# Quant developer Interview Questions

# 79

Quant Developer interview questions shared by candidates### Write numbers 2^1000 and 5^1000 in a decimal notation, next to each other. How many digits does the newly obtained number have?

6 Answers↳

1001 integer between 1000*lg2+1000*lg5 and 1000*lg2+1000*lg5 + 2 so the answer is 1000+1 Less

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The answer is 1001, but to prove it you need to note that 1000log2 is not an integer Less

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int(1000*lg2)+1 + int(1000*lg5)+1 = 1001

### row a dice, get one dollar if you rowed on, get two dollar if you rowed two, calculated the fair cost of the game, plus some complication. the answer on ha**errank platform is 35k DOLLARS,,,,,,,,,,

2 Answers↳

basic probability, independent event

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There is no stopping time? Usually this type of math question has a stopping time like "the game stops if you roll a 6". Less

### What is d x^x/dx?

2 Answers↳

If y = x x and x > 0 then ln y = ln (x x) Use properties of logarithmic functions to expand the right side of the above equation as follows. ln y = x ln x We now differentiate both sides with respect to x, using chain rule on the left side and the product rule on the right. y '(1 / y) = ln x + x(1 / x) = ln x + 1 , where y ' = dy/dx Multiply both sides by y y ' = (ln x + 1)y Substitute y by x x to obtain y ' = (ln x + 1)x x Less

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sorry, i copy pasted this, the x x is is really a x^x. Essentially this is just a logarithmic differential exercise, exploiting the fact that d/dx ln f(x) = f'(x) / f(x) so that f'(x) = d/dx ln(f(x)) * f(x) Less

### market equilibrium. given a couple companies, their initial market shares, and the probabilities of customer switching from one company to another, what;s the final market share of each company?

1 Answers↳

matrix mult

### 4 questions in coding, 2 hours. Choose your own language (they prefer Python).

1 Answers↳

Passed 2 questions

### You have an array of bulbs and corresponding switches, given a sequence of switch actions count the instances of all the bulbs being on

1 Answers↳

I looked at the permutations of the array of switch actions

### I have 12 poker chips, we (two people) take it in turns to pick up one or two chips, you win if you don't pick up the last chip. What is the optimal strategy? Do you want to go first or second? What about if there were 150 chips?

1 Answers↳

Have a think about it, reading the answer here isn't going to help you. Try starting from a smaller number of chips. Less

### How could you quickly decide when to exercise a Bermudan receiver swaption?

1 Answers↳

Consider for each exercise date the effective rate over the tenor of the swaption taking into account the prevailing rate up to the exercise date and the strike rate. Would it be advantageous to wait or exercise? Less

### tetris given a couple pieces of tetris pieces, ask if we can fit these pieces exactly into a given rectangle

1 Answers↳

DFS will pass the first test case, and time out the rest two