Interview Questions: Mental Math Problems Practice
I've heard that certain banks including Centerview ask you to do 4 digit multiplication or square roots.
What's the best way to break down problems like 1916*1912 or the square root of 2000?
Practice Solving Mental Math Interview Questions
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 @Matrick", a hedge fund analyst, shared a good website for working on your mental math skills - Windhoff.net.
Read more about resources to work on mental math skills on another WSO thread.
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Seriously? The hardest I have ever been asked was something like 13*72 or so, never 4 digits. Best advice would be to practice this. There are a few handy websites out there that allow you to do so and even show you how to break it down. I am sure there's also an app for that.
http://windhoff.net/mental_arithmetic/ for example
Never seen that before. A lot of accounting questions you get will require mental math, but usually you can pick the numbers to make the math easy for you (i.e. make everything divisible by 100). Usually these questions relate to depreciation schedules and related things like deferred tax assets.
Yeah, exactly my point. The only firm that ever gave me blank math questions was Greenhill. But then again, I think they are fairly known for this.
I've heard some of my friends who interviewed with Goldman say that they got on the spot multiplication questions as one of their first questions in the interview (just two digits x two digits). You'll also probably have to do some mental math indirectly when solving for other questions
Google is your friend.
Square root questions are tough, but 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.
@StudentLoanBackedSecurities
Little trick - for square root of 8, you can think of it as 2 * sq root(2) - so basically 2*1.44 = 2.88
mental maths (Originally Posted: 08/26/2010)
Is mental maths important for IB trading positions?
I've heard of candidates being asked problems like 37*49 for prop firms in interviews, can I expect similar questions for the investment banks?
Thanks for anyone who can share their knowledge.
Yes, although they will focus on tougher problems than simple arithmetic. Depending on how quantitative your major is, you may see a lot of stats and/or calculus questions, yield curve questions, or questions about algorithms.
Suggested reading for math, econ, and finance majors:
http://www.Amazon.com/Heard-Street-Quantitative-Questions-Interviews/dp/0970055277/ref=?ie=UTF8&s=books&qid=1282851526&sr=8-1
Additional suggested reading for Comp. E and CS majors:
http://www.Amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358/ref=?s=books&ie=UTF8&qid=1282851686&sr=1-1
Thanks for your input. I am a maths major. I have a strong grasp of the higher level stuff but ironically my mental arithmetic is poor.
Do the IB firms really ask stuff like what is 46 squared?
Yes. In one of my interviews at a BB, they asked me for the square root and cube roots of 10 to 2 decimal places. Not fun :/.
That's part of your job as a trader/TA. If you can't do math in your head, you may want to consider applying to structuring, portfolio analysis, or maybe as a quant. Ironically, quants do not need to do mental math as much as many traders do, even though the position is more mathematically oriented.
I worked with a number of portfolio analysis groups while I was a credit analytics developer, and your background as a math major- combined with your technical and modeling proficiency- would probably make you a very strong candidate in that area. It's not as in vogue as trading right now (neither is quant development), but it's a nice stable front-office job that involves a lot of finance and the potential for retirement before 35 if you save carefully.
46x46 is pretty easy if you FOIL (40+6)(40+6). Mental math is all about using algebra for shortcuts.
A stable front office job is exactly what I want. Whilst I want a good salary like everyone else I would rather earn less and have a more secure position. You advised me that I would be strong candidate in portfolio analysis, what area does that come under, wealth/Asset Management? I will certainly be looking into this, I thank you for your input.
I was originally hoping to land either a trading position or a structuring position - ideally structuring but I have read that there are a lot more trading positions available than structuring ones.
Where I worked, Portfolio Analysis was an institutional service of the bank under Research. We had a number of quants and math majors in the group and they basically ran a lot of scenario analysis (trying to answer the what-ifs of rates increases, decreases, and market crashes) and risk analysis on portfolios for clients.
Every firm that has an index group or institutional pricing service will have a group of quants that come along with it to make sure clients that are paying often north of seven figures are getting the custom service they need. Citi, JPM, BofA/ML, and Barclays all have either index groups or institutional portfolio analysis groups.
It's not particularly glamorous, but the money is reasonable for front office work, the hours are great, and the job is a little more stable than a typical investment manager's job.
Look up the different bond indices and start contacting firms saying you're interested in helping them serve their institutional clients with regards to the index. It's a niche field, but they're always looking for people with strong math backgrounds who aren't interested in academia, trading, traditional research, or IBD to help get a quantitative understanding of buy-side portfolios.
