 = $540,000. The final revenue is $540,000. A common mistake is to combine the percentages incorrectly, such as thinking +20% - 10% = +10% overall, which would incorrectly yield $550,000.

Question 5

1. 30
2. 185
3. 230
4. 170 (correct answer)
5. 160

Explanation: This question tests percent change, specifically a percent decrease from an original value. Percent change is calculated as (change ÷ original) × 100%, where the original value serves as the base. The store starts with 200 jackets and experiences a 15% decrease, so the decrease amount is 0.15 × 200 = 30 jackets. Therefore, the new number of jackets is 200 - 30 = 170 jackets. The correct answer is 170. A common error would be to calculate 15% of some other value or to add instead of subtract the change.

Question 6

1. $10,000
2. $9,900 (correct answer)
3. $9,000
4. $10,100
5. $11,000

Explanation: This question tests compound percent change where gains and losses are applied sequentially. Each percent change uses the current value as its base, not the original. Starting with $10,000, a 10% decrease gives: $10,000 × 0.90 = $9,000. Then a 10% increase on this amount gives: $9,000 × 1.10 = $9,900. The final value is $9,900. A common misconception is that a 10% decrease followed by a 10% increase returns to the original value, but this is false because the bases differ.

Question 7

1. $39.60
2. $33.00
3. $34.00
4. $32.40 (correct answer)
5. $27.00

Explanation: This question tests sequential percent changes: first a price increase, then a percentage discount on the new price. The price increases from $30 to $36 (a $6 or 20% increase). Then a 10% discount is applied to the new price of $36. The discount amount is 0.10 × $36 = $3.60. Subtracting this from $36 gives the final price: $36 - $3.60 = $32.40. The final advertised price is $32.40. A common error would be to apply the 10% discount to the original $30 price or to miscalculate the discount amount.

Question 8

1. \2{,}000$
2. \1{,}980$ (correct answer)
3. \2{,}020$
4. \2{,}200$
5. \1{,}800$

Explanation: This question tests successive percent changes where increases and decreases of the same percentage don't cancel out. Percent change uses the current value as the base for each calculation. Starting with $2,000, a 10% increase gives us $2,000 + 0.10($2,000) = $2,200. Then a 10% decrease from this new base gives us $2,200 - 0.10($2,200) = $2,200 - $220 = $1,980. The final rent is $1,980, which is less than the original $2,000. The key insight is that a 10$2,200) removes more dollars than a 10% increase from the original amount ($2,000) added.

Question 9

1. 60
2. 180 (correct answer)
3. 200
4. 300
5. 160

Explanation: This question tests percent change, specifically a percent decrease in the number of backpacks. Percent change is defined as the change amount divided by the original base value, multiplied by 100%. Here, the decrease is 25% of the original 240 backpacks, so the decrease amount is 0.25 × 240 = 60. The new number of backpacks is then 240 - 60 = 180. This result is correct because the percentage decrease is clearly applied to the original stock as stated. A common incorrect choice like 60 fails because it represents only the decrease amount, not the remaining stock. Another error, such as 200, might come from mistakenly subtracting 16.67% instead of 25%, confusing fractions like 1/6 with 1/4.

Question 10

1. $-16\%$
2. $-20\%$
3. $+20\%$
4. $0\%$ (correct answer)
5. $+16\%$

Explanation: This question tests calculating the overall percent change after multiple changes to a quantity. Starting with 300 members, a 20% increase adds 0.20 × 300 = 60 members, giving 360 members total. Then 60 members cancel, leaving 360 - 60 = 300 members. The percent change from the original 300 to the final 300 is (300 - 300) / 300 × 100% = 0%. The membership returned to its original level, so the percent change is 0%. The key insight is that the 60 members who joined equals the 60 who left, returning the gym to its original membership count.

Question 11

1. $512
2. $768
3. $820
4. $800 (correct answer)
5. $680

Explanation: This question tests finding an original price given a discounted price and the discount percentage. When an item is discounted by 20%, the customer pays 80% of the original price. If we let x be the original price, then 0.80x = $640 (the sale price). Solving for x: x = $640 / 0.80 = $800. Therefore, the original price was $800. A common error is to calculate 20% of $640 and add it back, which would give $768, but this incorrectly uses the sale price as the base instead of the original price.

Question 12

1. 240 grams (correct answer)
2. 260 grams
3. 280 grams
4. 220 grams
5. 320 grams

Explanation: This question tests calculating a new amount after a percent decrease. Percent decrease is calculated by multiplying the original amount by (1 - percent decrease). The original amount is 300 grams, and we need to decrease it by 20%. The new amount is 300 - 0.20(300) = 300 - 60 = 240 grams. Alternatively, we can calculate 80% of 300: 0.80(300) = 240 grams. The answer is 240 grams. A common error might be subtracting 20 grams instead of 20% of 300 grams.

