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CAT Quant

CAT percentages practice questions

Percentages sit underneath most of CAT arithmetic: profit and loss, interest, mixtures, data interpretation and even some algebra. Most mistakes come from using the wrong base for a percentage, so the first habit to build is asking one question every time: percentage of what? The questions below mix single step and successive change problems, with the working shown so you can compare your method.

Key ideas

  • A percentage change always refers to the original value, so a 20% rise followed by a 20% fall is a net fall of 4%, not zero.
  • Successive changes of a% and b% give a net change of a + b + ab/100 percent.
  • If A is x% more than B, then B is x/(100 + x) of A, which is less than x% below A.
  • Convert percentages to fractions for speed: 12.5% = 1/8, 16.67% = 1/6, 33.33% = 1/3.
  • In population and interest problems, use multipliers: a 10% rise for two years is a factor of 1.1 x 1.1.

Common traps

  • Using the new value as the base for a reverse percentage.
  • Adding successive percentages without the product term.
  • Forgetting that a percentage point and a percent are different.

Practice questions with solutions

Try each question first, then open the solution. Aim for about 90 seconds per question.

  1. The price of an item is increased by 20% and then decreased by 20%. What is the net change in the price?

    • A No change
    • B A decrease of 4%
    • C An increase of 4%
    • D A decrease of 2%
    Show answer and solution

    Answer: B. A decrease of 4%

    Multiplier = 1.2 x 0.8 = 0.96, so the price falls by 4%.

  2. A's salary is 25% more than B's. B's salary is what percentage less than A's?

    • A 25%
    • B 15%
    • C 20%
    • D 16.67%
    Show answer and solution

    Answer: C. 20%

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

  3. The population of a town is 50,000 and grows at 10% per year. What is the population after 2 years?

    • A 60,500
    • B 60,000
    • C 61,000
    • D 55,000
    Show answer and solution

    Answer: A. 60,500

    50,000 x 1.1 x 1.1 = 60,500.

  4. In an election 60% of the voters voted. The winner got 55% of the votes cast and won by 2,400 votes. How many voters are there in total?

    • A 36,000
    • B 40,000
    • C 44,000
    • D 48,000
    Show answer and solution

    Answer: B. 40,000

    Winner minus loser = 10% of votes cast = 6% of voters = 2,400. Voters = 2,400 / 0.06 = 40,000.

  5. Two successive discounts of 10% and 20% are equal to a single discount of:

    • A 30%
    • B 28%
    • C 25%
    • D 27%
    Show answer and solution

    Answer: B. 28%

    Price factor = 0.9 x 0.8 = 0.72, so the single discount is 28%.

  6. x is 20% more than y, and z is 25% less than x. z is what percentage less than y?

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

    Answer: C. 10%

    x = 1.2y and z = 0.75 x 1.2y = 0.9y, so z is 10% less than y.

  7. A student scores 40% and fails by 20 marks. With 50% marks he would pass by 40 marks. What are the total marks in the exam?

    Type in the answer (no options).

    Show answer and solution

    Answer: 600

    10% of the total is 20 + 40 = 60, so the total is 600.

  8. A shopkeeper marks an item 30% above cost and gives a 10% discount. If the selling price is Rs 1,170, what is the cost price in rupees?

    Type in the answer (no options).

    Show answer and solution

    Answer: 1000

    SP = CP x 1.3 x 0.9 = 1.17 CP. So CP = 1,170 / 1.17 = 1,000.

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