Mental Math Practice for Consulting Case Interviews

I have consulting interviews coming up, and urgently need mental math prep. Can anyone suggest online (free) resources I can use to pick up my terrible mental math skills? What math strategies are helpful to acing the math part of the consulting interviews?

Other advice on mental math prep is welcome.

Consulting Case Interview Math Prep

The best way to work on your mental math skills is practice. You should follow the advice broken down below and practice some mental math problems during your spare time.

For complex multiplication problems: one effective way to solve problems is to round one of the numbers you are working with to make it a multiple of ten and then add or subtract the difference.

For example: 163 * 242

  1. Round 163 to 200
  2. Multiple 200 by 242 = 48400
  3. Since we rounded up we need to subtract away (200 - 163) * 242
  4. 37 * 242 can be rounded to 40 * 242 = 9680
  5. 48400 - 9680 = 38720
  6. Finally, we need to add back the additional amount that we subtracted so (40 - 37) * 242 = 726
  7. 38720 + 726 = 39446

This process becomes much more simple with smaller problems. Example: 63 * 13 = 60 * 13 = 780 + (3*13) = 780 + 39 = 819

For square root questions - @StudentLoanBackedSecurity" offers good advice:

StudentLoanBackedSecurity:
Think of the nearest perfect squares. So for 2,000 I would look first at what the square root of 20 could be (obviously just approximate). The nearest perfect squares are 16 and 25. The square root of 20 would be in between 4 and 5, because obviously 4 squared is 16 and 5 squared is 25. Approximate and say the square root of 20 is 4.5. So now just move the decimal over, and I would have your answer as "about 45" and its basically very close and I would imagine that's all they expect.

User @Matrick", a hedge fund analyst, shared a good website for working on your mental math skills - Windhoff.net.

User @Proboscis", a consulting analyst, shared their advice:

Proboscis - Consulting Analyst:
There's an iPhone app called Mathemagics that you can practice with - focuses on math "tricks" though (ie. how to multiply 2 digit numbers by 11, etc.) - I found this less helpful overall.

I also memorized all of my fractions until 11/11. (ie., 1/1, 1/2, 2/2, 1/3, 2/3, 3/3, 1/4, 2/4, 3/4, 4/4, 1/5, 2/5,... etc.) Other fractions can then at least be ball parked or found exactly by basing it off of these memorized fractions. (ie. 1/12 is just half of 1/6)

User @Consultingrs" shared their advice on handling the numerical portion of case interviews:

Consultingrs:
  • Make no mistakes - watch out for units, as they are often there to purposely trick you (i.e., is it in $M or $B?, is it 100M lbs or just individual lbs?)
  • Perform math quickly - cancel out extra zeros quickly. For example, recognize that $B divided by $M, equals $K
  • Ask for permission to round - if you need to multiply 29 cents by 15 million, ask if you can round to 30 cents - the interviewer will tell you if it's acceptable or not
  • Put the answer in context - once you get a result from your calculation, put this in the context of the case. For example, if you calculate the payback period for the new competitor to be 17 years, you could confidently state that this doesn't seem to be a very good return for them and they might not be a threat for too long. Instead of generically stating, "it takes 17 years for them to payback their investment."
  • Organize your notepad so that one piece of paper is devoted only to your calculations. Then you have a separate piece of paper where you put the output of your calculations onto
  • Simply fractions whenever possible. The easiest way to do this is to divide the numerator and denominator by two in your head. This will make some of the divisions much easier when you simplify the fractions

You will almost never be asked to do anything other than simple addition, subtraction, division, or multiplication. The biggest challenge often isn't doing the calculations themselves. Rather, it's organizing the information, so that your calculations don't get messy and make you likely to make mistakes.

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Comments (68)

Nov 11, 2011 - 12:32pm
junior2012, what's your opinion? Comment below:

http://math.usask.ca/emr/menu_arith.html http://www.buildquiz.com/speed_math.swf

just practice

Nov 11, 2011 - 12:36pm
Proboscis, what's your opinion? Comment below:

https://www.caseinterview.com/math/home.php - developed by ex-McK Victor Cheng to help practice math skills

There's an iPhone app called Mathemagics that you can practice with - focuses on math "tricks" though (ie. how to multiply 2 digit numbers by 11, etc.) - I found this less helpful overall.

