# Typical Question Types in Written Tests

## Since there are different types of written tests across consulting firms, it would make sense to prepare for various question types that appear in these tests.

In this chapter we will provide you with an overview of common question types across written tests such as the PST. First of all, unless you know exactly what type of test you will get, it is advisable to prepare for the different question types that could appear in these tests. Also, given that most firms are not too generous with the materials they distribute, this approach will help you find more practice material without having to pay for commercially available practice tests.

The following are some common question types and strategies on how we can approach these questions.

## The general math questions

General math questions are used across most written tests. The key skill being tested is your ability to calculate quickly and accurately without a calculator.

### In order to solve these types of questions:

• Practice your general math skills to make sure you are able to calculate quickly and accurately. Also, make sure to compare your results with peers using PrepLounge's practice tool (see our case math section for additional practice material)
• Make sure to double check your calculations – this might seem straight forward but during the test you might calculate the wrong percentage or make an arithmetic error. If a table is provided (as shown later), be sure to immediately mark the columns/rows that you need to avoid confusion
• Estimate the answer before doing the exact calculations since you can generally eliminate 2 or more answers with a quick estimation in your head

### Example question:

FlipFlopCo, a major manufacturer of trendy flip flops asked [name of the consultancy you are currently taking the test at] to look into its sales development across several countries over the last years.

The table below shows the sales development of the flip-flop business unit across FlipFlopCo’s major markets. Which of these markets showed the fastest sales development (in %-terms) from 2009-2012?

 US\$ M 2008 2009 2010 2011 2012 US 233 274 333 393 455 CA 140 160 181 198 230 MX 44 47 56 73 80 EU 58 67 65 69 72 RoW 56 49 49 54 56

a)US

b)CA

c)MX

d)EU

e)RoW

The question wants you to calculate the relative increase from 2009 to 2012. We recommend to first highlight/mark the two columns labeled 2009 and 2012 to avoid mis-reading charts. Next, rather than doing exact calculations right away, we would first estimate to eliminate unlikely choices.

• US:
• Sales increased from 274 to 455
• We round this to 300-500, an increase that we are able to mentally calculate (~ 66%)
• To avoid making careless errors, we would write the result next to the 455 in the US line
• We then repeat these steps for other countries/regions
• CA: 150-200: ~33%
• MX: 50-80: ~60%
• EU: 70-70: ~0%
• RoW: 50-60: ~20%

Now, we can eliminate all answers but US and MX. To avoid caresless errors, we would cross out the eliminated answers on the table. Then, we can precisely calculate for US and MX to determine the correct answer.

## GMAT style questions

GMAT math is used very frequently in written tests. The good thing is that there is ample preparation material for these types of questions.

### In order to attack these types of questions:

1. Get acquainted with the types GMAT questions a particular consulting firm usually asks since GMAT math can be range from numerical reasoning to geometry. For example, while Bain is seemingly focused on numerical reasoning, Oliver Wyman can focus more on geometry skills
2. Practice solving the GMAT type of questions and here the goal should be to get fairly acquainted with solving GMAT types of questions. Practice general math, which is more important than any other skills on written tests

Chart reading is extremely important for both case interview and written tests. The prevalence of charts in interviews seems to be slightly higher at BCG compared to McKinsey and Bain.

• Read the title and understand the big picture of the chart/graph. Consultants call this ‘clearing the chart’. Example: ‘Ok, so this is a bar chart showing annual revenues from 2008 to 2013 in real numbers and the forecast for 2014 broken down by BU’.
• Make sure that you are looking at the right axis, e.g. the axis might be in relative terms or occasionally log scale
• Mark the numbers that you need to avoid making careless errors
• For example, in a chart with several lines, mark/highlight the column/row that you want to work with
• If the chart contains numbers only on the axis, write down the numbers you want to work with to avoid looking for the second time
• Resist the temptation to quickly draw visual conclusions and rather read carefully before making inferences.

