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Consulting brain teasers are interview questions occasionally asked during consulting interviews. Although case interviews and behavioral interview questions are more commonly asked, some consulting firms still use brain teasers when evaluating candidates.
If you have an upcoming consulting interview that has brain teasers, don’t worry because we have you covered.
In this article, we’ll cover everything you need to know about consulting brain teasers, including how to answer them, how to prepare, and we’ll provide you with plenty of practice questions.
If you’re preparing for your upcoming consulting interviews, make sure to check out our comprehensive consulting case interview course. These insider strategies from a former Bain interviewer helped 30,000+ land consulting offers while saving hundreds of hours of prep time.
Consulting brain teasers are questions designed to test a candidate's ability to think critically, solve complex problems under pressure, and demonstrate creative problem solving skills.
These are all qualities that are essential for success in consulting.
Unlike traditional interview questions that focus on assessing a candidate's knowledge or past experiences, consulting brain teasers present candidates with puzzling scenarios, mathematical problems, or logical conundrums that require quick thinking and strategic analysis to solve.
Consulting brain teasers are intentionally ambiguous and may lack clear instructions, forcing candidates to interpret the problem, identify key information, and devise a structured approach to reach a solution.
Consulting brain teasers come in various forms, ranging from numerical estimation questions and logic puzzles to hypothetical scenarios.
Consulting brain teasers are generally not used by top consulting firms, such as McKinsey, BCG, and Bain, as these firms generally feel that brain teasers are not the best way to evaluate candidates. These questions are more often asked by firms such as Accenture.
In the competitive world of consulting interviews, nailing consulting brain teasers can make the difference between getting an offer and getting rejected.
Therefore, by better understanding the nature of consulting brain teasers and doing some practice, candidates can significantly improve their chances of passing their interviews.
Consulting brain teasers evaluate analytical skills, problem solving ability, quantitative aptitude, stress tolerance, and communication skills.
1. Analytical skills
Candidates are expected to dissect complex problems, identify underlying patterns or structures, and develop systematic approaches to reach solutions.
Consulting brain teasers assess a candidate's ability to break down intricate scenarios into manageable components and apply logical reasoning to identify insights.
2. Problem solving ability
Consulting brain teasers evaluate a candidate's ability to solve new and challenging problems.
By presenting ambiguous or unfamiliar situations, these questions assess an individual's ability to think creatively, generate innovative solutions, and adapt their strategies.
3. Quantitative aptitude
Many consulting brain teasers involve numerical calculations, mathematical concepts, or data analysis exercises.
Candidates are required to perform quick mental calculations, estimate figures accurately, and manipulate numerical data to derive meaningful conclusions.
4. Stress tolerance
Consulting interviews are incredibly demanding, often placing candidates under significant time pressure and stress. Consulting brain teasers simulate the fast-paced and high-stakes environment of consulting work, assessing candidates' ability to perform while under stress.
Candidates are expected to maintain composure and focus throughout their interview.
5. Communication skills
Clear and concise communication is critical in consulting. Consulting brain teasers provide candidates with opportunities to showcase their communication skills.
Candidates are expected to articulate their problem solving strategies, justify their decisions, and engage in constructive dialogue with interviewers to demonstrate their thought process.
There are five major types of consulting brain teasers: estimation, math puzzle, “why is,” word play, and logic brain teasers.
We’ll cover each of these major types of consulting brain teasers in more detail. Later on in the article, we’ll provide plenty of consulting brain teaser examples with answers.
Consulting estimation brain teasers
The consulting estimation brain teaser, also known as the "how many" brain teaser, is a common type of brain teaser encountered in consulting interviews.
These questions include:
Consulting estimation brain teasers require candidates to make informed estimations without concrete data.
For these brain teasers, candidates are assessed on the approach that they take rather than on the actual correctness of the answer they land on.
There is often frequent communication between the candidate and interviewer on the approach that should be taken and key assumptions.
To learn how to solve this type of brain teaser, we have a step-by-step guide to consulting estimation and market sizing questions.
Consulting math puzzle brain teasers
Consulting math puzzle brain teasers are mathematical problems or puzzles that challenge individuals to apply mathematical concepts and principles to solve them. These puzzles often require logical reasoning, problem solving skills, and creativity to find the correct solution.
