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These are examples of simple word problems within business contexts. You may go back to the main Consulting Math 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% mark-up on milk bought from Fonterra. How much percent of the original price has been increased?

Question 2: The Leaning Tower of Pisa is a famous tourist attraction in Italy. Tourists pay $8 EUR per visit; 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 to break even?

Question 3: When combining a mixture for a special kind of building material, 1/3 of the mixture is sand, 3/5 is water and the rest is 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 the products are Vespa’s. If it 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; or $90 for a wholesale carton of 5 boxes. 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?


Hurdle 1 – Answers

  • Q1: 75%
  • Q2: 37,500 adult visits
  • Q3: 180 kg
  • Q4: 84 in total
  • Q5: 82,500 boxes


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 dollar units of thousands).

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 for 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. What are the savings a person generates if paying 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 certain pair of Bitis shoes is estimated to have the production cost of $8. The gross profit of 225,000 pairs of shoes sold in March is $787,500. Calculate the average selling price.


Hurdle 2 – Answers

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

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  • polludoemiliano

    Asnwer Q5 I thing is wrong. 65% 2,700,000 = 1,755,000 , then; 1,755,000/18 because 90/5=18 price of every box, results in 97,500 boxes.

    • Adriana

      I think the answer is correct. As 45% of the revenue comes from retail sales, it should be 55% coming from wholesales, not 65% rite?

  • SK

    Question: Can someone explain the Q1 (Hurdle 1) answer of 75% in detail i.e: how do you get to this conclusion. Thanks.

    • Jose Manuel

      It’s because the 25% markup of the 2nd stage also adds a 25% of the first markup, which was a 40%. So if the original price was $1, then it would be: $1*(1 + 40%)= $1,4 at the first markup, and then for the second markup: $1,4*(1 + 25%) = ($1 * 1,25 + $0,40 *1,25) = $1,75 which would be a 75% markup of the original price. Hope it helps!

      • SK

        Thank you very much Jose, appreciate it. So in the second stage a markup of 25% on 40% is added as well besides the 25% which is the second stage markup, am I right?

  • Alfie

    Can someone please explain where the 33 is derived in order to arrive at 76% (25/33).Thanks

    • Su Chen Lim

      I’m assuming you are asking about question1.

      Fonterra is selling at 140% of the original price
      The grocery store is selling at another 25% markup of Fonterra’s 140%

      140% divided by 0.25= 35%
      The grocery store is selling at 140% + 35% = 175%. That is 75% increased of the original price.

  • Hala

    Can someone show how Q5 was solve. no matter which was I do it, i do not get this number~!!!

    • Su Chen Lim

      Retail= $18.50/box
      Wholesale= $90/5 boxes = $18/box

      55% of target sales are from wholesale= 0.55 x $2,700,000 = $1,485,000
      $1,485,000 divided by $18/box= 82,500 boxes