Quant interview questions can generally be bucketed into the following categories:

Logic Problems

Logic games are focused on assessing your ability to reason through a problem that you have never seen before. These questions force you to think creatively, clearly communicate your ideas, and demonstrate your perseverance. Oftentimes, these questions are referred to as "brainteasers".

Math Questions

Math questions consist of problems that assess your quantitative skills. These questions can range from mental math to statistics and expected value. For these questions, you're often in a position where you need to make estimations rather than arrive at the perfect answers.

Strategy Games

Strategy games are problems in which you are presented with a game environment and are asked to figure out what the most optimal decision to make would be in this scenario. For these questions, you often have to think critically about the expected value of various actions. These questions hone in on your appetite for risk and reward.

Fermi Estimations

Fermi estimations gauge your ability to reason about uncertainty. For these questions, you are often presented with a random situation and have to guess a particular quantity in that situation. For example, "How many airplanes are flying above the United States at this moment?". For these questions, the correct answer isn't as important as the reasoning that you provide.

Finance

Finance questions are less commonly assessed in quantitative finance interviews but can appear from time to time. These questions will gauge your understanding of options pricing theory and may be more conceptual in nature.

Here is a list of questions that have helped me prepare for my interviews:

Statistics

1. Repeated Rolling
2. Number of Runs

Probability

1. Four of a Kind
2. 10 Floor Building
3. Eight of Hearts
4. Three Rings

Discrete Math

1. 2D Grid Game
2. Four Integers

Brainteaser

1. Hungry Truck Driver
2. Heaviest Coin