## Brain teaser questions

Brain teaser questions resemble solving mind puzzles and are not related to business cases. Oliver Wyman is known for using these types of questions in its interviews.

### In order to approach these types of questions:

• Familiarize yourself with brain teasers in general since most of them usually follow common principles
• Practice solving these types of questions until you feel more confident.

PrepLounge provides several examples to prepare you for brainteaser types of questions.

## Quiz

1
2
3
4
5

The selected solution is not correct.

The selected solution is correct.

### Question 5

4 Comment(s)
August 02, 2016 10:39 -
Julia

Hi Guillermo,
Thanks a lot for the note. We already corrected the mistake!

July 23, 2016 13:21 -
Guillermo

The question 4 of the Quiz has a mistake. The first sentence asks you to look to data from the years 2001 and 2002 in a Table but the Table has data for the years 2000 and 2001.

May 30, 2016 12:47 -
Ashkan

Hello Constance,

it's fixed now!
Thank you for the remark and sorry for the inconvenience.
Best wishes!

May 27, 2016 20:38 -
Constance Siyuan

why can't the exhibitions display? I tried several laptops they all don't work.....

Related consulting question(s)

Hey Constance, I have taken the McKinsey Problem Solving Test. It's a very interesting exam indeed - it's not a math test, it's not an English test, but it's a bit of both and something more.... (more)

Not exactly what you are looking for, but i suggest you spend 15-20 minutes a day on caseinterviewmath.com for rapid-fire practice. It will rank you by speed and accuracy as well, i used it to grest e... (more)

Hello Everyone, Did anyone interview with capital one ? They have a mix of qualitative and quanti... (more)

http://www.mckinsey.com/careers/interviewing/globapharm In the quant section of this case, why is... (more)

Related case(s)

## Brain Teasers - Barbershop

Solved 3373 times | Rating: (4.0 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

### Motel

Situation:
Three friends check into a motel for the night. The clerk tells them the bill is \$30, payable in advance. They each pay the clerk \$10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by \$5. He asks the bellhop to return \$5 to the 3 friends who had just checked in. The bellhop sees this as an opportunity to make \$2 as he reasons that the three friends would have a tough time dividing \$5 evenly among them; so he decides to tell them that the clerk made a mistake of only \$3, giving a dollar back to each of the friends. He pockets the leftover \$2 and goes home for the day!

Question:
Now, each of the three friends gets a dollar back, thus they each paid \$9 for the room which is a total of \$27 for the night. We know the bellhop pocketed \$2 and adding that to the \$27, you get \$29, not \$30 that was originally spent. Where did the other dollar go?

### Murder

Situation:

The midnight train is coming down the mountains. Art Farnanski seems to be sleeping in his seat. At the station, all the passengers get off the train except one. The conductor comes and taps him on the shoulder to let him know they have arrived. Art Farnanski does not answer. He is dead.
Hours later the four people that had shared the train compartment with the dead man are at the police station.
The man in the dark suit:
"I'm innocent. The blonde woman was talking to Farnanski."
The blonde woman:
"I'm innocent. I did not speak to Farnanski."
The man in the light suit:
"I'm innocent. The brunette woman killed him."
The brunette woman:
"I'm innocent. One of the men killed him."

Question:
The police detective comes up to you and says: “I know that four statements are wrong and four are true. Who killed Farnanski? (Only one person is guilty).”

### Trees

Statement:
You have 10 trees and you have to plant them in five rows, but each row must contain 4 trees.

Question:
How is this possible?

### Barbershop

Statement:
A business man is in a village for a meeting. He has time to spare before the meeting, so he decides to get a haircut. He looks at a street map and was surprised to find that there are only two barbers in town, right across the road from each other.

He went into the first one and was shocked by the dirtiness and the hair everywhere. The place was a mess! He looked at the barber and the barber had a really messy haircut, all in his face and uneven. He went across the street to the other barber and saw the place was immaculate, clean and shining like new. The barber was nicely dressed and had a dazzling haircut: it was perfect. However, the man walked across the street and got his haircut at the shabby barbers.

