# Fast Math: Quant Skills

Fast math. Just the term itself is enough to strike fear into any English or History major.

Here’s the thing: no matter your background, you will be expected to be comfortable with fast math during your consulting case interviews. If math isn’t your strong suit – don’t worry. Case interviews don’t require advanced calculus or geometry – think of the case interview as a series of fast math games!

In addition, you can use fast math rules as shortcuts. There’s nothing you need to know beyond simple addition, subtraction, multiplication, and division. With time and training, anyone can practice enough to be prepared for any consulting math. Just don’t wait too long and be forced to learn math fast – which isn’t as effective to learning fast math (see what we did there?)

## What is Fast Math Like in Case Interviews?

The math itself isn’t difficult in case interviews. However, with the pressure of an interviewer staring you in the face, the complexities of the other parts of the case, and limited time, fast math is challenging. To get yourself more acquainted with the math in case interviews, let’s talk about some of the commonalities in consulting math.

### 1. Fast Math Requires Large Numbers

Consulting firms work with some of the largest companies in the world, so naturally, your case interviews will deal with large numbers as well. Keeping track of your units, whether they are in thousands, millions, or billions, is very important.

As simple and preventable as it sounds, many candidates falter with their math by missing or adding extra zeroes. Though a simple mistake, one zero could change your entire recommendation, so it actually is a big deal.

### 2. Percentages Are Essential

Consultants love to think in percentages because it’s the most helpful way to compare numbers and strategies. It’ll be important for you get comfortable with calculating percentages, which involves a lot of multiplication and division.

For instance, let’s say your client is analyzing a potential investment opportunity that is projected to generate \$1 million in profit a year. Sounds like a great investment, but what if your client generates \$10 billion in profit a year? That would just be 0.1% of what your client currently earns, and there are probably larger opportunities you should recommend your client search for.

### 3. Multiple Steps Will Often Be Required

You may be provided a long list of data points and numbers that you’ll need to use to get to the insight you need to crack the case. This process will require multiple steps and can get tricky when there are a lot of numbers floating around.

Let’s use a profitability case as an example. The interviewer might tell you that your client sells 1,250,000 units a month at an average price of \$50. Your variable costs are \$15 per unit and overall fixed costs are \$1 million per month. The client wants to test out multiple pricing strategies and provides projections on how that will affect quantity – lowering the average price to \$40 will result in selling 2,000,000 units per month while increasing the average price to \$60 will result in selling 750,000 units per month. Calculating the optimal pricing and ultimate profitability clearly will require multiple steps. Managing all the data and the numbers while calculating your math quickly is challenging in a case interview setting.

## How Fast Are We Talking?

You’ll need to be able calculate most of your math steps within roughly 10 seconds (and all under 20 seconds). Let’s use an example. Try to calculate 150 million divided by 20 then multiplied by 125%.

How long did that take you?

If it took you longer than twenty seconds, it means you need some more practice. And if you were faster – good for you. You’ll have more time in the case to create analytical insights.

If 10 seconds per step sounds impossible, don’t worry – it just means you don’t yet know the tips and tricks you need for fast math. Let’s examine a few of them.

## Fast Math Tips, Tricks, and Facts

### 1. Using Round Numbers

One of the most important and easiest tricks for fast math is to use round numbers. In most cases, you will be able to round your numbers if you just simply ask. It’s not a secret fast math fact that you can ask to round. If the interviewer says, “No”, you still haven’t lost anything.

For example, let’s say you need to calculate 42 x 490,000. In such a case, it’s fair game for you to ask to calculate 40 x 500,000 instead, since you lose some by lowering to 40 but gain some by increasing to 500,000.

Rounding your numbers will make your calculations easier and is often what consultants do on the job, especially if they are calculating numbers on the fly in front of a client.

However, one note: McKinsey is the least likely to approve rounding, so in general, we recommend doing your first 10 cases with minimal rounding (only to the 1s place) so you are prepared for the toughest case interviewers around. And it’s not really that hard – for the above, it takes you 3 steps to not round ((42 x 500,000) – (42 x 10,000)) – only 30 seconds vs. 10 seconds.

### 2. Keeping Track of Large Numbers

Instead of writing down all your zeroes, notate your units in the following way:

• Thousands – “K”
• Millions – “M”
• Billions – “B”
• Trillions – “T”

Using these units allows you to focus on the numbers at hand and not get mixed up when your numbers have a lot of zeroes. You also save time.

For example, if you’re calculating 500,000 + 1,500,000 + 2,000,000 + 700,000, this instead simply becomes 0.5M + 1.5M + 2M + 0.7M = 4.7M.

### 3. The Halve and Double Method

Let’s say you need to multiply 140 x 450. How do you do this quickly? The halve and double method involves halving the smaller number and doubling the larger number to get to a more manageable calculation.

Here’s an example using the same problem of 140 x 450.

• 1st Step: 140 / 2 = 70
• 2nd Step: 450 x 2 = 900
• 3rd Step: 70 x 900 = 63,000

### 4. The Reordering Method

Sometimes, simply reordering your numbers is helpful to calculate the answer faster. This works for all types of calculations (addition, subtraction, multiplication, division) – it’s just a fast math trick! Here are a few examples:

• Addition: 430 + 210 + 170 = ?
• Step 1: 430 + 170 = 600
• Step 2: 600 + 210 = 810
• Subtraction: 1075 – 340 – 275 = ?
• Step 1: 1075 – 275 = 800
• Step 2: 800 – 340 = 460
• Multiplication: 250 x 20 x 4 = ?
• Step 1: 250 x 4 = 1000
• Step 2: 1000 x 20 = 20,000
• Division: 4200 ÷ 50 ÷ 60 = ?
• Step 1: 4200 ÷ 60 = 70
• Step 2: 70 ÷ 50 = 1.4