I also memorized all of my fractions until 11/11. (ie., 1/1, 1/2, 2/2, 1/3, 2/3, 3/3, 1/4, 2/4, 3/4, 4/4, 1/5, 2/5,... etc.) Other fractions can then at least be ball parked or found exactly by basing it off of these memorized fractions. (ie. 1/12 is just half of 1/6)

Good luck

Proboscis
  • 2
Nov 11, 2011 - 12:43pm
Proboscis, what's your opinion? Comment below:

Sometimes I personally found it helpful to write large numbers in scientific notation to help me deal with order of magnitude.

.....magnitude....pop pop!

Proboscis
Nov 11, 2011 - 2:32pm
cp26, what's your opinion? Comment below:

Just know how to break complicated problems into easier components.. ex. 73 * 25 = 7020 + 705 + 320 + 35 = 1400 + 350 + 60 + 15 = 1825

This makes mental math a lot easier... other than that, practice with large numbers

Jun 26, 2012 - 11:33am
FotoPhinish, what's your opinion? Comment below:

^^ (You could also do 73*25 as 7300/4 = 3650/2 = 1825).

I think a combination of (1.) practice and (2.) an awareness of different mental math tricks is the key. (For example: If you're asked to multiply 3743 during an interview, they're probably looking for the "trick" 3743 = 40^2 - 9 = 1591.)

For lists of tricks, both Wikipedia: http://en.wikipedia.org/wiki/Mental_calculation and "Wikibooks": http://en.wikibooks.org/wiki/Mental_Math have some.

I also recommend Ars Calcula: http://arscalcula.com/mental_math_multiplication_guide.shtml

Oct 14, 2014 - 8:56am
pr0ficient, what's your opinion? Comment below:

I can suggest a book and an app that were really helpful to me.

Bill Nye's Secrets of Mental Math Book: http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401 - I found this book to be superb. I read it twice and it changed the way I do mental math and at least doubled my speed.

Great free iPhone app to practice mental math on the go: http://www.bizmathtutor.com

Oct 14, 2014 - 10:30am
UTDFinanceGuy, what's your opinion? Comment below:

Go to your uni library.

Look into the psychology section. There will be books about mentalism. They contain GOLD in terms of mental math/cool tricks/body language/etc.

Or the math section, should have some mental math books. It's a great skill honestly which can show an illusion of great math comprehension even if you don't.

"It is better to have a friendship based on business, than a business based on friendship." - Rockefeller. "Live fast, die hard. Leave a good looking body." - Navy SEAL
  • 1
Oct 14, 2014 - 3:15pm
Consultingrs, what's your opinion? Comment below:

to get a great score on this dimension, you must:

Make no mistakes - watch out for units, as they are often there to purposely trick you (i.e., is it in $M or $B?, is it 100M lbs or just individual lbs?) Perform math quickly - cancel out extra zeros quickly. For example, recognize that $B divided by $M, equals $K Ask for permission to round - if you need to multiply 29 cents by 15 million, ask if you can round to 30 cents – the interviewer will tell you if it's acceptable or not Put the answer in context - once you get a result from your calculation, put this in the context of the case. For example, if you calculate the payback period for the new competitor to be 17 years, you could confidently state that this doesn't seem to be a very good return for them and they might not be a threat for too long. Instead of generically stating, "it takes 17 years for them to payback their investment." Interestingly, the case interview math is not supposed to be purposely hard. You will almost never be asked to do anything other than simple addition, subtraction, division, or multiplication. The biggest challenge often isn't doing the calculations themselves. Rather, it's organizing the information, so that you're calculations don't get messy and make you likely to make mistakes.

One easy trick to do is to organize your notepad so that one piece of paper is devoted only to your calculations. Then you have a separate piece of paper where you put the output of your calculations onto. That way, your notes don't get as messy. You can also write the letter A where you did your calculation, and then tie that to the letter A where you placed the output from your calculation. Then, if you make a mistake, you are easily able to find the calculation you did to try to quickly fix the error.

Performing math quickly is one of the key things to differentiate yourself on. The easiest way to do this is to always cancel out all excess zeros at every opportunity. If you are given numbers that are in the billions, just write the number and then put B after it. Likewise, if you are given numbers that are in the millions, just write the number and then put an M after it. Then you can put B over M and delete both to be left with K, which represents thousands. This trick will allow you to work though large numbers very quickly.