The BBs on This list or this list might be a good place to start looking.
Figure out if understanding return attribution and scenario analysis are something you could be passionate about, and if so, start making phone calls. If that's what you really want to do, and you've got a strong background for research at an investment bank, I'm pretty sure one of the BBs will want you.
Two digit multiplication isn't really that hard. I wouldn't worry about it.
That is excellent information illi, I will be doing some research on it.
Thanks!!
What's the best way to get better at mental math for interviews? Just do problems in your head all day? Is there a website or something out there that goes over some of the basic rules for quick mental math?
brainage.com
Mental Math Practice (Originally Posted: 09/13/2011)
Morning everyone,
Since recruiting season is just around the corner and some of you may be preparing like crazy for interviews/tests, I want to share a book on mental math that has been extremely helpful to me. It's called "Secrets of Mental Math" by Benjamin and Shermer. You can find it on Amazon here http://www.Amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401/ref=sr_1_1?ie=UTF8&qid=1315924413&sr=8-1
I don't think I'm slow at math but for some reasons calculating in my head under pressure isn't one of my strong suits. I am halfway through the book and find it not only smart, informative, engaging but also extremely fun. I guess this would be useful if you have to sit through numerical test, prepare for the GMAT or just simply want to have an interesting read!
Good rec. MM has always been the bain of my exsistence.
Looks like homophones and spelling are the banes of your existence too.
Haha, jk. You left yourself open to that one.
Has anyone got good recommendation for Blackberry apps for this? The ones I've found are rubbish, they'll ask you something of value then three successive permutations of X/0 or (X)0....
Found the book on google books for those interested:
http://books.google.com/books?id=ykz7uzPEMjEC&printsec=frontcover&dq=se…
Good rec, I've always struggled with mental math under pressure.
Mental Math questions (Originally Posted: 01/20/2012)
Hey everyone,
I know mental math has been covered on here some and there's always a link to the trader's test. The guy who made it says that the medium/hard level is the level for most interviews. On those levels it's something like five and six decimal spots, even in terms of multiplication. But I am expecting questions on the multiplication of any two digit numbers together. I can't imagine them asking 623x956...is that a reasonable assumption?
Also, what is the usual composition of the test in terms of addition and multiplication?
I have heard of the Trachentenburg system, which doesn't seem fast enough for trading interviews (6-8 seconds right?). Any other methods you monkeys recommend?
Thanks,
tuxcsean90
the 6-8 second questions are for the Optiver type tests, where they are multiple choice, and if you look at the answers, you usually can get it right without actually doing the hard number crunching. For the other tests, like the ones IMC gives you on the final round is very similar to the Trader's Test, and you get about 20 seconds per question.
I bought the Henry Sticker book, and it worked out very well. It is a lot of work, and takes a month or so to go through completely, but it made my mental math go from average to be able to pass any medium difficulty mental math exam.
That is so reassuring. Thanks! Are the tests usually conducted at the first phone interview or once you pass the phone screen?
From my very limited experience it seems they generally focus on fit with maybe a few simple brainteasers at the end of the first phone interview, but then it goes from there. I don't think the first interview will be anything outrageous unless its for a few specific places. I could be completely wrong on this though.
Mental math for consulting (Originally Posted: 09/02/2012)
Anyone know of any good websites/phone apps that are good for practice? I've tried Mathemagics on the iphone so far but I'm not sure how applicable that is, because it teaches tricks for solving tough arithmetic (e.g. multiply 19 x 18) with 100% accuracy, whereas this would be an estimation question in consulting.
Anyone have any experiences to share with the math portion of their consulting interviews?
trachtenberg system.
Lumosity helps you grow new brain neurons.
http://www.amazon.com/Short-Cut-Math-Gerard-W-Kelly/dp/0486246116 ^ buy it. read it. seriously one of the niftiest things $5 can buy.
Apps? Waste of time/money. The environment is totally different when you're put on the spot in an interview vs. doing drills on a tiny screen. I'd say just find a friend and have them toss out problems for you; that's what I did. Got to the point where I'd be hanging with a friend and he would random turn and say "27x25?!" and I would immediately spit back "675!" without stopping to blink. Get to that point.
Did you learn how to do sums like 27x25 by using that book? How long did you have to practice before getting to those arithmetic speeds?
.
