Mental math for consulting interviews
Each series runs through 10 calculations of the kind you are asked during a case: a percentage, a multiplication of large numbers, a division, a growth rate, a break-even point, a rule of 72. You type your answer, rounding within 1% is accepted, and you get your score and your time at the end.
10 calculations, the clock starts on the first. Take a sheet of paper.
The calculations that come up in interviews
A consulting case always draws on the same families of calculation. Percentages take you from a market to a market share, or from revenue to a margin. Multiplications and divisions of large numbers appear as soon as you size a market or bring a total down to a unit cost. Growth, simple or compounded over two or three years, is used to project revenue.
Two calculations recur in investment and launch cases. Break-even tells you how many units must be sold to cover fixed costs, and the rule of 72 gives, in one division, the time a quantity takes to double. Neither is hard in itself: the difficulty comes from chaining them without error while you talk.
Useful shortcuts
These shortcuts avoid long-hand operations, which take time and invite errors. Every example is exact.
- 1
Go through 10% and 5%
For 35% of 4,800, take 10% (480), multiply by three (1,440) and add half of 10% (240). The result is 1,680. - 2
Multiply by 25 by dividing by 4
36 × 25 is the same as 36 ÷ 4 × 100, so 9 × 100 = 900. In the same way, multiplying by 50 means halving then multiplying by 100. - 3
Split the two-digit factor
47 × 12,000 is done in two pieces: 40 × 12,000 = 480,000 and 7 × 12,000 = 84,000, so 564,000. - 4
Take the zeros out before dividing
For 4.8 million ÷ 1,200, remove two zeros on each side: 48,000 ÷ 12 = 4,000. Write down the zeros you remove so you do not lose them. - 5
Memorise common compound growth
Two years at 10% make 21%, not 20%, because 1.1 × 1.1 = 1.21. Two years at 20% make 44%, because 1.2 × 1.2 = 1.44. - 6
Double with the rule of 72
Divide 72 by the annual growth rate to get the number of years needed to double: 9 years at 8%, 12 years at 6%, 6 years at 12%. - 7
Find break-even through unit margin
With 600,000 euros of fixed costs, a price of 50 euros and a variable cost of 30 euros, the margin per unit is 20 euros. So you need to sell 600,000 ÷ 20 = 30,000 units. - 8
Know fractions as percentages
One eighth is 12.5%, one sixth about 16.7% and one seventh about 14.3%. With those three values, most market shares can be read off without calculating.
Frequently asked questions
Are calculators allowed in consulting interviews?
No. Case calculations are done by hand, on paper, while explaining what you are doing. That is why the tool shows no calculator: take a sheet of paper and set out your operations as you would in front of an interviewer.
What level of precision is expected?
An exact result when the calculation is simple, a stated rounding when it is not. The tool accepts a 1% gap, which matches a reasonable rounding: answering 1,690 for 1,680 passes, answering 1,700 does not.
How should I type my answer?
The way you would write it on paper. The tool reads "1680", "1,680", "2.9", "12.5%" and "4.2 million". When the question asks for an answer in millions, you can type "4.2" or "4.2 million".
How long should a series take?
There is no official benchmark. Aim for ten correct answers first, then try to cut your time from one series to the next: in an interview, a calculation error costs more than a few extra seconds.
Is the rule of 72 exact?
It is an approximation, and a very good one for common rates. At 8% a year, exact doubling takes 9.01 years and the rule gives 9. At 3%, the exact figure is 23.4 years and the rule gives 24. Present it as an order of magnitude.