During an interview, you will get asked many questions. What you are good at, what you are not good at, what you want to do in the future, etcetera, etcetera. Most recruiters, however, are starting to dive deeper into how a candidate thinks. Nowadays, specific knowledge can easily be taught and most information can be looked up in a second – character traits though, are what will make the difference in a good and a bad hire. The following questions have been used during application interviews with Tesla, Google, Apple, Microsoft, Facebook, LinkedIn, and other prestigious companies to evaluate how solution-oriented candidates are and if they can think practically and analytically. The good news is, that even if you do not know the answers to the following questions immediately, hiring managers are not necessarily looking at if and how fast you can solve the problem but at how you approach it and if you are able to break it into smaller parts. So if you ever happen to stumble upon one of the following questions during future interviews, do not panic – use them as an opportunity to show recruiters how you think and work through a problem.
You're standing on the surface of Earth. You walk one mile south, one mile west, and one mile north. You end up exactly where you started. Where are you?
This question has multiple answers: Firstly, if you are standing directly on the north pole and you walk one mile south, then one mile west, then one mile north, you will arrive back at the north pole.
The second answer is a little bit more complex. Imagine a circle with a 1-mile circumference that has the south pole at its center. If you were to start one mile north of this circle, you would travel one mile south, one mile west all the way around the circle, and then one mile north back to your starting point.
As for the third solution, it takes up on the second one. Imagine that the circle around the south pole has a circumference of only 1/2 mile. If you were to start one mile north of that circle, you would travel one mile south, one mile west around the 1/2-mile circle twice, and then one mile north back to your starting position. The same is true for any fraction of the original 1-mile circle.
You're on a small rowboat in a lake with a rock in the boat. You throw the rock overboard, does the water level in the lake rise or fall?
When the brick is in the boat it is displacing its own mass equivalence in water. When the brick is thrown over the side it is displacing its own volume in water, hence the water level goes down! This answer is easiest explained with an example. You need to know that 1 liter of water has a mass of 1kg. Let's say the brick weighs 3kg and is 1 liter in volume. When the brick is in the boat it is forcing the water to be displaced by 3kg or as we know 3 liters. When the brick is sat on the bottom of the lake it is only displacing its own volume which in our example is 1 liter.
You have a 3-gallon jug and 5-gallon jug, how do you measure out exactly 4 gallons?
First, fill the 3-gallon jug and pour it into the 5-gallon jug. Now the 3-gallon jug is empty, and the 5-gallon jug has 3 gallons in it. Fill the 3-gallon jug and again, pour into the 5-gallon jug until it is full. Since only 2 gallons will fit because it already has 3 in it you will be left with 1 gallon in the 3-gallon jug. Empty the 5-gallon jug and pour the 1 gallon into the 5-gallon jug. Fill up the 3-gallon jug and pour it into the 5-gallon jug. You have exactly 4 gallons.
There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled so that no label identifies the actual contents of its box. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?
You know all three boxes are incorrectly labeled. Hence the box labeled “apples + oranges” must contain either only apples or only oranges. Take out a piece of fruit and you will know what this box really contains. Let’s say you grabbed an apple. Now you know that the box that says oranges is still labeled wrong (because all 3 were labeled wrong to start with), and you know it is not apples because you already have the “apple box”. This means it has to be “apples + oranges”. Conclusively, the last box is “oranges”. The same process would have worked if you had pulled out an orange first.
Why are manhole covers round?
Of course, not all of these questions are math-related. Some just test if you can think logically and come up with a plausible answer. In this example, there are multiple solutions that all make a lot of sense if you think about it. Firstly, manhole covers are round because that is the only shape that cannot fall through itself, hence the cover can never accidentally fall down the hole. Further, a round cover does not have to be aligned to fit into the hole. A square cover, for example, would have to be aligned with the hole accordingly. Round covers are also easier to transport since they can be rolled. If someone is not capable of carrying them they can still easily be moved. The last answer we could think of is rather simple but still effective. Manhole covers are round because it is the best shape for humans to climb through. This might sound silly at first, but an answer like this shows that you can think analytically and come up with creative reasons for a problem.
You are a prisoner in a room with 2 doors and 2 guards. One of the doors will guide you to freedom and the other one into prison. One of the guards always tells the truth and the other one always lies. You can only ask one question to know which door leads to freedom.
The question is: “Is the liar in front of the door to prison?”.
If the truthful guard is in front of the door to prison he will tell you ‘no’ and if he is in front of the freedom door he will say ‘yes’. If you ask the liar, he will tell you ‘no’ if he is in front of the door to prison and ‘yes’ if he is not.
Hence, either way, if the answer is ‘no’, then you asked the guard in front of the door to the prison, so you go to the other door. If you get a ‘yes’, then you asked the guard in front of the door to freedom so you want to choose that one.
Someone works for you for seven days and you have a gold bar to pay them. You must pay the worker at the end of every day but you are only allowed to make two breaks in the gold bar. Assuming equal amounts of work is done during each day thus requiring equal amounts of pay for each day, how do you pay your worker?
The answer is relatively simple once you figure out how to cut the bar. You need to make a 1/7, 2/7 and a 4/7 piece, let’s call them 1,2 and 7. On day one you give him piece 1. On day two you give him piece 2 and he gives you back piece 1. On day three you give him piece one again. On day four, you take back pieces 1 and 2 and give him 4. On day five he gets piece 1 and on day six you take piece 1 back and give him 2. Finally, on day seven he gets piece 1 and has all seven parts.
You have 8 marbles, 7 of which are the same weight and one is a little bit heavier. To find out which one the heavier one is you are allowed to use a beam balance, but you can only weigh twice.
To solve this problem, it is important to break it down into smaller parts. If it were only three marbles, you would only need to weigh once to find out which one is the heavier one. If you put one marble on each side and they weigh the same you know the third one is the heavier one. If one of them is lighter than the other one, you also know the answer. Now split the 8 marbles into three groups with 3,3 and 2 marbles. Compare the two 3-marble groups on the beam balance. If they weigh the same then the heavier marble is in the 2-marble group and you can simply weigh them. If one of the 3-marble groups is heavier, you can use the second weighing to use the method we explain at the beginning of this answer.
How many golf balls would fit into the office you are in right now?
Our last question is possibly one of the trickiest ones, simply because there is no way that you could know the exact number. For a fact, the chances of the recruiter knowing the number are pretty low too. Questions like this are only asked to see how you approach this problem. Your goal is to think the problem through, make estimates, arrive at an answer and give a reasonable explanation of how you calculated this. Also do not be afraid to ask for a pen and a paper to write down your calculations. Similar questions to this could be: “How many cows are there in Germany?” or “How many yellow cars are there in Berlin?”
A possible answer to our question here could be: Let's assume that this office is 6 by 5 by 4 meters, this equals a volume of 120 cubic meters. A golfball has an assumable diameter of 4 centimeters. If it were a cube that would be 64 cubic centimeters, minus around one third because it is a ball, so let’s say 40 cubic centimeters, this equals 0.00004 cubic meters. 120 divided by 0.00004 equals 3,000,000 golf balls.
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