Here are a few examples of math puzzle brain teasers:
“Why is” consulting brain teasers
"Why is" consulting brain teasers assess your analytical skills by challenging you to explain phenomena in the world around you. They can be particularly challenging as they require you to delve into the underlying reasons behind commonly accepted facts.
Common examples of “why is” consulting brain teasers include:
This type of brain teaser encourages you to question the origins and intentions behind modern conveniences. By unraveling the logic behind seemingly mundane aspects of our world, you will develop a deeper understanding of the world while demonstrating your logic and analytical abilities.
Consulting word play consulting brain teasers
Consulting word play consulting brain teasers, also known as verbal or linguistic puzzles, involve playing with words, language, and logic to solve a problem or uncover a hidden meaning.
These brain teasers require creativity and a strong understanding of language. Here are a few examples of consulting word play brain teasers:
Consulting logic brain teasers
Consulting logic brain teasers, also known as logical puzzles or lateral thinking puzzles, require candidates to use deductive reasoning, inference, and creative problem solving to find the solution.
These brain teasers often involve scenarios or situations where the answer may not be immediately apparent and may require thinking outside the box.
Here are a few examples of consulting logic brain teasers:
To answer consulting brain teasers, candidates should understand the problem, develop a structured approach, make assumptions, apply analytical techniques, iterate and refine their answer, communicate their answer, and be adaptable.
1. Understand the problem
Understand the question carefully to grasp the scenario and identify key components. Clarify any ambiguities or uncertainties with the interviewer to ensure a shared understanding of the problem.
2. Develop a structured approach
Break down the problem into manageable steps or components. Determine a logical framework or methodology for approaching the problem systematically. Consider different perspectives or angles to gain comprehensive insights.
3. Make assumptions if necessary
Acknowledge any missing information or uncertainties in the problem. Make reasonable assumptions to fill in the gaps, ensuring they are logical and justifiable. Communicate your assumptions clearly to the interviewer to maintain transparency.
4. Apply analytical techniques if necessary
Leverage quantitative skills to perform calculations, estimate figures, or analyze data as needed. Use logical reasoning and critical thinking to derive insights and formulate hypotheses.
5. Iterate and refine your answer
Continuously reassess your approach and findings as you progress through the problem.
Be open to revising your assumptions or adjusting your methodology based on new insights or feedback. Refine your analysis through iterations to improve accuracy and comprehensiveness.
6. Communicate your answer
Clearly articulate your thought process, assumptions, and methodology to the interviewer.
Structure your response in a logical and organized manner, using clear and concise language.
Make sure to engage with the interviewer throughout the entire process, seeking clarification or validation as needed.
7. Be adaptable
Be prepared to adapt your approach, structure, or answer in response to unexpected challenges or new information. Maintain composure and flexibility, even in the face of uncertainty or pressure. You should showcase your ability to think on your feet and pivot when necessary.
Below, we’ve compiled 75 consulting brain teasers that are commonly asked in interviews and their answers.
1. How many golf balls fit in a Boeing 737?
Solution: Estimating the number of golf balls that could fit in a Boeing 737 involves several assumptions and calculations based on the available space in the aircraft's cabin. Let's make some general assumptions:
Volume of the cabin: The cabin of a Boeing 737 varies depending on the specific model, but let's assume a cabin volume of approximately 3,000 to 4,000 cubic feet.
Volume of a golf ball: A standard golf ball has a volume of about 2.5 cubic inches.
Packing efficiency: Considering that golf balls do not pack perfectly and there are other items in the cabin, we'll assume a packing efficiency of around 70%.
Now, let's calculate:
Cabin volume = 3,000 to 4,000 cubic feet ≈ 85,000 to 113,000 cubic inches
Number of golf balls = (Cabin volume * Packing efficiency) / Volume of a golf ball
Number of golf balls = (85,000 to 113,000 * 0.70) / 2.5
Number of golf balls = 23,800 to 31,640
So, based on these rough estimates, approximately 23,800 to 31,640 golf balls could fit in a Boeing 737.
