Case interview mental math skills can make the difference between acing a case interview and failing one.

 

Consulting firms such as McKinsey, Bain, and BCG expect candidates to quickly and accurately perform calculations as part of their problem solving process. Your case interview mental math skills demonstrate how you handle pressure, structure your thoughts, and deliver solutions in real time.

 

If you struggle with case interview mental math, then this article is for you. I’m a former Bain Manager and interviewer and in this article, we’ll cover 10 case interview mental math strategies that will immediately improve your case interview performance.

 

If you’re looking for a step-by-step shortcut to learn case interviews quickly, enroll in our case interview course. These insider strategies from a former Bain interviewer helped 30,000+ land consulting offers while saving hundreds of hours of prep time.

 

The Importance of Case Interview Mental Math

 

During a case interview, you might be asked to estimate market sizes, calculate profitability, or solve for an unknown variable, all on the spot. Interviewers use these case interview math exercises to assess your analytical capabilities and your approach to problem solving.

 

Here’s why case interview mental math matters:

 

• Efficiency and Speed: Case interviews are timed, and interviewers are looking for candidates who can think on their feet. Quick mental calculations save valuable time, allowing you to focus more on analysis and strategic thinking

 

• Accuracy and Reliability: In consulting, small errors can lead to big mistakes. Demonstrating strong mental math skills shows your ability to provide accurate data, which is crucial for making sound recommendations

 

• Client Confidence: As a consultant, you'll often be in situations where you'll need to provide immediate insights to clients. Strong mental math skills help build trust and credibility, as clients see you as someone who can handle complex data effortlessly

 

• Problem Solving: Mental math is integral to breaking down large problems into manageable parts. It aids in hypothesis testing and exploring different scenarios quickly

 

• Professionalism: Consulting firms look for polished, professional candidates. Being able to perform mental math seamlessly under pressure is a key part of presenting yourself as a competent and confident consultant

 

Therefore, if you want to excel at case interviews, then it's critical to hone your case interview mental math skills.

 

Case Interview Mental Math Techniques

 

1. Estimation Strategies

 

Estimation is an essential skill in case interviews, especially for market sizing cases. Estimation allows you to make quick, reasonable assumptions and simplify complex calculations. Effective estimation can help you navigate through cases faster and provide approximate answers when exact numbers aren't necessary.

 

Here are some key strategies:

 

• Rounding Numbers: Simplify numbers by rounding them to the nearest ten, hundred, or thousand. For example, you can round 496 to 500

 

• Benchmarking: Use known benchmarks to estimate unknown quantities. For instance, if you know there are approximately 330 million people in the US, you can use this as a basis for other population-related estimates

 

• Multiplication and Division by Powers of Ten: Quickly adjust numbers by shifting decimal places when multiplying or dividing by 10, 100, or 1000

 

2. Multiplication and Division Shortcuts

 

Quick multiplication and division are essential for efficiency in case interviews. Here are some shortcuts to enhance your speed:

 

• Break Down Numbers: Decompose larger numbers into smaller, more manageable parts. For example, to multiply 23 by 47, you can break it down to (20+3)*(40+7)

 

• Use the Distributive Property: Apply the distributive property to simplify multiplication. For example, to multiply 7 by 496, you can calculate 7*(500-4)=(7*500)–(7*4)

 

• Simplify Before Dividing: Simplify fractions before performing division. For instance, to divide 244 by 8, you can first reduce this to dividing 122 by 4 and then 61 by 2

 

3. Percentage Calculations

 

Percentage calculations are frequently used in consulting to analyze data and trends. Use these techniques for quick and accurate results:

 

 

• 10% Rule: Easily find 10% of any number by moving the decimal point one place to the left. For example, 10% of 250 is 25

 

• 5% and 1% Rules: Use the 10% rule to quickly find 5% and 1%. For example, 5% of 250 is half of 25 (which is 12.5), and 1% is 2.5

 

• Combining Percentages: Combine known percentages to find other values. For example, 15% of a number can be found by adding 10% and 5% of that number

