Firms like #janestreetare still hiring for #quanttrading #quantitativefinanceroles even now. Keep reading to see #brainteasers(with answering strategies) asked by #deshawand #janestreet

1️⃣ You have 23 red pens and 19 blue ones in a box. It is very dark. How many pencils do you have to pull out before you get a matching coloured pair?

💡Without specifying the color, you can guarantee a matching pair of socks by pulling out three socks. Regardless of the color of the first two socks, the third sock pulled will either match the first or the second sock, ensuring a matching pair.

2️⃣ In a best of 3 tennis match, the player that first wins 2 sets wins the match. For a 3-set tennis match, would you bet on it finishing in 2 or 3 sets?

💡To finish in 2 sets:

Either player 1 wins the first 2 sets = p^2

Or player 2 wins the first 2 sets = (1 – p)^2

So P(2 sets) = p^2 + (1 – p)^2

To finish in 3 sets:

Either player 1 wins the first set and player 2 wins the second set = p * (1 – p)

Or player 2 wins the first set and player 1 wins the second set = (1 – p) * p

So P(3 sets) = 2 * p * (1 – p)

P(2 sets) – P(3 sets) = p^2 + (1 – p)^2 – 2 * p * (1 – p)

This can be factored into a perfect square (p – (1 – p))^2 or just simplified to 4p^2 + 4p + 1. Either way, it’s clear that P(2 sets) – P(3 sets) ≥ 0, so it’s always better to bet on the match finishing in 2 sets.

3️⃣ How many chickens were sold in China last year?

💡 how many gallons of ice cream were sold in the U.S., how many fax machines are in use in NYC…or anything else that requires you to extrapolate from a limited set of information.

One of the many possible approaches is to start by looking at the total U.S. population, dividing the population into the most relevant age groups, estimating the “consuming habit,” etc., and assigning a consuming frequency for each group, before summing to arrive at the total market size.

Start with a close estimate like the Chinese population is approximately 1411 million (2022). Here, the answer will not matter so much as your thought process. Include seasonal impacts on consumption—more chickens may be bought or any special festivals/ holidays, accounting for uneven distribution across the year. How many chickens would be consumed by families on a weekly basis? With the rise in health and wellness, more people between ages 20 and 50 may be consuming chicken as a form of lean protein (demographic impact); each of these people may consume approximately 20 chickens a year…

4️⃣ How long do you think the thread would be, if we unravel a T-shirt? Can you provide a range that you are 90% certain is correct?

💡 You can assume that the thread is horizontally woven together in two layers to compute the answer

5️⃣ What is the sum of the numbers from 1 to 50?

💡 Pair up the numbers into groups of 51 (1 + 50 = 51; 2 + 49 = 51; etc). Twenty-five pairs of 51 = 1,275.

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