2. How many gas stations are there in the U.S.?
Solution: Estimating the number of gas stations in the U.S. involves several factors and can vary based on definitions (e.g., traditional gas stations, convenience stores with fuel pumps).
However, let's make some general assumptions to provide a rough estimate:
Population density: The United States has a population of approximately 331 million people.
Gas station density: Assume a density of gas stations around one gas station per 2,000 to 3,000 residents. We’ll use the midpoint of this range.
With these assumptions, we can estimate the number of gas stations:
Number of gas stations per capita = 1 gas station per 2,500 residents
Number of gas stations = Population of the United States / Number of residents per gas station
Number of gas stations = 331,000,000 / 2,500 ≈ 132,400
So, based on these rough estimates, there may be around 132,400 gas stations in the United States.
3. How many coffee shops are there in New York City?
Solution: Estimating the number of coffee shops in New York City involves several factors and can vary based on definitions (e.g., independent coffee shops, chain stores, cafes within other establishments).
However, let's make some general assumptions and provide a rough estimate:
Population density: New York City has a population of approximately 8.4 million people.
Coffee shop density: Assume a density of coffee shops of one coffee shop per 10,000 to 15,000 residents. We’ll use the midpoint of this range.
With these assumptions, we can estimate the number of coffee shops:
Number of coffee shops per capita = 1 coffee shop per 12,500 residents
Number of coffee shops = Population of New York City / Number of residents per coffee shop
Number of coffee shops = 8,400,000 / 12,500 = 672
So, based on these rough estimates, there may be around 672 coffee shops in New York City.
4. How much revenue does the average laundromat make per year?
Solution: Estimating the revenue of an average laundromat per year involves several factors and can vary significantly based on location, size, equipment, pricing, and other factors. However, let's make some general assumptions to provide an estimate:
Average revenue per machine: Assume each washing machine generates around $20 per day in revenue, accounting for various load sizes and cycles.
Number of machines: A small to medium-sized laundromat may have around 20 washing machines.
Operating days: Assuming the laundromat operates 7 days a week throughout the year.
With these assumptions, we can estimate the annual revenue:
Revenue per day = 20 machines * $20 = $400
Annual revenue = $400 * 365 days = $146,000
So, based on these rough estimates, the average revenue of a small to medium-sized laundromat could be around $146,000 per year.
5. Fill in the missing number in the sequence: 2, 6, 12, 20, __, 42
Solution: The missing number is 30. The differences between consecutive numbers are increasing by 2 each time.
6. Using up to four 4s and any mathematical operations (addition, subtraction, multiplication, division, exponentiation, etc.), create an equation that results in the numbers from 1 to 10
Solution:
7. You have two jugs, one holding 5 liters of water and the other holding 3 liters. How can you measure exactly 4 liters of water?
Solution: Fill the 5-liter jug and pour water into the 3-liter jug until it's full. This leaves 2 liters in the 5-liter jug. Then, empty the 3-liter jug and pour the remaining 2 liters from the 5-liter jug into it. Refill the 5-liter jug and pour water into the 3-liter jug until it's full, which requires 1 liter, leaving exactly 4 liters in the 5-liter jug.
8. If you place one grain of wheat on the first square of a chessboard, two on the second, four on the third, and so on, doubling the amount each time, how much wheat would be on the 64th square?
Solution: The amount of wheat doubles with each square, so there would be 2^63 grains on the 64th square.
9. Why is a tennis ball fuzzy?
Solution: A tennis ball is fuzzy to enhance its aerodynamic properties, allowing players to impart spin and control its flight path during play. The fuzziness creates drag and turbulence, making the ball easier to grip on the racket strings and enhancing visibility on the court.
10. Why are manhole covers round?
Solution: Manhole covers are round because a round shape cannot fall through its own opening, ensuring safety for workers and preventing accidents. Additionally, round covers are easier to roll and maneuver, making them more practical for maintenance purposes.
11. Why are hot dogs sold in packages of 10, but hot dog buns sold in packages of 8?
Solution: They are sold in different quantities to prevent the consumer from completely using up both ingredients. Therefore, the consumer will always have an excess of one ingredient and be forced to purchase the other ingredient again to avoid food waste. This helps increase sales.