 

4. Working with Fractions and Decimals

 

Understanding fractions and decimals is critical for precise calculations. These strategies can help:

 

• Convert Fractions to Decimals: Convert fractions to decimals to make calculations easier. For example, 3/4 is 0.75

 

• Common Fractions: Memorize common fractions and their decimal equivalents, such as 1/2 (0.5), 1/3 (0.33), and 1/4 (0.25)

 

• Simplify Decimals: Round decimals to a manageable number of decimal places to simplify calculations where you don’t have to be perfectly exact

 

5. Handling Complex Calculations

 

Complex calculations can seem difficult, but breaking them down can make them more manageable:

 

• Divide and Conquer: Split complex problems into smaller, more straightforward steps. For example, to calculate 17% of 348, first find 10% of 348 (34.8), then 5% (17.4), and finally 2% (6.96), and add them up

 

• Step-by-Step Approach: Tackle each part of the problem methodically, ensuring accuracy at each stage before moving on

 

6. Breaking Down Large Numbers

 

Breaking down large numbers simplifies calculations and helps you stay organized:

 

• Chunking: Divide large numbers into smaller chunks. For instance, to multiply 234 by 56, break it down into (230+4)*(50+6)

 

• Simplified Multiplication: Use simplified multiplication techniques, such as the lattice method or long multiplication, to handle large numbers

 

7. Mental Addition and Subtraction

 

Adding and subtracting numbers quickly is essential for mental math proficiency.

 

• Compensation Method: Adjust numbers to make them easier to add or subtract. For example, to add 47 and 38, you can round 47 to 50 and 38 to 40, then add 50+40=90, and subtract the rounding difference, 90-3-2=82

 

• Breaking Down Numbers: Break down numbers into parts and add or subtract them separately. For example, to add 123 and 456, break it down to 100+400, 20+50, and 3+6, and then combine the sums

 

8. Cross-Multiplication for Ratios

 

Ratios are commonly used in case interviews to compare different quantities. Cross-multiplication is an efficient technique for solving ratio problems.

 

• Cross-Multiplication: To compare two ratios, cross-multiply the terms to find equivalence. For example, to determine if a/b=c/d, check if a*d=b*c

 

• Proportional Scaling: Scale ratios up or down to find equivalent values. For instance, if a/b=c/d, you can find unknown values by scaling proportionally

 

9. Rule of 72

 

The Rule of 72 is a simple formula used to estimate the number of years required for something to double when given a growth rate:

 

Divide 72 by the annual growth rate to find the approximate doubling time. For example, at a 6% growth rate, an investment will double in about 72/6=12 years.

 

Use the Rule of 72 for quick back-of-the-envelope calculations during case interviews when evaluating investment or revenue growth

 

10. Weighted Averages

 

Weighted averages are useful for finding the average of different groups with varying sizes. Multiply each group's average by its weight (proportion of the total), sum the results, and divide by the total weight.

 

For example, if Group A (weight=3) has an average of 50 and Group B (weight=2) has an average of 80, the weighted average is [(3*50)+(2*80)]/(3+2)=62.

 

Case Interview Mental Math Practice Problems and Solutions

 

Use the case interview mental math strategies that we covered to try solving the following math problems. Answers are included at the end of this section.

 

Case Interview Mental Math Practice Problems

 

1. Estimate 495 + 378.

 

2. Round 1526 to the nearest hundred.

 

3. Multiply 23 by 47.

 

4. Divide 240 by 8.

 

5. Find 15% of 480.

 

6. Calculate 35% of 1200.

 

7. Convert 3/8 to a decimal.

 

8. Simplify the fraction 18/24.

 

9. Estimate 47 * 86.

 

10. Divide 324 by 12.

 

11. Find 25% of 640.

 

12. Calculate 5% of 980.

 

13. Convert 0.75 to a fraction.

 

14. Simplify the fraction 45/60.

 

15. Estimate 63 * 19.

 

16. Divide 550 by 11.

 