You might be better off doing proper numerical reasoning tests with charts, bars, estimations etc. Just doing a bunch of additions/multiplications might not be terribly useful
some of these resources are helpful
@melvvvar, trachtenberg seems to have a lot of steps in its algorithms. Not sure if that's good or not?
@BTbanker, is Lumosity any good? I heard it's made by some stanford psychologists or something.
@kenripley, yeah I know what you mean, but I've read that consulting interviews have a precise math and estimation math portion, which you need to pull off really well. Online numerical tests won't help for on-the-spot arithmetic.
don't be lazy. if you suck at mental math, you need to put in the work.
Don't forget to practice multiplying/dividing numbers with large amounts of zeros at the end. It sounds silly, but it comes up surprisingly often and is quite easy to mess up if you haven't gone over it.
This will blow the minds of your interviewers: http://en.wikipedia.org/wiki/Scientific_notation
Thanks for the replies everyone. Will get to it :)
To build mental math speed try: calculationrankings.c
Good luck! Chip
how do most people do on brainteasers / mental math during interview? (Originally Posted: 06/03/2013)
Have you guys ever experienced making a fool of yourself on brainteaser/mental math questions? It appears that more and more interviews are asking random brainteaser / mental math questions and I just freeze up. If I were expecting it, I could do much better, but I end up screwing myself over and looking stupid.
How do most candidates perform on brainteasers and mental math questions during interview? Do most people look not as sharp as well?
the thing i most hate in an interview. rather get ask a brutal accounting question than face the brainteaser
Go to fincampus . com and take their quizzes (they have a pretty comprehensive practice quiz available too).
Just hope you've done well until that moment. Show disappointment in yourself for not being able to answer a "simple" question -exhibiting humility might save you?
Never tried this before, but perhaps you can buy yourself some time, and relax a bit, by adding in fluffy sentences like "Hmmm...(make this Hmm long) Now that's an interesting question,..." "Is there any more information?" (Don't think these two can harm you. But they can only buy you that much time. You'd have to start answering now) Or delay even further by "Please allow me some time to think over this" or .."My current thoughts are,...but [your thought process, which may overturn your intitial conclusion]"
I think to some extent, the brainteasers are testing your ability to deal with the unknown and your thought process and perhaps less so about whether you can actually get it or not (but ofc the latter is still impt).
My experience is that most kids who get offers answer most or all of them correctly. You should practice more.
brainteasers aren't really that common from what I have heard, but Heard On the Street has a ton of prep questions/answers if you were looking to master them.
How Fast Are You At Mental Math? (Originally Posted: 04/20/2014)
www.calculationrankings.com/game/2
Any top scores, gentlemen?
84, rank 18. Fun game.
I kept careful track of the rankings and nobody got bumped - you sure about that?
It only gets bumped if you submit your score. Seeing as this is an anonymous forum I saw no point in doing that. I can play again and submit a screenshot if you'd like.
just play and submit a fake alias (e.g itoldyousoeuro), if you'd like. emails don't have to be real either.
20 is my score. Whatever, I'm drunk.
damn 84, that's sick. 51 is my high score
Everybody playing at level 1 or 2?
Guess I'm going to get less work done today haha
How do you improve your mental math? My mental math tended to be pretty good but ever since I started working it has been getting worse.
practice, and sleep
Been addicted to this game for 2 days now. There's an Optiver guy in the top 10.
Logic behind Mental math tests for trading jobs (Originally Posted: 12/27/2014)
Hi, I realize that many equity derivative market making shops want people who can do math in their head, and do it very fast at that. I've never traded derivatives, only spot forex.
I realize that derivatives trading is what Chess is to checkers, so could someone please fill me in on how these skills make one a good trader and or market maker?
It's a residual skill from the old days of trading in the pit. The guys who were the fastest at recalculating new prices for derivatives given movements in the underlying(s) ate slower guys alive.
Computers are doing all those recalculations now, but having a guy sit behind the screens and checking the work is valuable as well. The computer says that x is the new fair value, but is that right?
Mental math also certainly helps for on-the-fly risk assessments and trading decisions: how much to bet, what is my max loss, slippage, etc.
thank you!
In addition to seeing how quick you think, how quickly and effectively can you evaluate risk under pressure. Get the question wrong you get -2 and you've lost valuable time, on the other hand if you pass (cutting your losses) you get -1 but more time for other questions. Just a thought.
The point is not that you know tricks to do the math the point is that you can figure it out.
Just played the mental math game at http://www.calculationrankings.com/game/2
How the HELL do people get legitimate scores of 100+ when you only have two minutes.