12. Why do birds sitting on an electrical power line all sit facing in the same direction?
Solution: Birds sitting on an electrical power line often face the same direction to help minimize wind resistance and conserve energy. By facing in the direction of the wind or prevailing airflow, birds reduce the force exerted on their bodies and maintain balance while perching on the narrow wire.
13. What comes next in this sequence of letters: O, T, T, F, F, S, S, __?
Solution: The next letter is "E." The sequence represents the first letter of each number, starting from one.
14. Transform the word "CAT" into the word "DOG" by changing one letter at a time, with each step resulting in a valid English word
Solution: CAT → COT → DOT → DOG.
15. What word is spelled incorrectly in every dictionary?
Solution: "Incorrectly." In this case, "incorrectly" is spelled "i-n-c-o-r-r-e-c-t-l-y" in every dictionary.
16. What seven-letter word becomes longer when the third letter is removed?
Solution: "Lounger." Removing the third letter "u" results in "longer."
17. You are presented with two doors and two guards. One door leads to freedom, while the other leads to certain death. One guard always tells the truth, and the other always lies. You can ask only one question to one guard to determine which door leads to freedom. What question do you ask?
Solution: Ask either guard, "If I were to ask the other guard which door leads to freedom, what would he say?" Then, choose the opposite door of the one they point to.
18. Two suspects, A and B, are arrested for a crime. They are held in separate cells and cannot communicate with each other. The police offer each suspect the following deal:
What should the suspects do?
Solution: Both suspects are better off remaining silent. This ensures the lowest combined sentence (2 years in total) compared to any other scenario.
19. A group of people is standing in a line, each wearing either a black or white hat. They can only see the hats of the people in front of them, not their own or those behind them. Starting from the back of the line, each person must guess the color of their own hat. If they guess correctly, they are saved. Otherwise, they are executed. The group is allowed to discuss a strategy before guessing begins. What strategy can they use to maximize their chances of survival?
Solution: The person at the back of the line can count the number of white hats in front of them. If it's even, they guess white; if it's odd, they guess black. The next person then follows the same logic based on the remaining hats in front of them, and so on, with each person's guess providing information for the next person in line.
20. You are in a room with three light switches, each connected to a different light bulb in another room. You cannot see the bulbs from where you are. You are told that each switch corresponds to one bulb, and you must determine which switch controls which bulb. You are only allowed to enter the room with the bulbs once. How do you figure it out?
Solution: Turn on one switch for a few minutes, then turn it off. Turn on another switch, and enter the room with the bulbs. The bulb that is on corresponds to the second switch, the bulb that is off and hot corresponds to the first switch, and the bulb that is off and cold corresponds to the third switch.
21. Three people check into a hotel room that costs $30. They each contribute $10, and the clerk takes them to the room. Later, the clerk realizes there's a promotion, and the room only costs $25. He gives $5 to the bellboy and asks him to return it to the guests. On the way, the bellboy decides to keep $2 for himself and gives $1 back to each guest. Now, each guest paid $9, totaling $27, plus the $2 the bellboy kept equals $29. What happened to the missing dollar?
Solution: The trick is that the guests didn't really pay $27. They paid $25, and the bellboy kept $2. There is no missing dollar; it's just a misleading presentation of the math.
22. You need to cross a river with a wolf, a goat, and a cabbage. You can only take one of them at a time in your boat, and you can't leave the wolf alone with the goat or the goat alone with the cabbage. How do you get them all across?
Solution: Take the goat across first, then return for the wolf. Leave the wolf on the other side and take the goat back. Leave the goat and take the cabbage across. Finally, return for the goat.
23. What walks on four legs in the morning, two legs in the afternoon, and three legs in the evening?
Solution: A human. In the morning (youth), they crawl on all fours; in the afternoon (adulthood), they walk on two legs; and in the evening (old age), they use a cane (three legs).
24. What 5-letter word becomes shorter when you add two letters to it?
Solution: Short.
25. A clock is broken so that the minute hand is on the hour and the hour hand is on the minute. What time is it?
Solution: It's 6:30. The hour hand is pointing to the 6, and the minute hand is pointing to the 30.