17. Find 20% of 750.

 

18. Calculate 10% of 1250.

 

19. Convert 5/6 to a decimal.

 

20. Simplify the fraction 30/45.

 

21. Estimate 78 * 34.

 

22. Divide 684 by 9.

 

23. Find 12% of 550.

 

24. Calculate 2.5% of 200.

 

25. Convert 0.4 to a fraction.

 

26. Simplify the fraction 12/16.

 

27. Estimate 97 * 13.

 

28. Divide 720 by 15.

 

29. Find 8% of 375.

 

30. Calculate 3% of 450.

 

31. Convert 7/8 to a decimal.

 

32. Simplify the fraction 36/48.

 

33. Estimate 56 * 72.

 

34. Divide 144 by 16.

 

35. Find 18% of 600.

 

36. Calculate 1.5% of 320.

 

37. Convert 0.625 to a fraction.

 

38. Simplify the fraction 20/25.

 

39. Estimate 84 * 49.

 

40. Divide 432 by 12.

 

41. Find 30% of 270.

 

42. Calculate 4% of 950.

 

43. Convert 3/5 to a decimal.

 

44. Simplify the fraction 48/60.

 

45. Estimate 67 * 23.

 

46. Divide 500 by 20.

 

47. Find 14% of 430.

 

48. Calculate 6% of 750.

 

49. Convert 0.875 to a fraction.

 

50. Simplify the fraction 27/36.

 

51. Estimate 92 * 54.

 

52. Divide 648 by 18.

 

53. Find 22% of 350.

 

54. Calculate 7% of 280.

 

55. Convert 1/3 to a decimal.

 

56. Simplify the fraction 40/50.

 

57. Estimate 73 * 39.

 

58. Divide 256 by 4.

 

59. Find 9% of 410.

 

60. Calculate 12.5% of 320.

 

61. Convert 0.2 to a fraction.

 

62. Simplify the fraction 15/20.

 

63. Estimate 81 * 65.

 

64. Divide 990 by 11.

 

65. Find 16% of 625.

 

66. Calculate 3.5% of 700.

 

67. Convert 2/5 to a decimal.

 

68. Simplify the fraction 21/28.

 

69. Estimate 104 * 29.

 

70. Divide 400 by 25.

 

71. Find 27% of 520.

 

72. Calculate 5.5% of 800.

 

73. Convert 0.333 to a fraction.

 

74. Simplify the fraction 14/21.

 

75. Estimate 59 * 37.

 

76. Divide 324 by 6.

 

77. Find 11% of 900.

 

78. Calculate 1.25% of 160.

 

79. Convert 4/9 to a decimal.

 

80. Simplify the fraction 16/20.

 

81. Estimate 89 * 42.

 

82. Divide 810 by 9.

 

83. Find 19% of 290.

 

84. Calculate 2.75% of 360.

 

85. Convert 0.6 to a fraction.

 

86. Simplify the fraction 25/30.

 

87. Estimate 77 * 51.

 

88. Divide 450 by 15.

 

89. Find 13% of 720.

 

90 Calculate 8.5% of 470.

 

91. Convert 7/10 to a decimal.

 

92. Simplify the fraction 22/33.

 

93. Estimate 95 * 25.

 

94. Divide 675 by 5.

 

95. Find 21% of 310.

 

96. Calculate 4.25% of 240.

 

97. Convert 0.125 to a fraction.

 

98. Simplify the fraction 35/50.

 

99. Estimate 66 * 38.

 

100. Divide 550 by 25.

 

Case Interview Mental Math Practice Solutions

 

1. Estimate 495 + 378.

 

Solution: 500 + 400 = 900

 

2. Round 1,526 to the nearest hundred.

 

Solution: 1,500

 

3. Multiply 23 by 47.

 

Solution: 1081

 

4. Divide 240 by 8.

 

Solution: 30

 

5. Find 15% of 480.

 

Solution: 0.15 * 480 = 72

 

6. Calculate 35% of 1200.

 

Solution: 0.35 * 1200 = 420

 

