Case Interview Brain Teasers

Brain Teasers are one of (if not) the most exciting types of interview questions. They are widely used for recruitment in many different fields, from Management Consulting, to Wall Street, to even Google. These questions often require thinking in unconventional ways.Just like for the McKinsey PST, the systematic approach is to break down the complex and the ambiguous into specific question types. What I’ve found out is that once the questions are placed into their appropriate groups, even Brain Teasers can be very, very predictable!

The 7 most common types of Brain Teasers:

  • Illusive questions
  • Visual-explanation questions
  • Wording questions
  • Pattern/ Trend questions
  • Logical questions
  • Wordplay questions
  • Market-sizing and Guesstimate questions

This is not a MECE breakdown of the question types. Some questions fall into more than one categories. But for the purpose of learning, we will temporarily ignore the important concept of MECE here. Now, let’s get into each of these types.(See examples of each type in the video!)

Type No.1: Illusive questions

Brain Teasers of this type may vary in formats or contexts but all share one characteristic: They create illusions and draw your attention to insignificant details. Exactly like how magicians do their tricks.The key is to realize the illusion and quickly identify the important details you overlooked at first sightLet’s look at a famous example of this type of brain teaser:Tracy’s mother had four children. One child was name April. The second one is May. The third is June. What‘s the fourth one’s name?…Are you thinking “July”?Wel, here the question wants to draw your attention to the interesting but insignificant sequence of names: from April to May to June. Many people don’t realize that right at the beginning of the question, the other child’s name had actually already been revealed. It’s Tracy!Wanna try another illusion brain teaser?An electric train is traveling on a 2000-mile journey from Chicago, IL to Los Angeles, CA. It has 16 cars with a total of 320 passengers. The weather is cloudy and cool, with a warm front approaching from the south. Which direction will the steam blow?If you are getting it, please put your answer to a comment below!

Type No.2: Visual-explanation questions

These questions are somewhat similar to Root-cause reasoning in the McKinsey PST and Hypothesis questions in Case interviews. But since there are a lot of non-consulting viewers for this video, I decided to give this a non-consulting and more straight-forward name.Visual-explanation questions often provide you with weird and “impossible” situations and your task is to think of a story that “explains” all the facts.The key to cracking these questions is a little creativity and imagination. Don’t be afraid to tell bold and unordinary “stories”, as long as they do explain the situation.For example, a brain teaser of this type is:“A man is lying dead in the middle of a forest, in the middle of a puddle, in a scuba suit. How did he die?”…A perfectly-accepted explanation is that he was swimming in a sea and a tornado picked him up and dropped him in a middle of a forest.… a little creepy but it works!Here’s an exercise for you:A woman and a daughter walked into a restaurant. A man walked past and the women both said, “Hello, Father”. How is this possible?Please answer this question by commenting below!

Type No.3: Wording questions

Brain Teasers of this type usually have at least one word with multiple meanings, and often time your default interpretation (misled by the context) makes the question impossible to answer.The key is to question your mind’s interpretation of every word in the question and in your thinking. Usually, you will find at least one word with alternative meanings that significantly changes the whole context.Here is an example:“You walk across a bridge and you see a boat full of people yet there isn\’t a single person on board. How is that possible?”The misleading word here is “single”. The context of the question suggests single should be interpreted as opposed to many (as in crowding the boat), which creates an impossible situation.However, when you explore the word further, you’d find out that “single” can also be interpreted as opposed to “married”. This yields the answer: the boat is still full of people; yet they are all married, hence no single person!Wanna try another one? Here we go:What two words, when combined, hold the most letters?… Interesting hah? Feel free to show off your answer on the comment section!

