GMAT Quantitative: GMAT Quantitative: Percentages Practice Questions
Test yourself on GMAT Quantitative: Percentages with 13 original GMAT practice questions. Pick an answer to see instant feedback and a full explanation.
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1. A store increases the price of an item by 20%, then offers a discount of 20% on the increased price. The final price is what percent of the original price?
Explanation. Let original price be 100. After 20% increase: 120. After 20% discount: 120 × 0.8 = 96. So final price is 96% of original. A successive +20% then −20% always nets a 4% loss because (1.2)(0.8)=0.96.
2. If 40% of a number is 60, what is 25% of that number?
Explanation. 40% of x = 60 means x = 60/0.40 = 150. Then 25% of 150 = 37.5.
3. A quantity increases from 80 to 100. What is the percent increase?
Explanation. Percent increase = (change/original) × 100 = (100−80)/80 × 100 = 20/80 × 100 = 25%. Note the base is the original value 80, not the new value.
4. In a class, 60% of students are girls. If there are 18 boys, how many students are in the class?
Explanation. If 60% are girls, then 40% are boys. Boys = 40% of total = 18, so total = 18/0.40 = 45.
5. The price of a stock fell by 25%. By what percent must it now rise to return to its original value?
Explanation. Let original = 100. After 25% drop: 75. To return to 100, rise needed = 25/75 = 1/3 ≈ 33⅓%. The base changes to the lower value, so the required rise exceeds the original fall.
6. A worker's salary was increased by 10% and then by another 10%. What is the total percent increase?
Explanation. Successive increases multiply: 1.10 × 1.10 = 1.21, a 21% total increase. Adding 10% + 10% to get 20% ignores the compounding on the increased amount.
7. If x is 30% more than y, then y is what percent less than x?
Explanation. x = 1.3y. Then y/x = 1/1.3 = 10/13 ≈ 0.7692. So y is 1 − 10/13 = 3/13 ≈ 23.08% less than x, i.e., 23 1/13%. The percent less is not simply 30% because the base differs.
8. A solution of 50 liters contains 20% salt. How many liters of water must be added to make it 10% salt?
Explanation. Salt amount = 20% of 50 = 10 liters (this stays constant). For 10% concentration: 10 = 0.10 × total, so total = 100 liters. Water added = 100 − 50 = 50 liters.
9. After a 10% discount, an item sells for $90. What was the original price?
Explanation. After a 10% discount, the selling price is 90% of original: 0.90 × original = 90, so original = 90/0.90 = $100. Adding 10% to $90 ($99) is wrong because the discount base is the original price.
10. A's income is 25% more than B's. By what percent is B's income less than A's?
Explanation. A = 1.25B, so B/A = 1/1.25 = 0.80. B is 20% less than A. The clean fraction: +25% = ×5/4, and the reverse is ×4/5, a 1/5 = 20% reduction.
11. If the length of a rectangle increases by 20% and the width decreases by 20%, the area changes by what percent?
Explanation. New area factor = 1.20 × 0.80 = 0.96, so area decreases by 4%. Equal percentage increase and decrease on the two dimensions never cancel; the product is less than 1.
12. In an election with two candidates, the winner got 60% of the votes and won by 720 votes. How many total votes were cast?
Explanation. Winner 60%, loser 40%, so margin = 20% of total = 720. Total = 720/0.20 = 3600 votes.
13. The number of employees grew 50% in year 1 and fell 40% in year 2. The number at the end of year 2 is what percent of the starting number?
Explanation. Apply factors: 1.50 × 0.60 = 0.90. So ending count is 90% of the original — a net 10% decrease. Adding +50% and −40% to get +10% wrongly ignores changing bases.
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FAQ
What is the most common percentage trap on the GMAT?
Confusing the base. 'Percent increase/decrease' uses the ORIGINAL value as the base, and 'A is x% more than B' uses B as the base while 'B is what % less than A' uses A. The percentages are not symmetric—e.g., a 25% drop requires a 33⅓% rise to recover.
How should I handle successive percentage changes?
Multiply the decimal factors rather than adding the percents. A +20% then −20% gives 1.2 × 0.8 = 0.96 (a 4% loss), not 0%. Picking a starting value of 100 makes the arithmetic fast and concrete.
What value should I assume to solve quickly?
When no specific number is given, choose 100 (or 1) as the base. It turns percentages into easy multiplication and prevents base-confusion errors. For multi-quantity problems, pick smart numbers that match the percentages cleanly.