What are the best tools to practice consulting maths?

Hi there,

Because you already have great answers on the types of tricks you can use to do mental math, I will focus my response on tools and resources available:

Mobile Apps:

• Mathemagics: focuses on teaching mental math tricks and techniques.
• Mental Math Master: exercises to improve speed and accuracy.
• Elevate: a range of brain training exercises, goes beyond math, but includes math skills. 

Websites:

• Khan Academy: there are lessons to solve big additions in your head and identify patterns in numbers.
• Mathway: not the nicest user interface, but it breaks down calculations step-by-step, often with simplification steps you can use during case studies.
• Mental Math Trainer: again, not greatest user interface, and also doesn't give step-by-step solutions, but it generates sets of problems for you to practice.

Books:

• "Secrets of Mental Math" by Arthur Benjamin and Michael Shermer
• "The Trachtenberg Speed System of Basic Mathematics" by Jakow Trachtenberg
• GMAT Quant prep books

YouTube Channels:

• Numberphile: wide range of math topics, look for the number tricks videos. 
• Math Antics: also wide range, look for the multi-digit addiction, substraction, etc. 
• MindYourDecisions: look for the videos that are labeled with something such as “x% of people don't know this math secret”, also has brain teasers and problems used by companies (e.g., Amazon) to hire
   

Best of luck! 

Hi there - first of all congratulations on taking the first steps in your consulting prep journey. You have 3 months of time that is plenty as long as you are diligent and consistent in your preparation. 

Now let’s dive into the specifics of your question i.e. how to get better at mental maths. Please note though that is only one half of the quantitative thinking part. Figuring out the correct approach is the other one. I won’t talk about that part in this post since your question is specifically asking about the mental math part. 

Free resources on mental math include - google, working with chatgpt, watching youtube videos that will talk about this in a lot of detail. There is plenty of free content on this topic.

I will just summarize four effective tricks for your convenience. 

1. Rounding up or down: this is the first thing that you should try to do. This will make your calculations much much faster. However you need to be smart about how you round and of course check with the interviewer before proceeding. Also you need to use rounding in a way such that your final answer is not too far off (+/- 2-5% is generally acceptable). I always suggest that you adjust your answer after you are done to bring it closer to the actual answer. That is smart rounding. 
2. Breaking down into smaller bits: This involves taking the initial problem and figuring out a way to break it up so that the bits are easier to calculate. This is applicable to additions, subtractions, multiplications, divisions and any percentage calculations
3. Getting familiar with easy calculations: 10% of anything is always 1/10th of that quantity, 25% is 1/4th, 33% is 1/3rd and so on
4. Using scientific notation to manage zeroes: Scientific notation uses powers of 10 to express numbers. 1 million is 10^6, 1 Billion = 10^9, % = 10^(-2). This will ensure that you never mess up your zeroes

Let’s bring it all together with an example

What is 37% of 1.365M? 

• Rounding: let’s make it 35% of 1.4M (increase one and decrease other so the impact on final answer is mitigated to some extent)
• Breaking down into components: 30% of 1.4M + 5% of 1.4M
• Using easy calculations cheat sheet: 3 * (10% * 1.4M) + ½ * (10% of 1.4M) = 3*(0.14M) + ½ * 0.14M = 0.42M + 0.07M = 0.49M
• Scientific notation (use don't have to use this in this example but I am just showing you how to use it): 30 * 10^(-2) * 1.4 * 10^(6) + 5 * 10^(-2) * 1.4 * 10^(6) = 42 * 10^(4) + 7*10^(4) = 49*10^4 = 490,000

If you actually compute this answer it is 505,050. So you would be off by ~3%. You can definitely make smart adjustments to bring your answer even closer. I won’t go into smart adjustments here as mentioned earlier.

If you need more personalized help feel free to reach out. We can equip you with all the tricks in about an hour or 2 and then it is all about practice. 