26. You're in a room with three chests: one containing gold coins, one containing silver coins, and one containing a mixture of both. Each chest is labeled with a statement: "All gold," "All silver," or "Mixed." However, you know that all the labels are incorrect. You are allowed to open one chest and take only one coin from that chest. Which chest should you open to maximize your chance of getting a gold coin?
Solution: You should open the chest labeled "Mixed." Since all the labels are incorrect, the chest labeled "Mixed" must contain either all gold or all silver coins. Taking one coin from this chest will either confirm it as all gold (if you get a gold coin) or all silver (if you get a silver coin). In either case, you know the contents of the other two chests.
27. You're a king who suspects that one of your 1000 goblets has been poisoned. You have an unlimited number of prisoners whom you can use to test the goblets. What is the minimum number of prisoners you need to use to find out which goblet is poisoned?
Solution: Use ten prisoners. This is the number of digits needed to represent 1000 in binary. Number the goblets from 1 to 1000 and make each prisoner drink from a different set of goblets according to their number in binary. For example, prisoner 1 will drink from goblets 1, 3, 5, 7, and so on. If a prisoner dies, their binary number indicates which goblets are poisoned.
28. You have two ropes, and each rope takes exactly one hour to burn when lit at one end. However, the ropes don't burn at a uniform rate, meaning that it might take half an hour for one rope to burn halfway and then another half an hour to burn the rest. How do you measure exactly 45 minutes using only these two ropes?
Solution: Light one end of the first rope and both ends of the second rope simultaneously. When the first rope burns out (30 minutes), light the other end of the second rope. When the second rope burns out (15 minutes later), 45 minutes have elapsed.
29. You're on a game show where you're presented with three doors. Behind one door is a car, and behind the other two are goats. You choose one door, and then the host, who knows what's behind each door, opens another door revealing a goat. He then gives you the option to switch doors. Should you stick with your original choice or switch? What gives you the best chance of winning the car?
Solution: You should switch doors. When you initially choose a door, you have a 1/3 chance of picking the car, and a 2/3 chance of picking a goat. When the host opens a door revealing a goat, he effectively offers you the choice between sticking with your original 1/3 chance or switching to the other unopened door, which has a 2/3 chance of containing the car.
30. On a remote island, there are 100 blue-eyed people, each of whom can see everyone else's eye color but not their own. They are not allowed to communicate with each other. If a person finds out they have blue eyes, they must leave the island at dawn the next day. One day, a visitor arrives and tells them, "At least one of you has blue eyes." What happens next?
Solution: On the 100th day, all blue-eyed people leave the island. Each blue-eyed person realizes that if they were the only one with blue eyes, they would leave on the first day. Since they don't, they must deduce that there are others with blue eyes. Once the 100th day passes with no one leaving, they all realize they have blue eyes and leave the island together.
31. Kevin’s father has four children: Keith, Kenneth, and Karl. Who is the fourth?
Solution: The brain teaser mentions “Kevin’s father,” implying that Kevin is one of his children.
32. The day before yesterday Sally was 17. Next year he will be 20. What day is her birthday?
Solution: Sally’s birthday is December 31. The day before yesterday is December 30 and Sally was 17. Yesterday was December 31 and Sally turned 18. Today is January 1 and Sally will be 19 this year. Next year, Sally will be 20.
33. Two mothers and two daughters sat down to eat toast for breakfast. They ate exactly three pieces of toast, each person had one piece of toast. Can you explain how?
Solution: One of the mothers is both a daughter and a mother.
34. You are in a dark room. You have a lot of red socks and blue socks in your drawer. You want to get a matching pair, but your socks are not organized. All socks are identical except for the color. What is the minimum number of socks you need to take to take to get a matching pair?
Solution: You need at least 3 socks. If the first sock is red and the next sock is red you got a pair. If the first sock is red, the second sock is blue, you will get a pair regardless of if the third sock is red or blue.
35. What has a head and a tail, but does not have a body?
Solution: A coin has a heads side and a tails side.
36. How many times can you subtract the number 5 from 30?
Solution: You can only subtract the number 5 once. After the first subtraction, you are subtracting from the number 25, not 30.
37. What has many keys but cannot open any doors?
Solution: A piano.
38. How far can a dog run into the woods?
Solution: Only as far as the middle of the woods. Afterwards, the dog will be running out of the woods.
