Interviews for positions such as Quantitative Researcher, Quantitative Analyst and Quantitative Developer are known to be fiendishly difficult and typically entail tough questions around probability, statistics, algorithms and mental maths. Occasionally, they may throw in a random brainteaser to catch you out! So what do these questions look like?

# What is the sum of the numbers 1 to 10000?

# Is 294801 a prime number?

# What is the square root of 1000 to 4 d.p.?

# How many times do you need to roll a die to get 3 even numbers in a row?

*A bag contains N socks, some of which are blue, and some of which are green. If two random socks are picked, the probability that they are both blue is 1/2. What is the smallest possible value of N for which this is possible?*

# What is 17.5% of 354?

# You have 1000 bottles of water, one of which is poisoned. You can test the water and try to figure out which bottle is poisoned. Unfortunately, since the poison takes 24 hours to activate in the test, and you only have 24 hours to figure out which bottle is poisoned, you must choose which bottles to test right now. How many tests do you have to use to figure out which bottle of water is poisoned?

# If I throw three darts at a dartboard, what is the probability that they all land in the same half of the board?

# How many times do you need to flip a coin to get HTH consecutively?

# There are 14 identical-looking balls. 13 of them have the same weight while one of them is heavier than the rest. What is the minimum times you can weigh to identify the heaviest ball? How do you generalise for N balls?

# Let’s say random variable X is distributed as N(a, b) and random variable Y is distributed as N(c, d). What is the distribution of X*Y?