Thursday, June 25, 2009

Math for an MBA, Part 1

A few days ago, someone asked me to give him a hand with the MBA entrance exam he was taking on Saturday morning. "You still remember what we learned in Math class," he told me, "and you obviously practice it a lot."

"Yeah, well... the math in an MBA course isn't that tough. I've helped out at least one other person with his MBA homework, and it didn't go any farther than algebra and number theory. It's high school stuff."

"I don't remember most of what we studied in high school. And it's the entrance exam... who knows what questions will come out? You know this better than I do, so give me a hand here."

I admit that I couldn't deny him the favor, and I suppose that part of me was itching to do some heavy-duty tutoring, so I said yes. Since we only had about one night's worth of time to go through the basics (us being working stiffs and all), I needed to gather my thoughts and imagine what kind of math was likely to come out in a bunch of MBA classes.

Eventually I came up with a list of eight questions for discussion, which I'll post here. I've come up with Math tests before (mostly for my siblings when they were in school), but this is the first time I've come up with a series of questions for an MBA applicant. If there was any point to this entire exercise, it lay in the matter of what was likely to come out, and what was not.

I eliminated such irritants as Calculus and Trigonometry right off the bat, for example. I felt that these were highly unlikely to come up in a Business Administration course, because they obviously require a lot of theoretical background and advanced thinking. Geometry was the next to go, because as basic as the math is, the concepts didn't apply to management principles. Probability and Combinatorics remained by the wayside as well, although those were among my favorites to explore.

After an hour's worth of thought, I had pared down my ideas into a limited set of concepts that felt as though they belonged in an MBA environment, and were fundamental enough to appear in an entrance exam. From these, I pulled together eight questions that my friend and I could discuss, and I now post them below for your viewing pleasure:

1. Three chickens can lay three eggs in three days. In how many days can you expect 18 chickens to lay 18 eggs?

2. You have exactly Php 35,000.00 in a bank account that gains 2% compound interest per annum. Assuming that you neither deposit nor withdraw any money from that account, how much will the account contain after two years?

3. I need an average score of 93 among my exams in order to pass one of my courses. So far, the grades that I got in five earlier exams were 90, 97, 87, 100, and 86. What is the minimum grade that I should get on the sixth (and final) exam in order to pass?

4. A bicyclist travels at a steady rate of 8 kilometers per hour. She leaves her house at 2:00pm and rides her bike to the supermarket. Halfway there, she realizes that she's forgotten her shopping list and returns home to get it, then sets out for the supermarket again. She arrives there at 4:30pm. What is the distance from her house to the supermarket?

5. A 200-liter mixture is comprised of 20% water, 30% salt, 10% sugar, 15% sand, and 25% gold. This mixture is left out in the sun for a few hours, after which all the water is found to have evaporated. What percentage of the resulting mixture is made up of gold?

6. A motorboat needs three hours to travel upstream, but it only needs one hour to travel downstream. When there is no current, the motorboat moves at a constant four kilometers per hour. What is the rate at which the river's current flows?

7. Three bowling balls and four frying pans weigh 54 pounds in total. Four bowling balls and one telephone weigh 54 pounds in total. Three telephones and eight frying pans also weigh 54 pounds in total. What is the total weight of one bowling ball, one frying pan, and one telephone?

8. Anthony, Beatrice and Charles win the lottery on a single ticket. They decide that they will each take 30% of the total, and then set aside the remaining 10% for future needs. After the money is deposited in their bank, however, each of the three friends arrives separately to claim their share. Anthony arrives first and withdraws 30% of the money. Beatrice arrives a few hours later, and withdraws 30% of what's left. Finally, Charles arrives some time later and withdraws 30% of what's left. At this point, only Php 205,800.00 is left in the account. How much did the three friends originally win in the lottery?

While it would be easy for me to just put up the answers to each of these and call it a day, that wouldn't be enough for a second article on this subject. I feel that there's a specific reason why I prepared each one of these questions... and that these reasons are worthwhile to discuss.

That said, those words will have to wait till tomorrow, I think. It's almost two in the morning at this time, and in the intervening hours, you're welcome to have a crack at these. I know that it's no Sudoku, but wouldn't you be interested to see how much you remember from your high school math?

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