Three friends - Adam, Barbara and Carla – depart successively at equal intervals of 60 minutes towards Paris from Brussels, a distance of 240 km. If they all reach Paris at the same time, what’s the difference between Carla’s and Adam’s speed? It is known that Barbara traveled at an average speed of 60 km per hour.

## Math Assignments for Case Interviews – Pack 1

Consulting companies like McKinsey, BCG or Bain usually demand entry-level applicants to take multiple-choice tests as part of their selection process. These tests are designed to assess your ability to think under pressure and seed out unqualified candidates. In many cases, it can be even impossible to complete all exercises of the tests in the given time. Therefore, training your case math skills is a key factor to succeed and make it to the next round.

So let's get started with the first set of questions!

### Your result

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### Question 1/10

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer b

Solution:

- Time taken by Barbara = 4 hours – solution to the problem, with tips
- Time taken by Adam and Carla = 5 and 3 hours respectively
- Difference in their speeds: 240/3 – 240/5 = 80 – 48 = 32 km/hour

### Question 2/10

50% of a class is composed of boys and the rest are girls. 24% of the boys and 40% of the girls are blue-eyed. If there are 12 blue-eyed boys in the class, find the number of students who don’t have blue eyes.

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer c

Solution:

- No. of students in the class = 12/(0.24*0.5) = 100
- No. of blue eyed girls = 40% * 50 = 20
- No. of students who don’t have blue eyes = 100 – 32 = 68

### Question 3/10

Between the only two schools A and B in Beliebertown, B has 50% more students than A. The number of girls in A is equal to the number of boys in B. If the percentage of girls is the same in each school, what percentage of Beliebertown’s students are girls?

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer c

Solution:

If the number of students in Beliebertown is 100, and that in A is x, 2.5x = 100, or x = 40. No. of students in B = 60. If G% of students in each are girls, G*0.4 = 60 – 0.6*G or G = 60% = percentage of girls in Beliebertown (since % of girls is same in each school)

### Question 4/10

5 liters of rum are mixed with 20 liters of Coca Cola by Lukas to produce a formulation he calls Kuba Liveray. His friends, who are new to drinking, prefer to mix 100mL of the soda with each double-shot of the novel cocktail (a single shot is 60 mL). If the rum has 40% alcohol, find the volume percentage of alcohol in the drink consumed by Lukas’s friends.

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer a

Solution:

% of alcohol in Kuba Liveray = 5/25*0.4 = 8%. Vol. of alcohol in 120 mL of the cocktail = 0.08*120 = 9.6 mL ~ 10 mL Therefore % of alcohol in friends’ drinks = 10 / (100+120) ~ 4.5%

### Question 5/10

The distance between Charles Bridge and the Prague castle, two landmarks in the Czech Capital, is 1,500 meters. A visitor to the city can use the tram (which travels at an average speed of 24 km/hour for the distance), or walk at a speed of 6 km/hour. If the visitor wants to spend exactly 10 minutes to reach the castle using a combination of the two means, how far should he walk before taking the tram? (assume no waiting time)

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer c

Solution:

- 6 km/hour = 6000/60 m/min = 100 m/min. Tram’s speed = 400 m/min
- Let’s say the visitor walks X m. Time spend walking: X/100 min. Time taken in tram = (1500-X)/400 min. So, X/100 + (1500 – X)/400 = 10, or 3X + 1500 = 4000, or X = 2500 / 3 = 833.33m

### Question 6/10

A businessman has a chain of 100 shops selling various types of cakes all over Paris. His average gross margin (revenues minus cost of goods sold) is 50%. He pays different rent for each store, but has an overall net profit (gross margin minus rent) of 20%. If 60 of his stores pay €1,000 rent per month each on average, what is the maximum average monthly rent for the other stores for his profit targets to be met? His total revenue for the year is €5 million.

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer d

Solution:

- Total gross profit = 0.5*€5 M = €2.5 M; Profit required = 20% of
- €5 M = €1 M
- Maximum total rent payable in the year = €1.5 M
- Rent paid by 60 stores = €1000*12*60 = €0.72 M Remaining = €0.78 M
- Average rent per remaining store = €780,000/(40*12) = €1625

### Question 7/10

Ahmed is driving his car and is currently 200 meters behind his friend Bahram. He judges that if he increases his speed by 12 km/hour, he will overtake Bahram in 2 minutes. However, if he stops immediately at his current spot, their distance will increase to 1000 meters in 1 minute. If Bahram is travelling at the same speed throughout, what is Ahmed’s speed?

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer d

Solution:

- Let Ahmed and Barham’s speeds be a and b m/min. Since 12 km/hour = 200 m/min, then we know that
- [(a+200)-b]*2 = 200, because
- Relative speed = (Increased speed of Ahmed) minus (speed of Barham)
- Time = 2 minutes
- Distance = 200 meters
- Also, Barham is travelling at 800 m/min (from the second statement), so b = 800. Substituting in the previous equation,
- (a+200-800)*2 = 200
- Or a = 700 m/min = 42 km/hour
- Note: the key here is to choose the right unit for the job. Choosing km/hour will make the calculations more difficult.

### Question 8/10

Two skilled labourers can build a wall in 5 days. 3 unskilled labourers take the same time to build the wall. If 2 skilled and 2 unskilled labourers are working together, how many days will the wall take to build?

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer b

Solution:

- The key here is to calculate speed of each type of labourer in wall/day.
- Skilled = 1/10 wall/day. Unskilled = 1/15 wall/day.
- 2 Skilled + 2 Unskilled = 2/10+2/15 = 10/30
- Number of days = 3

### Question 9/10

A mixture of milk contains 50 mL milk and 150 mL water. If 100 mL of this mixture is taken out and replaced with water, what will be the percentage of water in the remaining mixture?

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer a

Solution:

- In 100 mL of the mixture, vol. of water = ¾*100 = 75 mL.
- vol. of milk = 25 mL.
- Therefore in new mixture, quantity of water = 175 mL, hence % = 175/200*100 ~ 88%

### Question 10/10

Andy starts driving from Lisbon to Warsaw on Monday at 00:00 hours, to cover a distance of 3400 km. If he drives at an average speed of 60 km per hour and rests for 9 hours a day (including Monday), which day of the week does he reach Warsaw?

#### Find the right answer

##### Your answer is correct

##### Your answer is wrong, the correct solution is answer b

Solution:

Andy drives 15 hours a day. Distance covered per day = 15*60 = 900km. Therefore, he reaches on the 4th day, i.e. Thursday.