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
- Round 163 to 200
- Multiple 200 by 242 = 48400
- Since we rounded up we need to subtract away (200 - 163) * 242
- 37 * 242 can be rounded to 40 * 242 = 9680
- 48400 - 9680 = 38720
- Finally, we need to add back the additional amount that we subtracted so (40 - 37) * 242 = 726
- 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:
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 @Proboscis, a consulting analyst, shared their advice:
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:
- 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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