Cheers

Nilay

Hi there,

Math is a very typical area where people struggle. I'd say around 80% of case candidates have issues here.

1. Start with isolated drills: Focus on calculation accuracy first (directionally correct), then speed. For example, practice multiplying and dividing large numbers like 347 x 58 or 1250 ÷ 25 until you can do these accurately without mistakes. Use flashcards or apps designed for mental math to reinforce these skills daily.
2. Practice case math: Do calculations within the context of case problems. For instance, work through a sample case where you need to calculate market size, revenue projections, or cost structures. This will help you become comfortable with the types of calculations you'll need to perform during actual interviews. The context matters!
3. Learn some tricks: Techniques like rounding and simplification can be incredibly helpful. Again, the interviewer looks for directionally correct results you come up with swiftly. 100% precision is not required. For example, if you need to multiply 492 by 23, round 492 to 500 and 23 to 20, then multiply 500 by 20 to get 10,000. Adjust the final answer by considering the rounding you did initially to get an estimate quickly.
4. Manage zeros effectively: Handling large numbers and zeros can be tricky. For instance, when multiplying 3,000 by 50, first multiply 3 by 50 to get 150, then add the three zeros back to get 150,000. This method simplifies the process and reduces the risk of errors.
5. Develop your own tricks: As you practice, you might discover your shortcuts and methods that make calculations easier for you. For example, if you find a specific way of breaking down percentages that works well for you, use that consistently.
6. Work with a coach or program: Consider getting a coach or enrolling in a case math program that covers both theory and practice. Programs like my Case Math Academy working with a coach can provide structured learning and personalized feedback, which can be invaluable. They often include modules that start with basic arithmetic and build up to complex problem-solving in business scenarios. Reach out for more info!

Three months is more than enough time to improve numeracy skills and be well-prepared for consulting interviews.

Cheers,

Florian

Hi there,

Q: I have an average of three months for preparing while working. Do you think this could be enough?

Yes, with daily practice that should be enough. I would recommend keeping track of the mistakes you make and prioritizing those that you repeat the most rather than doing random math drills.

In terms of general math tips, I would recommend the following:

1. Use the power of 10 correctly. For example, 3.2B / 723M can be written as 3200*10^6 / 732*10^6.
2. Ask if it is fine to approximate. You can ask the interviewer if you can approximate complex math. If allowed, this will help solve simpler problems. In the previous example, you could get 320*10^7 / 70*10^7. 
3. Keep good notes. This helps to avoid forgetting or misreporting numbers. 
4. Divide complex math into multiple simpler steps. For example: (96*39)*10^6 → 96*40 - 96*1 = 100*40 - 4*40 - 96*1 = 4000 – 160 – 100 + 4 → 3744*10^6.
5. Learn the main fractions results. You can learn by heart fractions and speed up or simplify the computation - the most useful to know are 1/6 ~ 17%, 1/7 ~ 14%, 1/8 = 12.5%, 1/9 ~ 11%.

Best,

Francesco

If your main issue is mental math I would highly recommend the following

• Apps that help improve mental math speed (see photomath or mental math practice) 
• Websites that guide you on the same - Khan Academy is brilliant as is Math Trainer

The key to math is always practice practice practice. Having the right tools to practice will help you improve quickly.

All the best,
Udayan

Wow, I see you received already several great answers. 

Sharing here also a cheat sheet with all the formulas that you need to know for the interviews:

Cheatsheet: The Must-Know Consulting Terms for Interviews

Best,
Cristian

Hi,

It is good that you have started identifying your weakes areas and want to come up with a plan to improve.

I would suggest buying a mental math book from Amazon. Don't buy something thick - read the reveiws and just a short book that teaches you some basics and tips. From experience I can say it is helpful.

Both tips and practice perspective. The more mental math you do the better you will get at it. Last think you want is to worry about the math in a consulting interview. All the best!

Thanks.

Try RocketBlocks. They have a good math drill tool.

In the resources section here a preplounge there's a tool you can use for mental math.