39. A man went for a walk and got caught in the rain. The man did not have an umbrella and was not wearing a hat. Not a single strand of hair on his head got wet. How is it possible?
Solution: The man was bald.
40. How many months have 28 days?
Solution: Twelve months. Every month has at least 28 days.
41. What can travel around the world while staying in a corner?
Solution: A stamp.
42. I speak without a mouth and hear without ears. What am I?
Solution: An echo.
43. What is full of holes but still holds water?
Solution: A sponge.
44. What has to be broken before you can use it?
Solution: An egg.
45. What belongs to you but is used more by others?
Solution: Your name.
46. What comes once in a minute, twice in a moment, but never in a thousand years?
Solution: The letter "M".
47. The more you take, the more you leave behind. What am I?
Solution: Footsteps.
48. What can you catch but not throw?
Solution: A cold.
49. What has a neck but no head?
Solution: A bottle.
50. What gets wetter as it dries?
Solution: A towel.
51. What has a thumb and four fingers but is not alive?
Solution: A glove.
52. I'm tall when I'm young, and I'm short when I'm old. What am I?
Solution: A candle.
53. What has one eye but can't see?
Solution: A needle.
54. I'm light as a feather, yet the strongest person can't hold me for much longer than a minute. What am I?
Solution: A breath.
55. What goes up but never comes down?
Solution: Your age.
56. I have cities but no houses, forests but no trees, and rivers but no water. What am I?
Solution: A map.
57. What can you hold in your right hand but not in your left hand?
Solution: Your left hand.
58. If you have three apples and you take away two, how many apples do you have?
Solution: Two apples. You took them, but they are still yours.
59. I am an odd number. Take away a letter and I become even. What number am I?
Solution: Seven. Remove the "s," and it becomes "even."
60. What three positive numbers give the same result when multiplied and added together?
Solution: 1, 2, and 3. 1 x 2 x 3 = 6 and 1 + 2 + 3 = 6.
61. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
Solution: 5 minutes. Each machine takes 5 minutes to make one widget, regardless of the number of machines.
62. What number is one-half of one-quarter of one-tenth of 800?
Solution: 10. One-tenth of 800 is 80, one-quarter of 80 is 20, and one-half of 20 is 10.
63. What is the next number in the sequence: 1, 4, 9, 16, __?
Solution: 25. Each number is a perfect square: 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25.
64. If you have 12 coins and one of them is fake, but you don't know if it's lighter or heavier than the real ones, how can you find the fake coin using a balance scale only three times?
Solution: Divide the coins into three groups of four. Weigh two groups against each other. If they balance, the fake coin is in the third group. If one side is heavier, the fake coin is in that group. Then repeat the process with the group containing the fake coin, identifying the fake coin after the third weighing.
65. How many times does the digit 9 appear between 1 and 100?
Solution: There are 20 occurrences of the digit 9 between 1 and 100. These occurrences are: 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 90, 91, 92, 93, 94, 95, 96, 97, and 98. Note that a 9 appears twice for the number 99.
66. A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?
Solution: The ball costs $0.05. If the ball costs x dollars, then the bat costs (x + $1). So, the total cost is x + (x + $1) = $1.10.
67. Tom's age is half of Sally's age. In 20 years, Sally will be twice as old as Tom. How old are they now?
Solution: Tom is 10 years old, and Sally is 20 years old. Let Tom's age be T and Sally's age be S. So, T = (1/2)S. In 20 years, Sally will be S + 20, and Tom will be T + 20. So, S + 20 = 2(T + 20). Solving these equations gives Tom as 10 and Sally as 20.
68. If you have 10 fish and half of them drown, how many are left?
Solution: Fish can't drown; they live in water. So, all 10 fish would still be there.
69. What is the sum of the first 100 positive integers?
Solution: 5,050. Notice that 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on. There are 50 pairs of numbers that added together total 101. Therefore, 50 * 101 = 5,050.
70. A plane crashes on the border of the United States and Canada. Where do they bury the survivors?
Solution: You don't bury survivors.
71. You're in a race and you overtake the second person. What position are you in now?
Solution: You are in second place. Overtaking the second person means you are now second.