Another key trick that allows you to perform math quickly is to simply fractions whenever possible. The easiest way to do this is to divide the numerator and denominator by two in your head. This will make some of the divisions much easier when you simplify the fractions. - Craig (PM me for more info)

Mar 7, 2016 - 10:11pm
jkay121, what's your opinion? Comment below:

Improving Mental Math Ability (Originally Posted: 08/27/2009)

What do people think of books which claim to improve your ability to perform quick mental math (like http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401)? I assume if it could help you perform better during interviews, this couldn't be a bad thing.

Does anyone have any suggestions on other ways to improve mental math ability (or comments on this being a potentially wasted pursuit)?

  • 1
Mar 7, 2016 - 10:13pm
ShreddiesBrah, what's your opinion? Comment below:

There are many of them but most of them teach the same thing. I've been reading "Secrets of Mental Math" by Arthur benjamin and Michael Shermer this summer, and some of the techniques are very helpful. My mental division has definitely gotten a lot better and I can now calculate 29/35 = 5.8/7 = 0.8285714 within 10 seconds. It's astonishing reading about some of the techniques out there which aid in breaking down complex calculations. Mental calcs use to be one of my major weaknesses and I can't wait to flex my newly found prowess.

edit: Just realised the book you linked to is the same one I'm reading. Tip: I found mine free online (ebook)

Mar 7, 2016 - 10:19pm
Xptboy, what's your opinion? Comment below:

mental math (Originally Posted: 06/03/2010)

How many of you guys are good at mental maths? Is it important? I'm really bad at mental maths lol, is there any way I can improve it quickly?

Mar 7, 2016 - 10:20pm
junkbondswap, what's your opinion? Comment below:

Most of the finance and calculations performed in IB/PE/HF are fairly straight-forward so you should review and practice basic math concepts. Most mental math is pure arithmetic and I cant think of any way of practicing beyond rote learning and case study. You dont have to be a mathematician to do well in most areas of finance but if you cant calculate a simple annual increase of 20% on a $120 million investment you may want to rethink your chosen field or crack open a book.

Mar 7, 2016 - 10:21pm
insight123, what's your opinion? Comment below:

Mental math isn't really that important, but there's absolutely no harm in getting good at it.

There are actually small things you can do to get better. This may sound a little silly but just perform random calculations in your head when you're walking or bored etc. As you keep crunching, you will get better and see tricks and patterns. For instance;

when you're squaring any number that ends in 5; 65^2 = 67 and 55, put them together and you'll get 4225

works with 85^2 = 89 and 55 = 7225.

Mar 7, 2016 - 10:23pm
bigmonkey31, what's your opinion? Comment below:

i think the most mental math i got in a IBD interview was... 'what's 7 cubed'

Mar 7, 2016 - 10:26pm
LIBOR, what's your opinion? Comment below:

yah my friend was asked 'whats 4% of 9' in an interview... its obviously not hard but they do ask it

looking for that pick-me-up to power through an all-nighter?
Mar 7, 2016 - 10:29pm
bobbymac, what's your opinion? Comment below:

I had 19x17. Again straight forward as long as you take the simple approach.
I also had a few Physics 101...two cars travelling towards each other, one @10mph, the other....when will they meet.

If if don't make dollars, it don't make sense.

Mar 7, 2016 - 10:30pm
D M, what's your opinion? Comment below:

Isn't the answer to that last one... 1?

"You stop being an asshole when it sucks to be you." -IlliniProgrammer "Your grammar made me wish I'd been aborted." -happypantsmcgee
Mar 7, 2016 - 10:33pm
islandoffmorocco, what's your opinion? Comment below:

insight's trick is from a book called "secrets of mental math" (benjamin and shermer). buy it for 10 bucks on Amazon, read it, and then practice the art whenever you can. i checked it out recently, it's pretty good.

i agree about trying to develop that skill every chance you get. i have always thought it natural to calculate in my head whenever possible. it gets easier and quicker over time. i think it's a lot about memory, being able to store lots of digits in your head. also give memorizing your phone numbers a go. i didn't use the phonebook on my cell for the longest time, and it became natural for me to remember 200+ phone numbers. or, even if you store numbers, try actually typing them out when you make calls to develop your memory.

bah i'm rambling.

