Consulting Case Interview Fast Math Drills 4

Posted on January 5, 2011 by ibh

Feel nervous about your number-crunching math skills? Try to improve by practicing our Consulting Case Interview Fast Math Drills quiz. Note: No calculator is allowed during the quiz, and you may use a pencil and a piece of scratch paper. Try your best to answer all 10 questions in 10 minutes. The correct answers will be shown at the end of the quiz.

1. At Bain & Company's Boston office Christmas party, 1/2 in attendance are Bain employees. Employees' spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not Bain employees or employee spouses?






2. After having to pay increased income taxes this year, Edmond decided to sell his 2010 BMW X5. Edmond bought the car for $49,500, but he sold it for a 20% loss. What did Edmond sell the car for?






3. If Carlos Solis can do a project in 4 days that Mike Delfino can do in 6 days and Tom Scavo can do in 3 days, how long would the project take if Carlos, Mike, and Tom worked together to complete it?






4. At MIT Sloan School of Management, some courses contribute more towards an overall GPA than other courses. For example, Financial Accounting is worth 4 points; Microeconomics is worth 3 points; Macroeconomics is worth 2 points; and Investments is worth 3 points. The values of the grade letters are as follows, A=4, B=3, C=2, D=1, F=0. What is the GPA of a first-year MBA student who just got a “C” in Financial Accounting, a “B” in Microeconomics, an “A” in Macroeconomics, and a “B” in Investments in his first semester.






5. A Chevy car dealer in San Diego, CA sells a 2011 Chevy Equinox Crossover SUV for $39,000, which represents a 25% profit over the cost. What was the cost of the 2011 Equinox Crossover SUV to the car dealer?






6. On average Americans pay 20% more than Europeans for medications. They also consume 20% fewer pills than Europeans. How much does an American pay for a pill that a European pays $1.00 for?






7. A small Subway in Seattle, WA sells an average of 238 sandwiches per day at a price of $5.95. The total cost to make a sandwich is $3.20. How much profit does the Seattle Subway make in a week on sandwiches?






8. This year investment bank Morgan Stanley (NYSE: MS)'s CEO received $750,000 in salary, unchanged from last year. His bonus however, was $13.75 million, up from $10.25 million of last year. What kind of a percent increase did he get with his bonus? His salary makes up what percentage of his total compensation this year?






9. An MBA student from the Wharton Business School of the University of Pennsylvania just got a starting salary of $110,000 with McKinsey. His signing bonus was $15,000. A PhD student from Department of Bioengineering got a starting salary of $120,000 with BCG. Her signing bonus was $20,000. Each then promptly spent $1,500 on a first-class flight to Las Vegas and $1,200 on a ridiculous night of partying. What percentage of the MBA's new income was just consumed? What about the PhD student's?






10. I have 0.2 liters of Glenlivet 21 Year Old left in my apartment and 1.5 liters of Captain Morgan. A 750ml bottle of the Glenlivet 21 Year Old costs $120.00, a 1.75L bottle of Captain Morgan costs $38.00. Is my remaining Glenlivet worth more than my Captain Morgan?







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10 Responses to Consulting Case Interview Fast Math Drills 4

  1. Tyler says:
    October 8, 2012 at 5:39 pm

    Eh, it still skips parts of my response… I guess you’ll just have to try to figure out the bits of the hints that are missing. I’m not wasting my time re-typing the hint a third time.

    Reply
  2. VK says:
    April 5, 2012 at 11:39 am

    I agree with other comments on #6. The question needs to be rephrased. Good set otherwise. Thanks!

    Reply
  3. dcc says:
    December 20, 2011 at 1:02 pm

    Yeah, I don’t get #6. The wording made it seem like the difference in consumption was irrelevant.

    Reply
  4. Donna Yule says:
    November 12, 2011 at 10:36 pm

    Thank you for allowing me to take this math test, as I have not been to school for many years and after doing two of the test and going over the correct answers was challenging, we did not take math as it is today, but I found it quite interested and being able to figure the answer out. I will continue to take further test, and see if I am able to improve as in my day I was quite good in math, of course it was just muliplication, subtract, add and divide. And was able to obtain a better grade than what I am doing with your test. Thank you again, will let you know how I progress. So far I am only 4 – 10

    Reply
  5. Medved says:
    September 29, 2011 at 2:10 am

    I don’t understand #4.. why is the formula (2*4 + 3*3 + 4*2 + 3*3) / (4+3+2+3) ? What does the (4+3+2+3) represent – the combined weights? I need to learn how to weighted average problems, I guess.