72. What is always in front of you but can't be seen?
Solution: The future.
73. What letter comes next in the sequence: J, F, M, A, M, J, ...?
Solution: The letter J. These are the first letters of the months in order: January, February, March, April, May, June, and July.
74. What is the next number in the sequence: 1, 3, 7, 15, ...?
Solution: 31. Each number is doubling and then adding one: (12)+1 = 3, (32)+1 = 7, (7*2)+1 = 15, and so on.
75. I am taken from a mine, and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?
Solution: The answer to this brain teaser is "pencil lead" or simply "lead". It's mined from the ground, encased in wood to create pencils, and used by almost everyone for writing or drawing.
Consulting brain teasers can be difficult to prepare for because there are thousands of different questions you could get asked across multiple different types of brain teasers.
However, there are a few actionable steps you can take to ensure that you are prepared to the best of your ability for any consulting brain teaser question that could get asked.
1. Understand the different types of consulting brain teasers
Familiarize yourself with the different types of consulting brain teasers, such as estimation questions, logic brain teasers, and math puzzle brain teasers. Identify common patterns, structures, and themes within each type of brain teaser to better anticipate and tackle them during interviews.
2. Practice regularly
Dedicate time to regular practice sessions where you solve consulting brain teasers under timed conditions. You can use the brain teaser questions and answers in this article for practice. If needed, you can find other online resources or books for more brain teaser examples with answers.
3. Develop analytical skills
Strengthen your analytical skills by practicing mental math, numerical reasoning, and data interpretation. Sharpen your logical reasoning skills through puzzles, riddles, and logic games to enhance your ability to identify patterns and solve complex problems.
4. Develop a structured problem solving approach
Learn and apply structured problem solving frameworks commonly used in consulting, such as MECE (Mutually Exclusive, Collectively Exhaustive), hypothesis-driven analysis, and issue trees. Practice breaking down complex problems into manageable components and developing logical, step-by-step approaches to address them systematically.
5. Improve communication skills
Practice articulating your thoughts clearly and concisely, both verbally and in writing.
Work on structuring your responses in a logical and organized manner, using bullet points or frameworks to convey your ideas effectively.
6. Practice managing time and stress effectively
Practice time management techniques to allocate sufficient time to each stage of solving a consulting brain teaser. Develop a positive mindset and confidence in your abilities through consistent practice and preparation so that you don’t get stressed on interview day.
7. Learn from experience
Reflect on past consulting brain teaser questions you've encountered during interviews or practice sessions. Analyze your approach, identify successful strategies, and learn from any mistakes or challenges you encountered.
To perform your best while answering consulting brain teasers, make sure to stay calm and composed, listen carefully, clarify ambiguities, break down the problem, show your work, and be flexible and adaptable.
1. Stay calm and composed
Maintain a calm and composed demeanor throughout the interview, even when faced with challenging brain teasers. Remember that interviewers are assessing not just your problem solving skills but also your ability to handle pressure and uncertainty with grace.
2. Listen carefully
Listen attentively to the instructions provided by the interviewer and ensure you understand the problem statement fully. Pay attention to any hints, clues, or additional information provided during the course of the interview.
3. Clarify ambiguities
Don't hesitate to ask clarifying questions if you encounter any ambiguities or uncertainties in the brain teaser. Seek clarification on key assumptions, constraints, or parameters that may impact your analysis.
4. Break down the problem
Break down the problem into smaller, more manageable components to simplify the analysis.
Identify the key variables, factors, or metrics that need to be considered in your solution approach.
5. Show your work
Clearly articulate your thought process and reasoning behind each step of your analysis. Explain the rationale for your assumptions, calculations, and decisions to demonstrate your analytical thinking to the interviewer.
6. Be flexible and adaptable
Be prepared to adapt your approach based on new information, feedback from the interviewer, or unexpected challenges. Stay flexible in your thinking and consider alternative perspectives or solution paths as needed.
Recommended Consulting Case Interview Resources
As you prepare for consulting brain teasers, make sure you are also preparing for case interviews in parallel. You will need to ace every single one of your consulting case interviews in order to land a consulting offer.
Here are the resources we recommend to learn the most robust, effective case interview strategies in the least time-consuming way: