## Short Practice Questions

These are examples of simple word problems within business contexts. You might want to go back to the Consulting Math overview article for more in-depth information on improving your quantitative capabilities for the McKinsey PST and Case Interviews!

### Hurdle 1:

Question 1: Fonterra charges a 40% markup on milk supplies for dairy stores. A grocery store charges a 25% markup on milk bought from Fonterra. How much, in percentage, has the original price been increased?

Question 2: The Leaning Tower of Pisa is a famous tourist attraction in Italy. Adult tourists pay \$8 EUR per visit, while children only have to pay \$5 EUR. The maintenance cost each year for the tower is \$500,000 EUR. If the revenue from the Children’s tickets covers up to 40% of the maintenance cost, how many adults need to visit the tower for the Board of Tourism to break even?

Question 3: A special kind of building material consists of 1/3 sand, 3/5 water, and 12 kg of soil. What is the total weight of the mixture?

Question 4: At a motorbike store, 20% of the motorbikes are Honda products and 1/9 of them are Vespa’s. If the store had exactly 270 motorbikes, how many of them are either Honda or Vespa made?

Question 5: DuckThat! is a brand of prank tool boxes. A retail box from DuckThat! costs \$18.50, and a wholesale carton of 5 boxes costs \$90. If 45% of the target sales of \$2,700,000 is already coming from retail sales, how many boxes would have to be sold through wholesale?

• Q1: 75%
• Q3: 180 kg
• Q4: 84 in total
• Q5: 82,500 boxes

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### Hurdle 2:

Question 6: EV Bank invested \$1.5 million in the stock market for a period of 2 years and expected a CAGR (i.e. percentage of return each year) of 12%. Calculate the expected value of EV Bank’s investment after 2 years (in unit of thousand dollars).

Question 7: Io Bar serves an average of 350 customers and 1450 drinks per night. It takes 40 seconds to prepare a drink. Calculate the average time spent on serving one customer in Io Bar.

Question 8: The fee for renting a flat on Green Street is \$ 10 per week or \$33 per month. How much can a person save if he or she pays for whole months instead of individual weeks in a year? Assuming there are 4 weeks in a month.

Question 9: 30% of students of an English class at BC Centre passed the IELTS exam in July. Among the failed students, 12 joined another course at BC, while the other 30 people did not. How many students were there in the English class above?

Question 10: A pair of Bitis shoes is estimated to have the production cost of \$8. The gross profit from 225,000 pairs of shoes sold in March is \$787,500. Calculate the average selling price.

• Q6: \$1,882 thousand
• Q7: 2.76 minutes
• Q8: \$84
• Q9: 60 students
• Q10: \$11.5

• brian

Can anyone explain Q6? Isn’t it 1.5M*12%*12%+1.5M?

• Karthick Jayakumara Sarma

Interest is calculated annually once in this case.

After the first year the interest we get = 1500 thousand * .12 = 180 thousand
Amount after first year = 1500 thousand + 180 thousand = 1680 thousand

Now the second year the interest we get will be = 1680 thousand * .12 = 202 thousand
Amount after second year = 1680 thousand + 202 thousand = 1882 thousand

OR

Use: The Compound Interest Equation

P = C (1 + r/n)^nt
where
P = future value
C = initial deposit
r = interest rate (expressed as a fraction: eg. 0.06)
n = # of times per year interest in compounded
t = number of years invested

P = 1500 thousand ( 1 + .12/1)^(1*2) = 1500 thousand * 1.2544 = 1882 thousand