Question:
Why?

### Bridge

Statement:
During WWII, there was a bridge connecting Germany and Switzerland. On the German side, there was a sentry tower with a guard in it who would come out every three minutes to check on the bridge. He had orders to turn back anyone who tried to get into Germany, and shoot anyone trying to escape without a pass.

There was a woman who desperately needed to get into Switzerland, and she knew she didn't have time to get a pass. It would take her at least six minutes to cross the bridge, but she managed to do it.

Question:
How did she escape into Switzerland successfully?

## Brain Teasers - Barkeeper

Solved 3163 times | Rating: (4.4 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

### Firefighter

Situation:

A firefighter stood on the middle rung of a ladder, spraying water on a burning house. He then climbed up 6 rungs before the heat of the flames caused him to come down 10 rungs. After some minutes he was able to climb 18 rungs to the very top of the ladder.

Question:
How many rungs did the ladder have?

### Bartender

Situation:
There are two twin old men that go into the same bar every day. The bartender at the bar hates one of the twins, but there is only one way he could tell the difference between them: The one that he hates drinks very slowly and the one that he likes drinks fast.

One day the bartender decides to kill the one that he hates. So when they came in that day he put the same amount of the drink in their cups, the same amount of ice, and the same amount of poison. When they are both done with their drinks the one that the bartender hates dies, but the one he likes lives.

Question:

How is this?

### Hats

Situation:
There are 4 people sitting in a row, trying to win a riddle.

• The one in front was wearing a red hat.
• The second from the front was wearing a blue hat.
• The third from the front was wearing a red hat.
• The last was wearing a blue hat and is blind-folded.

Each of them was informed that they are all wearing a hat, the last person is blind-folded and that there are 2 red and 2 blue hats. They can only see the persons in front of them and are not allowed to turn around and see behind them.

Question:

The one who guesses the color of his hat wins the prize. Who is it?

### Pirates

Situation:

Five pirates are trying to split up 1000 gold pieces. The rules are as follows:

Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose a solution to the remaining 3 pirates, and the same rules will follow. This continues until someone comes up with a plan that earns a majority vote.

The pirates are infinitely greedy, infinitely ruthless (the more dead pirates the better), and infinitely intelligent.

Question:

What is the highest amount of gold pieces that pirate #1 can keep and what would his proposal be?

### Chicken

Situation:

A man is traveling with a fox and two chickens, if he leaves the fox alone with the chickens the fox will eat the chickens. He arrives at a river and needs to cross it. He finds a small boat that can carry only him and one animal.

Question:

How does he get himself, the fox and the two chickens across the river safely?

## Brain Teasers - Lethal Duel

Solved 2783 times | Rating: (4.4 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

### Coins

Situation:
Imagine, we are sitting together at a perfectly round table. We both have an infinite pile of quarters. These are the rules of the game: “We'll take turns putting one quarter down on the table, no overlapping allowed, and the quarters must rest flat on the table surface. The first guy who can't put a quarter down loses."

Question:
Who should start in order to win, why and how does your strategy work?

### Marbles

Situation:

There are 8 marbles that weigh 1 ounce each, and 1 marble that weighs 1.1 ounces. The marbles are all uniform in size, appearance, and shape. You have a balance that contains 2 trays. You are only able to use the scale 2 times.

Question:

How do you determine which marble is the heaviest using only the scale and marbles in 2 weighings.

### Duel

Situation:

Three men, Adam, Bertie and Charlie, agree to take part in a lethal three-way duel. They each have a pistol and several rounds of ammo, and they draw lots to see who will shoot first and who second. Then they stand an equal distance apart, and they take turns to fire. When it is a player's turn, he can take one shot at any target of his choice. Then, the turn passes to the next player. The duel continues until only one player is left alive.

For simplicity, we can ignore the possibility of a player becoming injured and unable to shoot: a player is either alive or dead. We also assume that each player chooses to play in such a way as to give himself the best chance of winning.

