2021 Quant Interview Questions

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These are questions I routinely ask in interviews. Candidates can have access to a computer if they want, to give or test their answers for those marked with * below. These are ice-breaker type questions at the AVP or VP level positions in Finance. You should be able to do them in 2-3 minutes or so. For the coding questions say a max of 5 minutes would be very generous. Enjoy!

Note: the * questions are especially useful when, during COVID times, interviews are conducted remotely. Rather than ask people to code up solutions (in HackerRank, say) and check them, easier to simply check if they are able to write the code snippet on the fly, and give the correct answer.

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1. I toss a fair coin 5 times, and get H, H, H, H, and H. The other interviewer tosses the same coin 5 times, and gets H, T, H, T, H. Which sequence is more likely, and why?
2. I toss a fair coin 1 time. If it comes up heads, I pay you $1M, if tails, you pay me $1M. The other interviewer offers you a different bet. She tosses the same coin 1000 times - each time, if it comes up heads, she pays you $1K, if tails, you pay her $1K. Which bet would you take, and why?
3. Imagine a spreadsheet with 1M rows. In Column A, you have all the numbers 1 to 1,000,000. In Column B, you have the squares of the corresponding numbers in Column A (i.e. you have 1, 4, 9, 16, ...). In Column C, in each row you have the last (unit's place) digits of all numbers from Column C. Then I take all the digits from Column C and create a set (unique list) of them. The number of elements in that set is? How would this answer change if in Column B, I had used cubes instead of squares?
4. *Alice offers you a bet. She first charges you $1, and then rolls a fair die three times. If each roll score is (strictly) higher than the last, you win, otherwise you lose. How much should you ask to be paid when you win, so the game is fair to you?
5. *I sample 3 letters from the alphabet without replacement. What is the probability they are in increasing alphabetical (or lexicographic) order? e.g. p, r, w 
6. *The digital root of a number is the iterated sum of its digits till you end up with one digit. For example, the digital root of 412312 is equal to the digital root of 13 which is 4. The Fibonacci series is a series of numbers that starts with 0 and 1, and where every subsequent number is the sum of the previous two numbers. What is the digital root of the 3000th Fibonacci number?
7. What is the probability that two people in Manhattan have the same number of hairs on their respective heads as each other? What is the mathematical principle you used to solve this?
8. *I roll a fair die until I get two sixes in a row. Angela rolls the same fair die until she gets a six followed by a five. On average, who has to roll more times to reach their objective? Can you explain intuitively why this is the case?

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To keep things fresh, I will of course swap questions from time to time, so it is unlikley that even if we were to meet, I will ask the same questions. However, good to prepare!

ChiPrime tries to answer problem #5 above here. But it is trivial to code a simulation in python with itertools to get the same answer.

The python code is below: 

import itertools; # module that performs permutations

import string; # to get the lowercase letters with less computational gymnastics

alpha=string.ascii_lowercase; # gives all lowercase letters 'abc...z'

x=itertools.permutations(alpha,3); # all 3-letter permutations from alpha

p=[i for i in x if i[0]<i[1]<i[2]]; # all permutations that meet the condition

print(len(p)); # computer prints 2600, the correct answer.

[8] above is solved here, and [4] here. 

For more of these kinds of questions, check out ChiPrime.com (click button below for more!)

ChiPrime