Type No.4: Pattern/ Trend questions

Brain Teasers of this type involve a series of numbers or letters with a certain pattern or trend. The questions then ask candidates to either identify the next item or to fill in a hole.For example: What’s next in this series?2              2              4              12           48           …The key to these questions is to think of a lot of possible trends, apply them into the string, and see if those trends correctly predict the string. It’s worth noticing that it’s absolutely ok to come up with a trend different from the interviewer’s mind. As long as you can come up with a trend that fits the data, the interviewer can’t to reject your answer.In the above example, one possible trend is to take the previous number and multiply it with its position. So the next number would be 48 times 5, which equals 240.Here is another exercise for you to tackle: <just show on the screen the following:2  3 = 107  2 = 636  5 = 668  4 = 969  7 = ….. >Please let everybody know the missing number by commenting below!

Type No.5: Logical questions

Let’s try a difficult one:During lunch hour a group of boys from Mr. Bryant’s homeroom visited a nearby grocery store. One of the five took an apple. Jim said, “It was Hank or Tom”.Hank said, “Neither Eddie nor I did it.”Tom said, “Both of you are lying.”Don said, “No, one of them is lying, the other is speaking the truth.”Eddie said, “No, Don, that is not true.” When Mr. Bryant was consulted, he said, “Three of these boys are always truthful but two will lie every time.”Who took the apple?As always, please comment below on your answer to this!

Type No.6: Wordplay questions

These questions play with the organization, demonstration, and compositions of letters. For example, what does this represent?COF FEE…The answer is “Coffee break”.The key to these questions is to look at as many aspects as possible. Synonyms, visual, verbal, etc.Here is another exercise for you. What does this mean?<only show this on screen: gges egsg segg esgg>Don’t forget to comment your answer below!

Type No.7: Market-sizing and Guesstimate questions

Technically, market-sizing and guesstimate is a type of Brain Teaser. But because of its popularity and importance, we have devoted a whole separate video for it.If you would like hundreds of Brain Teasers neatly sorted into these categories, you may want to join hundreds of candidates around the globe and get access to our Case Interview End-to-End Secrets Program. We devoted a whole eBook on Brain Teaser questions. There are flexible packages for you to get the whole program or just the Brain Teasers or Market-sizing parts.Here is the link to some extra practices for Brain Teasers.

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  • Jenny Li

    Thank you Ki, very helpful and informative.
    Here are my answers:
    3.wording questions: most letters;
    4.Pattern: 9 7=9(9+7)=144;
    5.logic: Tom ;
    6. wordplay: my answer is “scrambled eggs”.

  • Vaihingen

    For Type No.5, Tom took the apple.
    Let’s start from Tom and Don. Since Tom and Don’s statements could not be true at the same time, at least one of them did not tell the truth – there remains three cases:
    (1): Tom(T)+Don(F)
    (2): Tom(F)+Don(T)
    (3): Tom(F)+Don(F)
    For (1)
    Since Tom is true, his statement (Both of you are lying) is true, that means Jim(F)+Hank(F)
    However, so far there are three boys (Jim, Hank, Don) lying, a contradiction of Mr. Bryant’s statement that 2 of 5 boys lie every time, so (1) does not work.
    For(2)
    Since Don is true, his statement (one of them, i.e. one of Jim and Hank, is lying) is true.
    The case becomes Tom(F)+Jim or Hank(F).
    Following Mr. Bryant’s statement that 2 of 5 boys lie every time, there is no “quota” for the remaining boy (Eddie) to be false. In other words Eddie (T).
    However, when Eddie(T), his objection to Don’s statement is true. That means Don’s statement is not true.
    So Don (F). It is impossible for Don to be T and F at the same time, so (2) does not work.
    For(3)
    Since Tom(F)+Don(F), considering Mr. Bryant’s statement that 3 of 5 boys are always truthful, so we have Jim(T)+Hank(T)+Eddie(T).
    Since Jim(T), Hank or Tom took the apple.
    Since Hank (T), neither Hank nor Eddie took the apple.
    So Tom took the apple.
    (Moreover, Eddie’s objection to Don does not violate the original assumption that Don (F))