    Q#1. Is incorrect from a logical standpoint. The employess’ wives could simultaneously be employees of Bain, meaning there is possible overlap between the 50% and 33% groups. Meaning, you cannot cleanly deduce that the people who are not Bain employees or spouses necessarily comprise the remaining 16.7%.

    Q#6. Seems to contain an error, IMO. When you say “how much does an American pay for a pill that a European pays $1.00 for?”, you ask for ONLY the difference in price per pill, WITHOUT factoring in the difference in average pill consumption. The American is not buying 20% less of the same pill, while paying 20% more for it.

    I found questions 8, 9, and 10 completely impossible to do in a 1-min timespan. At least not with precision – and the possible answers are too close to each other to allow estimation. I dare anyone to calculate 13.75/10.25 – 1 = 1.34-1 = 0.34 = 34%, 0.75/(13.75+0.75) = 0.75/14.50 = 0.05 = 5% by hand WITH PRECISION in under a minute – and that’s even without time needed to read the question and put it into the perfect formula presented here.

    This is beyond most anything on the GMAT from my memory, and there you have 1.5-2 mins for each Q.

    Reply
    • Xingjian says:
      September 29, 2011 at 1:52 pm

      Not to brag, but with a pencil and a piece of scratch paper, I can get 13.75/10.25 – 1 = 1.34-1 = 0.34 = 34%, 0.75/(13.75+0.75) = 0.75/14.50 = 0.05 = 5% right easily within 60 seconds. Students from China (and India maybe) are trained to solve hundreds of math problems ever since grade school. It indeed was a lot of work as I recall, but it paid off.

      Reply
      • D says:
        March 12, 2012 at 11:31 am

        Xingjian, How do you calculate 13.75/10.25 so fast (question 8)? The same for 27/1.250 and 27/1.400 (question 9)? And 0.2/0.75 and 1.5/1.75 (question 10)? What is it you do in your head? I just stare at the numbers, estimating but not calculating. What are the tricks to calculate simple but precise?

        Reply
        • Tyler says:
          October 8, 2012 at 5:34 pm

          Not to brag even more, but I did 8, 9 and 10 in less than 30 seconds each, without using a calculator. I made scratches for number 8 (wrote down 4 different numbers strictly to keep track of them) and didn’t use any aid whatsoever for 9 or 10. It just takes a lot of practice.

          I’ll admit however that I got 8 wrong, although that was a function of the actual correct answer not being present rather than my miscalculation. It said 5.0%, whereas the calculation comes out to 5.17%, which clearly doesn’t round to 5.0%. I deduced that 5.0% means the value must be 1/20th of total salary, however 750K x 20 = 750K x 4 x 5 = 3M x 5 = 15M > 14.5M. So I immediately knew the value was higher than 5.0% and since I knew from the other part of the question that the raise was about 34% (was just over 1/3), the only remaining option was the 5.5% option.

          As for hints, the above explains how I approached 8.
          For 9:
          Salary = 125K
          Consumption = 2.7
          Answer ~ 2.7% /1.25 = 2.2

          Salary = 140K
          Answer ~ 2.7%/1.4 = 1.9
          Although the math actually wasn’t necessary at all. We know 125K $160/L ( = 120 * 1/3 + 120)
          0.2 * 160 = 32
          1.5/1.75 reduces to 6/7
          6/7 * 38 = 6/7 * 35 + 6/7 * 3 = 30 + 18/7 = 32 + 4/7 > 32
          Captain Morgan is worth more.

          Reply
          • Tyler says:
            October 8, 2012 at 5:38 pm

            Oh, it looks like part of my answer was cut off.
            Where it says “Although the math actually wasn’t necessary at all. We know 125K” that should have continued as ” 32
            Captain Morgan is worth more.

  6. Jessica says:
    September 24, 2011 at 5:36 pm

    This one is easy! I finished all 10 questions in 8 mins and got 9/10 right.

    Reply

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