7. Convert 3/8 to a decimal.

 

Solution: 3/8 = 0.375

 

8. Simplify the fraction 18/24.

 

Solution: 18/24 = 3/4

 

9. Estimate 47 * 86.

 

Solution: 50 * 90 = 4,500

 

10. Divide 324 by 12.

 

Solution: 27

 

11. Find 25% of 640.

 

Solution: 0.25 * 640 = 160

 

12. Calculate 5% of 980.

 

Solution: 0.05 * 980 = 49

 

13. Convert 0.75 to a fraction.

 

Solution: 0.75 = 3/4

 

14. Simplify the fraction 45/60.

 

Solution: 45/60 = 3/4

 

15. Estimate 63 * 19.

 

Solution: 60 * 20 = 1,200

 

16. Divide 550 by 11.

 

Solution: 50

 

17. Find 20% of 750.

 

Solution: 0.20 * 750 = 150

 

18. Calculate 10% of 1,250.

 

Solution: 0.10 * 1,250 = 125

 

19. Convert 5/6 to a decimal.

 

Solution: 5/6 ≈ 0.8333

 

20. Simplify the fraction 30/45.

 

Solution: 30/45 = 2/3

 

21. Estimate 78 * 34.

 

Solution: 80 * 30 = 2,400

 

22. Divide 684 by 9.

 

Solution: 76

 

23. Find 12% of 550.

 

Solution: 0.12 * 550 = 66

 

24. Calculate 2.5% of 200.

 

Solution: 0.025 * 200 = 5

 

25. Convert 0.4 to a fraction.

 

Solution: 0.4 = 2/5

 

26. Simplify the fraction 12/16.

 

Solution: 12/16 = 3/4

 

27. Estimate 97 * 13.

 

Solution: 100 * 10 = 1,000

 

28. Divide 720 by 15.

 

Solution: 48

 

29. Find 8% of 375.

 

Solution: 0.08 * 375 = 30

 

30. Calculate 3% of 450.

 

Solution: 0.03 * 450 = 13.5

 

31. Convert 7/8 to a decimal.

 

Solution: 7/8 = 0.875

 

32. Simplify the fraction 36/48.

 

Solution: 36/48 = 3/4

 

33. Estimate 56 * 72.

 

Solution: 60 * 70 = 4,200

 

34. Divide 144 by 16.

 

Solution: 9

 

35. Find 18% of 600.

 

Solution: 0.18 * 600 = 108

 

36. Calculate 1.5% of 320.

 

Solution: 0.015 * 320 = 4.8

 

37. Convert 0.625 to a fraction.

 

Solution: 0.625 = 5/8

 

38. Simplify the fraction 20/25.

 

Solution: 20/25 = 4/5

 

39. Estimate 84 * 49.

 

Solution: 80 * 50 = 4,000

 

40. Divide 432 by 12.

 

Solution: 36

 

41. Find 30% of 270.

 

Solution: 0.30 * 270 = 81

 

42. Calculate 4% of 950.

 

Solution: 0.04 * 950 = 38

 

43. Convert 3/5 to a decimal.

 

Solution: 3/5 = 0.6

 

44. Simplify the fraction 48/60.

 

Solution: 48/60 = 4/5

 

45. Estimate 67 * 23.

 

Solution: 70 * 20 = 1,400

 

46. Divide 500 by 20.

 

Solution: 25

 

47. Find 14% of 430.

 

Solution: 0.14 * 430 = 60.2

 

48. Calculate 6% of 750.

 

Solution: 0.06 * 750 = 45

 

49. Convert 0.875 to a fraction.

 

Solution: 0.875 = 7/8

 

50. Simplify the fraction 27/36.

 

Solution: 27/36 = 3/4

 

51. Estimate 92 * 54.

 

Solution: 90 * 50 = 4,500

 

52. Divide 648 by 18.

 

Solution: 36

 

53. Find 22% of 350.

 

Solution: 0.22 * 350 = 77

 

54. Calculate 7% of 280.

 

