Consulting Maths: The Only Techniques That Actually Come Up

Case maths is not competition arithmetic. It is a small set of operations on large round numbers, performed out loud, without mistakes, while you keep hold of what the number means.

Drill these and you cover the overwhelming majority of what appears.

The five techniques

Round and correct. 47 times 21 becomes 47 times 20, which is 940, plus 47, which is 987. Faster and more reliable than long multiplication, and much easier to do out loud.

Shuffle factors. 25 times 48 becomes 100 times 12 by moving a 4 across. Look for 25, 50 and 125 and pair them with their complements.

Work in units, not zeros. Write 4.2 billion as 4.2 and track the unit in the margin. Almost every arithmetic disaster in a case is a misplaced zero.

Percentages via fractions. 12.5 percent is one eighth. 16.7 percent is one sixth. 37.5 percent is three eighths. Dividing is faster than multiplying by a decimal.

Estimate before you compute. Say "this should land near 900" before starting. You will catch order-of-magnitude errors instantly, and catching your own error costs almost nothing.

The three formulas

Breakeven volume

Breakeven units = Fixed Costs / (Price - Variable Cost per unit)

The denominator is contribution per unit. Name it as such out loud; it signals that you know why the formula works rather than that you memorised it.

This is the single most frequently requested calculation in the entire interview.

Rule of 72

Years to double = 72 / growth rate (%)

Nine percent growth doubles in about eight years. Reliable between roughly four and fifteen percent, which is where cases live.

Payback period

Payback (years) = Upfront Investment / Annual Cash Flow

Crude but ubiquitous. If pushed for something better, mention net present value and note that payback ignores the time value of money and everything after the payback date.

Percentage points versus percent

Margin moving from twenty percent to twenty-five percent is five percentage points, or a twenty-five percent relative increase.

Interviewers listen for this distinction specifically. Using the wrong one reads as sloppiness with client numbers, which is exactly the trait the interview is designed to detect.

The habit that matters most

Translate every number into a judgement before moving on.

Not this:

Breakeven is 240,000 units.

This:

Breakeven is 240,000 units, which is twelve percent of the market we sized. That looks ambitious for a new entrant in year one.

The arithmetic earns you very little on its own. Converting it into a claim about the client's decision is the step that scores.

How to narrate

Say the equation out loud. Go quiet and compute. State the answer with its unit.

Narrating each digit is slow and makes a small slip sound catastrophic. Narrating the setup gets you credit for the method even when the arithmetic wobbles, and it lets the interviewer correct an input rather than mark down the whole answer.

A drill that works

Ten questions, timed individually, mixing all five techniques. Do it daily for two weeks and the difference is obvious.

The point is not to become a calculator. It is to stop spending working memory on arithmetic so you have some left for the actual problem.