Question 13

1. 16%
2. 20% (correct answer)
3. 25%
4. 60%
5. 80%

Explanation: This question tests calculating percent increase from an absolute change. Percent increase is defined as (increase ÷ original) × 100%, where the original value is the base. The factory's production increases from 300 to 360 units per day, an increase of 60 units. The percent increase is (60 ÷ 300) × 100% = 20%. The correct answer is 20%. A common error would be to use the new production (360) as the base instead of the original (300), which would give an incorrect percentage.

Question 14

1. $30\%$
2. $70\%$
3. $42\frac{6}{7}\%$ (correct answer)
4. $\frac{30}{70}\%$
5. $40\%$

Explanation: This question tests finding the percent increase needed to return to an original value after a percent decrease. Percent change is always calculated relative to the starting value of that specific change. The printer's price after a 30% reduction is $500 - 0.30($500) = $350. To find the percent increase from $350 back to $500, we calculate: (500 - 350)/350 × 100% = 150/350 × 100% = 3/7 × 100% = 42 6/7%. The required increase is 42 6/7%. A common error is thinking a 30% decrease requires a 30% increase to return to the original, but the bases are different.

Question 15

1. 1,242 (correct answer)
2. 1,260
3. 1,320
4. 1,200
5. 1,230

Explanation: This question tests successive percent changes where each percentage is applied to the membership at the start of that year. Percent change uses the current value as the base for each calculation. Starting with 1,200 members, a 15% increase gives us 1,200 + 0.15(1,200) = 1,200 + 180 = 1,380 members. Then a 10% decrease from this new base gives us 1,380 - 0.10(1,380) = 1,380 - 138 = 1,242 members. The final membership is 1,242. The key is recognizing that each percentage applies to the membership count at the beginning of its respective year.

Question 16

1. $50,000
2. $49,280 (correct answer)
3. $56,000
4. $44,000
5. $50,720

Explanation: This question tests compound percent change with the same percentage applied as both an increase and decrease. Starting with $50,000, a 12% increase gives $50,000 × 1.12 = $56,000. Then a 12% decrease from this new salary gives $56,000 × 0.88 = $49,280. The final salary is $49,280, which is less than the original $50,000. This demonstrates that equal percentage increases and decreases don't cancel out because they're applied to different base values. The common misconception is thinking the salary returns to $50,000, but the 12% decrease is calculated on the larger base of $56,000, resulting in a larger absolute decrease than the original increase.

Question 17

1. $55
2. $60 (correct answer)
3. $20
4. $105
5. $65

Explanation: This question tests percent change, specifically calculating a discounted price after a percentage decrease. Percent change is always calculated relative to the original or base value, which here is the original price of $80. To find the sale price after a 25% decrease, we calculate 25% of $80, which equals 0.25 × $80 = $20. Since this is a decrease, we subtract this amount from the original price: $80 - $20 = $60. Therefore, the sale price of the jacket is $60. A common error would be to calculate 25% of some other value or to add instead of subtract the discount amount.

Question 18

1. 90%
2. 125%
3. 20%
4. 80% (correct answer)
5. 100%

Explanation: This question tests comparing percent changes between different base values. Percent change is calculated relative to each town's original population. Town A increases by 10% of 40,000 = 4,000 people, while Town B increases by 10% of 50,000 = 5,000 people. The question asks what percent Town A's increase (4,000) is of Town B's increase (5,000): (4,000 ÷ 5,000) × 100% = 80%. The answer is 80%. A common mistake is to compare the populations themselves rather than the increases.

Question 19

1. $20\%$
2. $25\%$ (correct answer)
3. $10\%$
4. $80\%$
5. $12.5\%$

Explanation: This question tests the calculation of percent increase using the correct base value. Percent increase is defined as the change in value divided by the original value, multiplied by 100%. The change in price is $50 - $40 = $10, and the original price (the base) is $40. Therefore, the percent increase is ($10/$40) × 100$50) as the base instead of the original price ($40), which would incorrectly give 20%.

Question 20

1. 920
2. 880
3. 924 (correct answer)
4. 900
5. 915

Explanation: This question tests percent growth over two successive years in school enrollment. Percent growth is defined relative to the base enrollment at the start of each year, as (increase / base) × 100%. First year: 5% increase from 800 gives 800 × 1.05 = 840. Second year: 10% increase from 840 gives 840 × 1.10 = 924. This is correct as it compounds the growth on updated bases. A common incorrect choice like 880 assumes additive percentages (15% on original), ignoring compounding. Another error, such as 900, might average the percentages wrongly.