Now Adam and Bertie are crack shots and will always get a kill, but Charlie is only a moderate shot and will only get a kill two thirds of the time. All three men know this.

Question:

Of the three men, who has the best chance of winning the duel?

### Murder

Situation:

A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis:

• The Wife said she was sleeping.
• The Cook was cooking breakfast.
• The Gardener was picking vegetables.
• The Maid was getting the mail.
• The Butler was cleaning the closet.

Question:

The police instantly arrested the murdered. Who did it and how did they know?

### Boxes

Situation:

Three closed boxes have either white marbles, black marbles or both, and they are labeled white, black and both. However, you're told that each of the labels is wrong. You may reach into one of the boxes and pull out only one marble.

Question:

Which box should you remove a marble from to determine the contents of all three boxes?

## Brain Teasers - U2 Concert

Solved 2221 times | Rating: (4.4 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

### Number sequence

Situation:

“You and I will take turns saying numbers. The first person will say a number between 1 and 10. Then, the other person will say a number that is greater than the first number. The difference between both numbers must be between 1 and 10. We will keep going back and forth in this way until one of us says the number 50. That person wins. You will start.”

Question:

### U2 Concert

Situation:

U2 has a concert that starts in just 17 minutes. To get there, all the band members must cross a bridge. Since the bridge is old, a maximum of two people can cross the bridge at any one time. To make matters worse, it is dark and there is only one torch. Anyone crossing the bridge must carry a torch. The torch cannot be thrown across the bridge. Instead, someone must walk it back to the other side. Each band member walks at a different speed. If two members cross at the same time, both must walk at the speed of the slower band member.

• Bono takes 1 minute to cross.
• Edge takes 2 minutes to cross.
• Adam takes 5 minutes to cross.
• Larry takes 10 minutes to cross.

Question:

Can the band make it to the concert in time? How will they manage this?

### Buckets

Situation:

You have a 5-gallon bucket and a 3-gallon bucket. (Assume that you have an unlimited supply of water and that the buckets do not have any markings for measurement.

Question:

How can you get 4 gallons of water into the 5-gallon bucket?

### Cigars

Situation:

A homeless man collects cigar butts. He uses 5 cigar butts to make a new cigar. Today, he has collected 25 cigar butts.

Question:

How many cigars can he smoke?

## Brain Teasers - Light Bulb

Solved 1674 times | Rating: (3.8 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

### Light Bulb

Situation:

You are standing in front of a room with one light bulb inside of it. You cannot see if it is on or off. Outside the room there are 3 switches in the off positions. You may turn the switches any way you want to. You can open the door and enter the room, but you cannot use a switch anymore afterwards

Question:

How can you determine which switch turns the light on and off?

### Coins

Situation:

You have a pile of 24 coins. Twenty-three of these coins have the same weight, and one is heavier. Your task is to determine which coin is heavier and do so in the minimum number of weighings. You are given a beam balance (scale), which will compare the weight of any two sets of coins out of the total set of 24 coins.

Question:

How many weighings are required to identify the heavier coin?

### Truth or Lie

Situation:

You are in a room with 2 doors leading out. Behind 1 door is a coffer overflowing with jewels and gold, along with an exit. Behind the other door is an enormous, hungry lion that will eat anyone opening the door.

You do not know which door leads to the treasure and exit, and which door leads to the lion. In the room you are in with 2 men. The first is a knight, who always tells the truth, and a knave, who always lies. Both of these individuals know what is behind each door. You do not know which individual is the knight, or which one is the knave.

Question:

You may ask one of the individuals exactly 1 question. What should you ask in order to be certain that you will open the door with the coffer behind it, instead of the hungry lion?

### Dogs

Situation:

Two scruffy dogs were walking down the street. The first dog turned to the other and said, "Do you realize that if one of your fleas jumped onto me we would have the same number of fleas?" The second replied, "Yes, but if one of your fleas jumped onto me I would have five times as many fleas as you."

Question:

How many fleas are on each dog to begin with?