Mar 7, 2016 - 10:35pm
tequilazombie, what's your opinion? Comment below:

mental math shortcut (Originally Posted: 08/30/2012)

If someone at an interview asked me for example "whats 36 * 42" i would do it mentally by breaking it down into (30+6)(40+2) = 1200 + 60 + 240 + 12

is there any faster shortcut or trick?

Mar 7, 2016 - 10:37pm
BTbanker, what's your opinion? Comment below:

Yeah, there's no reason you need to make both numbers multiples of 10.

You should be able to do 3640 mentally (3040+6*40).

Mar 7, 2016 - 10:40pm
leveredarb, what's your opinion? Comment below:

if you expect alot of these i would advise getting trachtenbergs book of speed maths, its pretty useful (but I forgot most of it lol, I think their method is similar to the one you posted)

I personally would just do 3640+236

Mar 7, 2016 - 10:41pm
oreos, what's your opinion? Comment below:

for numbers between 10 and 19

eg. 1817 - i) 18 +7 =25 (must add the largest to the right of the smallest) ii) 25 *10 =250 iii) 87 = 56 iv) 250+56 =306

this will work for any number in the teens

"After you work on Wall Street it’s a choice, would you rather work at McDonalds or on the sell-side? I would choose McDonalds over the sell-side.” - David Tepper
Mar 7, 2016 - 10:42pm
blahblahblahnyc, what's your opinion? Comment below:

Mental Math (Originally Posted: 03/20/2013)

I was quite good with mental math when I was younger (think junior, senior HS) but as might be the case with many of you guys out there, calculator and technology kind of dampen the skills quite a bit. What are the best websites or books or techniques to improve mental math?

Mar 7, 2016 - 10:48pm
VanillaGorilla, what's your opinion? Comment below:

I bought this book, but haven't taken the time to start it yet. Looks like a good purchase though:

http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401

Array

Mar 7, 2016 - 10:52pm
chip201, what's your opinion? Comment below:
bondtradercu:
I was quite good with mental math when I was younger (think junior, senior HS) but as might be the case with many of you guys out there, calculator and technology kind of dampen the skills quite a bit. What are the best websites or books or techniques to improve mental math?

There are several books including: Secrets of mental math. For practice... try to solve as many in 120 sec on: calculationrankings com

Mar 7, 2016 - 10:55pm
TheTwoHacker, what's your opinion? Comment below:

Getting better in mental math (Originally Posted: 04/12/2013)

I have been struggling in doing calculations in my head. How do you guys practice this? Or is it something that comes natural? Lastly, is it really that important in finance, I mean, isn't that what computers are for?

Mar 7, 2016 - 11:02pm
chip201, what's your opinion? Comment below:

try www.calculationrankings.com, solve as many mental math questions within 120 sec with 4 different levels.

Apr 4, 2017 - 11:26am
Marya-Mrzp, what's your opinion? Comment below:

I found a iOS app very helpful: "Cmath by Behrad Bagheri"

The cool feature of this is that you can choose to either see the questions or hear them. I found it helpful because I wanted to be able to calculate by only hearing numbers.

Best Response
Apr 16, 2017 - 1:47pm
StreetShark, what's your opinion? Comment below:

2 iOS apps I found to be user friendly / relatively decent UI

  • Ninimaths: Train the Calculation Ability (by Ninicode)

  • Brain Training: Mental Calculation (by Koki Yoshida)

I'll also add 2 points, based on my own experience in prepping / interviewing.

  1. Might be helpful to understand and be familiar with compounding of common rates / years (e.g. 5% growth y-o-y for 5 years = +~30%). While you might have to do an actual NPV calculation, some interviewers may also be okay with you taking ballpark figures, esp for CAGR numbers (of course, please ask before assuming this is okay).

  2. Doing mental math prep (or any other prep) by yourself - behind a screen, using your phone, hearing the questions read to you - is very different from having to do the same calculations in an interview setting under pressure, with an interviewer staring/waiting for you to complete your calculations. Once you get your basics right, I would suggest either doing live case practice (and focusing on more quantitative cases) or getting a friend to grill you on math problems in person.

Mar 31, 2019 - 10:42am
toribashcash, what's your opinion? Comment below:

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Jul 23, 2021 - 5:27pm
plzfixsusan, what's your opinion? Comment below:

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