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GMAT Quantitative Reasoning

GMAT percentages and ratios practice questions

Percentages and ratios make up a large share of GMAT Quantitative Reasoning because they test how carefully you set up a problem. Almost every error comes from using the wrong base for a percentage or from mixing up which part of a ratio is which. Work these ten original questions with a timer of about two minutes each, then read the solution even when you were right.

Key ideas

  • A percent change is always measured against the original value, so a 20% rise followed by a 20% fall is a net fall of 4%.
  • Picking a convenient base such as 100 turns most percentage questions into arithmetic.
  • In a ratio problem, write the actual quantities as multiples of the ratio parts, for example 3k and 5k.
  • For mixtures, track the amount of the pure ingredient, which does not change when water is added.

Common traps

  • Using the new value as the base when reversing a percentage change.
  • Treating a percentage point change as a percent change.
  • Adding the same amount to both parts of a ratio and assuming the ratio stays the same.

Practice questions with solutions

Try each question first, then open the solution. Aim for about two minutes per question.

  1. A shop marks a jacket up 40% above its cost price and then sells it at a 25% discount on the marked price. What is the shop's profit as a percent of the cost price?

    • A 10%
    • B 15%
    • C 3%
    • D 5%
    • E 0%
    Show answer and solution

    Answer: D. 5%

    Take cost = 100. Marked price = 140. Selling price = 140 x 0.75 = 105. Profit = 5 on a cost of 100, which is 5%.

  2. The ratio of boys to girls in a class of 64 is 3 : 5. How many girls must leave the class so that the ratio of boys to girls becomes 3 : 4?

    • A 6
    • B 4
    • C 10
    • D 12
    • E 8
    Show answer and solution

    Answer: E. 8

    The class has 24 boys and 40 girls. For a 3 : 4 ratio with 24 boys, there must be 32 girls, so 8 girls leave.

  3. A salary is increased by 20% and later reduced by x% so that it returns to its original value. What is x?

    • A 16 2/3
    • B 15
    • C 16
    • D 18 1/3
    • E 20
    Show answer and solution

    Answer: A. 16 2/3

    The multiplier after the rise is 1.2, so the reduction multiplier must be 1/1.2 = 5/6. That is a fall of 1/6, which is 16 2/3 percent.

  4. The population of a town grows by 10% each year. It is 12,100 now. What was it two years ago?

    • A 10,500
    • B 11,000
    • C 10,000
    • D 10,200
    • E 9,680
    Show answer and solution

    Answer: C. 10,000

    Two years of 10% growth multiplies by 1.21. 12,100 / 1.21 = 10,000.

  5. A 40 litre solution is 25% alcohol. How many litres of water must be added to make it 20% alcohol?

    • A 10
    • B 5
    • C 12
    • D 8
    • E 15
    Show answer and solution

    Answer: A. 10

    The alcohol is 25% of 40 = 10 litres and stays the same. For 20%, the total must be 10 / 0.2 = 50 litres, so 10 litres of water are added.

  6. Two positive numbers are in the ratio 5 : 7. When 10 is added to each, the ratio becomes 3 : 4. What is the sum of the original numbers?

    • A 132
    • B 108
    • C 96
    • D 120
    • E 144
    Show answer and solution

    Answer: D. 120

    Let the numbers be 5k and 7k. (5k + 10)/(7k + 10) = 3/4 gives 20k + 40 = 21k + 30, so k = 10. The numbers are 50 and 70, and their sum is 120.

  7. In an election between two candidates, the winner received 55% of the votes and won by 2,000 votes. How many votes were cast in total?

    • A 40,000
    • B 20,000
    • C 25,000
    • D 18,000
    • E 22,000
    Show answer and solution

    Answer: B. 20,000

    The winner got 55% and the other 45%, so the margin is 10% of the total. 10% of the total = 2,000, so the total is 20,000.

  8. A's income is 25% more than B's income. B's income is what percent less than A's income?

    • A 22.5%
    • B 20%
    • C 12.5%
    • D 15%
    • E 25%
    Show answer and solution

    Answer: B. 20%

    Let B = 100. A = 125. B is 25 less than A, and 25 / 125 = 20%.

  9. A tank is 60% full. After 24 litres are removed, it is 35% full. What is the capacity of the tank in litres?

    • A 120
    • B 96
    • C 60
    • D 80
    • E 100
    Show answer and solution

    Answer: B. 96

    The 24 litres are 60% minus 35% = 25% of capacity. Capacity = 24 / 0.25 = 96 litres.

  10. Two items are each sold for 1,200. One is sold at a 20% profit and the other at a 20% loss. What is the overall result on the two sales?

    • A A loss of 2%
    • B A gain of 4%
    • C No gain or loss
    • D A loss of 4%
    • E A loss of 5%
    Show answer and solution

    Answer: D. A loss of 4%

    The first cost 1,200 / 1.2 = 1,000. The second cost 1,200 / 0.8 = 1,500. Total cost 2,500, total revenue 2,400, a loss of 100, which is 4% of 2,500.

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