Solution: 0.07 * 280 = 19.6

 

55. Convert 1/3 to a decimal.

 

Solution: 1/3 ≈ 0.3333

 

56. Simplify the fraction 40/50.

 

Solution: 40/50 = 4/5

 

57. Estimate 73 * 39.

 

Solution: 70 * 40 = 2,800

 

58. Divide 256 by 4.

 

Solution: 64

 

59. Find 9% of 410.

 

Solution: 0.09 * 410 = 36.9

 

60. Calculate 12.5% of 320.

 

Solution: 0.125 * 320 = 40

 

61. Convert 0.2 to a fraction.

 

Solution: 0.2 = 1/5

 

62. Simplify the fraction 15/20.

 

Solution: 15/20 = 3/4

 

63. Estimate 81 * 65.

 

Solution: 80 * 70 = 5,600

 

64. Divide 990 by 11.

 

Solution: 90

 

65. Find 16% of 625.

 

Solution: 0.16 * 625 = 100

 

66. Calculate 3.5% of 700.

 

Solution: 0.035 * 700 = 24.5

 

67. Convert 2/5 to a decimal.

 

Solution: 2/5 = 0.4

 

68. Simplify the fraction 21/28.

 

Solution: 21/28 = 3/4

 

69. Estimate 104 * 29.

 

Solution: 100 * 30 = 3000

 

70. Divide 400 by 25.

 

Solution: 16

 

71. Find 27% of 520.

 

Solution: 0.27 * 520 = 140.4

 

72. Calculate 5.5% of 800.

 

Solution: 0.055 * 800 = 44

 

73. Convert 0.333 to a fraction.

 

Solution: 0.333 ≈ 1/3

 

74. Simplify the fraction 14/21.

 

Solution: 14/21 = 2/3

 

75. Estimate 59 * 37.

 

Solution: 60 * 40 = 2,400

 

76. Divide 324 by 6.

 

Solution: 54

 

77. Find 11% of 900.

 

Solution: 0.11 * 900 = 99

 

78. Calculate 1.25% of 160.

 

Solution: 0.0125 * 160 = 2

 

79. Convert 4/9 to a decimal.

 

Solution: 4/9 ≈ 0.4444

 

80. Simplify the fraction 16/20.

 

Solution: 16/20 = 4/5

 

81. Estimate 89 * 42.

 

Solution: 90 * 40 = 3,600

 

82. Divide 810 by 9.

 

Solution: 90

 

83. Find 19% of 290.

 

Solution: 0.19 * 290 = 55.1

 

84. Calculate 2.75% of 360.

 

Solution: 0.0275 * 360 = 9.9

 

85. Convert 0.6 to a fraction.

 

Solution: 0.6 = 3/5

 

86. Simplify the fraction 25/30.

 

Solution: 25/30 = 5/6

 

87. Estimate 77 * 51.

 

Solution: 80 * 50 = 4,000

 

88. Divide 450 by 15.

 

Solution: 30

 

89. Find 13% of 720.

 

Solution: 0.13 * 720 = 93.6

 

90 Calculate 8.5% of 470.

 

Solution: 0.085 * 470 = 39.95

 

91. Convert 7/10 to a decimal.

 

Solution: 7/10 = 0.7

 

92. Simplify the fraction 22/33.

 

Solution: 22/33 = 2/3

 

93. Estimate 95 * 25.

 

Solution: 100 * 25 = 2,500

 

94. Divide 675 by 5.

 

Solution: 135

 

95. Find 21% of 310.

 

Solution: 0.21 * 310 = 65.1

 

96. Calculate 4.25% of 240.

 

Solution: 0.0425 * 240 = 10.2

 

97. Convert 0.125 to a fraction.

 

Solution: 0.125 = 1/8

 

98. Simplify the fraction 35/50.

 

Solution: 35/50 = 7/10

 

99. Estimate 66 * 38.

 

Solution: 70 * 40 = 2,800

 

100. Divide 550 by 25.

 

Solution: 22

 

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