Brainteaser Calculation Method (Originally Posted: 04/29/2012)
Just wondered how people go about doing mental maths, as in, how do you go about answering the brain teasers that IB will ask you
for example 6448 or 7295 etc etc
I consider my self quite good at maths and have my own methods but feel I am sometimes a little slow at working out the answer and worry that I might take too long for the interviewers liking so any advice or tips on speeding up with better methods cant hurt!
walk your way through the answer verbally out lout to the interviewer. Thinking out loud is the best way to show your interviewer clear, concise, structured logic as well as buy yourself more time to go over the problem in your head.
Another way is to use a reference point or block out large multiplication or fraction teasers IE:
For 72*95:
72*100 = 7200 -easy reference point
Now walk your way back down by breaking down 72*5
70 * 5 = 350 2 * 5 = 10 = 360
7200- 360 = 6840
Same with 64 x 48--> I would start with 64 x 100= 6400
Then cut in 2 to get 64 x 50--> 6400/2 = 3200
Now get the subtraction --> 64x2 = 128
3200-128= 3072
nice one! good tips here thank you
how quick are you expected to answer these by the way?
I have a few videos of math tricks that are actually very easy to remember and practice. I spent 1 week looking at each one of them every day (collectively about 1 hour and 20 mins) and by the 8th day, I remembered all of them and now apply them to brain calculations all the time. Now of course some of them are more useful than others like the tricks we use in multiplication of double and triple digits while others like square roots of 10 digit numbers rarely come handy.
I am more than happy to send the .rar file to you if you'd like.
yes please Disincentivy!
that would be amazing if you could pm some sort of link to download it or even email it?
bump
Email works better. PM me your addy, please.
thank you! PM sent
how quickly are you expected to be answering these brainteasers they give you?
If you break it down out loud, it will be better and time won't exactly matter as long as they see how you are thinking about the problem.
Exactly. I got asked a question about how many golfballs I thought would fit inside a 747. If for some off reason you knew the answer and just blurted it out after 5 seconds, that would be just about the WORST way to answer the question. You just try to use logical reference or starter points and work your way through the problem. Same applies for math/fraction teasers except you should be able to find an exact answer
Very good, thanks for the advice.
Thats put me at ease, I was worried that I would be expected to churn out double digit multiplications in under 5 seconds haha
Also, bullbythehorns, out of interest, what did you answer for the golf balls and 747 question
64 x 48
60 x 40 60 x 8 40 x 4 8 x 4
Simple breakdown in your head and add them up
I had seen the question in a prep guide but its not that difficult in reality. Cubic feet = length x width x height. est. length at 250 ft. est height: 20 ft. est width 10 ft. >>> 2502010 = 50,000 cubic ft. ^in hindsight that is wrong because I assumed square dimensions and an airplane is cylindrical but you get the jest.
golf ball est. around 2 cubic inches. Cubic feet = 12 * 12* 12 = 1728 cubic inches in a cubic foot.
Round 1728 to 1800. 1800 / 2 = 900 golf balls per cubic foot.
50,000 cubic ft of space * 900 golf balls per cubic foot = 45,000,000 golf balls.
Math questions during interviews (Originally Posted: 02/19/2007)
I am going for a final round interview at Lehman tomorrow, and I was wondering what math tricks I should familiarize myself with. I know that they ask things like what's the square root of 100 or what's the sum of 1 to 100. Are there any other types of question I should know about? Thanks guys!
You really can not answer a question about a sum of 1 to 100? Its very easy and it doesn't need preparation. There are no math questions that need special preparation, if you have financial background
learn some approximation stuff like calculating squares cubes etc quickly
I also had some questions that required me to make an estimation and then make calculations from that. For instance, what is the total value of computers in this building? Talking through my thought process seemed like a good way to go about answering.
No math. None whatsoever for me. I had a large amount of accounting ?'s but most of it was behavorial/fit.
2nd what Khameer said; No math, some accounting, mostly fit.
CS was the only firm that I had ask me math q's; along the lines of compute 31*29 without pen/paper.
Math Books for Interview Prep? (Originally Posted: 03/29/2011)
I feel like this has been discussed before, but are there any solid books out there on mental math tricks, interview prep questions and review topics?
I've been interviewing for HF jobs and have gotten many brain teasers and mental math / statistics questions. Can anyone recommend any good books to brush up on this stuff?
Thanks in advance...
Heard on the Street--Google a PDF
For the mental math stuff, look up Trachtenberg (sp?) Math.
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