# Designed for Real Case Calculations

## Overview

One of the most significant differentiators of the *FastMath Ace the Case* Online Course when compared to other quantitative Case Interview preparation resources, is that this course is carefully tailored for the specific calculations and the **kinds of numbers** that you will actually encounter in Case Interviews at management consulting firms, or at other firms that use management consulting-style Case Interviews.

Before I created this course, I carefully examined many quant problems given that top Management Consulting firms like McKinsey, Bain, BCG, Accenture, and Deloitte had given to candidates in Case Interviews. While reviewing these problems, I noticed that the specific numbers required for calculations in Case Interview (what I will call **Case Numbers**) looked to me like they had been carefully chosen to have specific properties that could be used to dramatically simplify the calculations — if you knew the proper methods!

Since I have always looked for the simplest way to solve quantitative problems, many of these methods were apparent to me — but at MIT I saw that these methods weren’t apparent to many of my peers. I created the *FastMath Ace the Case* material to teach the most efficient ways to perform the actual calculations and quantitative analysis required in Case Interviews — using the **types of numbers** you would actually see in Case Interviews.

## Properties of Case Numbers

Case Numbers (i.e. numbers actually used in Case Interview calculations) have a few properties that make them easier to calculate with. First, Case Numbers are often “round” numbers with one or two significant digits, such as 300,000, 4,000,000, or 25 Million. Some people may be intimidated by having to do a calculation like (4,000,000 × 20,000) without a calculator. In this course, I’ll teach you efficient methods to manage the zeroes (see Multiplication Lesson), so calculations like these will become easy. A Case Calculation is an actual calculation required in a Case Interview (with the specific numbers). In the sample above, (4,000,000 × 20,000) would be a Case Calculation while 4,000,000 and 20,000 would be Case Numbers.

**Example Case Calculation**

When Case Numbers have more than one significant digit, they usually have certain properties that can make calculations like multiplication and division much easier — here’s an example:

**Question: **A company sells a Product for $32 per unit and sells 25,000 units per year. What is their annual Revenue?

These numbers are representative of actual Case Numbers, and you would need to do the calculation: ($32 × 25,000). Most people would execute this by multiplying (32 × 25) and then writing the three zeroes from “25,000” at the end of this result. This will give the proper answer, but most people find this hard to do quickly, especially without using a pen and paper.

Here is an efficient *FastMath* method to perform the calculation (32 × 25) using relevant properties of these Case Numbers. Decompose 25 as: (25 = ¼ × 100); then use the decomposition to perform the calculation:

32 × ¼ = 8

8 × 100 = 800

Therefore (32 × 25 = 800). If you’re uncertain of this, you should verify this result with pen and paper.

This method works because (25 = ¼ × 100), and so (4 x 25 = 100); so, when you divide 32 by 4, the result is the “number of groups of 100.” Here’s another way to think about the problem: if you had 32 quarters (e.g. American coins), how much money would you have? Well, there are 4 quarters to 1 dollar and 32 ÷ 4 = 8, so you would have $8, with is 800 cents. Since a quarter is 25 cents and we have 32 quarters which we just determine dis is 800 cents, then 32 × 25 = 800. We can view the calculation as follows:

32 × 25 = 32 × ¼ × 100 = (32 × ¼) × 100 = 8 × 100 = 800

In general, to multiply any number N by 25, you divide N by 4, and then multiply the result by 100. The answer to our original problem of ($32 × 25,000) is then $800,000 (800 with three more ‘0’s at the end).

**Clean Numbers**

Case Numbers are frequently what I call “Clean Numbers,” which means they are a “clean fraction” times a power of 10. where a “clean fraction” means a fraction with both numerator and denominator which are 10 or less. For example, 25 is a clean number because: (25 = ¼ × 100). Most multiplication and division calculations required in Case Interviews involve Clean Numbers. The following are examples of typical Case Calculations involving Clean Numbers:

- 120 Million × 250
- 48 Thousand × 75 Thousand
- 240 Thousand × 150 Thousand
- 360 Billion ÷ 75 Thousand
- 40 Billion ÷ 50 Thousand
- 16% of 25 Million

While these calculations probably aren’t easy for most people, unless they have specifically practiced calculating with these types of numbers, you can dramatically simplify these calculations with the proper methods. In the *FastMath Ace the Case* Online Course I will teach you you a comprehensive set of methods for performing calculations with the types of Case Numbers you will actually encounter in Case Interviews, along with efficient methods for solving more complex Case Interview problem types. See the **Practice Problems** page for more examples of Case Calculations and examples of several Case Interview problem types.

## Beware of “Imposter” Case Calculations

Nearly all the other quantitative Case Interview preparation resources I have reviewed have practice calculations with numbers that you are **highly** **unlikely** to encounter in an actual Case Interview, such as multiplying by a number like 23,487 — or a number with five (or more) significant digits. In summary, the practice problems are not representative of actual Case Numbers or Case Calculations. Practicing calculating with numbers with many significant digits is not an effective way to prepare for Case Interviews, as you will be practicing brute-force calculation skills that you won’t need in an actual Case Interview. Furthermore, you won’t get experience looking for or applying methods to simplify calculations that use the specific properties of Case Numbers.

If you see example problems where you are multiplying or dividing by numbers several significant digits which aren’t Clean Numbers (like 247 × 89) or adding numbers with four or more significant digits, this is a red flag indicating these calculations are likely “made up” and not representative of actual Case Numbers and Case Calculations. As a result, there likely won’t be a method you can apply to simplify the calculation — and practicing with these types of problems is not an effective way to prepare for actual Case Interviews. If a Case Number has three or more significant digits, the last digit is often a “5” which makes all types of operations easier to perform. Therefore, even a calculation like 37 × 89 in unusual in a Case Interview — you are more likely to see something like 45 × 80 which is much simpler to do, and there are *FastMath* methods you can apply to make it extremely simple.

## Summary

In the *FastMath Ace the Case* Online Course I will teach you practical methods you can use to dramatically simplify nearly all the calculations you might encounter in a Case Interview. All the calculation methods, example problems, and practice problems in this course are based on actual Case Calculations (and the specific Case Numbers involved) from leading management consulting firms like McKinsey, Bain, BCG, Accenture and Deloitte. For these reasons, I believe the *FastMath Ace the Case* Online Course is the best quantitative Case Interview preparation resource available because all the material in this course is specifically tailored towards the types of calculations you will encounter in actual Case Interviews at elite management consulting firms.