Case1: I'm assuming that the situation is Capital One is launching a credit card with the department store. I'm assuming (I rephrased the questions) given data the questions are to 1) What is the profit for Capital One; 2) What is the break even point?; 3) What will be the impact of progressive opening bonus based on accounts opened?; 4) How does the profit curve look like?; 5) What is the maximum number of accounts and price? My Answer: Hmm... These are interesting questions. Since I don't really know the business structure of credit cards and department stores is I would first ask what the nature of the business is and also to ask definitions to terminology that might be alien to me. For example I would ask what is the opening bonus is. Is the interest cost cost to customers or department stores or Capital One? Then once I identified the problem type I would apply a framework. For example to answer question 1) I would apply the profitability framework. I'm assuming linear profit function. Profit can be segmented into total revenue and total cost. Revenue then can be segmented into revenue's per unit and number of unit's sold. I would ask the information about the revenue's per unit and the number of unit's sold. On the cost we can segment it into cost per unit and number of units sold. These also can be segmented into fixed cost and variable cost. I also would ask information about it also. Given these information it is pretty much a straight forward elementary mathematics. The equation might have several variables depending on what the final revenue and cost structure may be. To answer question 2) we know the profit function from answering question 1). Thus we need to know when profit equals zero. If the unknown is Q(=# of units) then solve for Q when profit is nil. An algebra problem. To answer question 3) I would first question what the relationship is for the quantity (or volume). For example for an increment in accounts opened what is the opening bonus? Profit will vary according to this quantity. You can see that profit will vary because the profit equation will NOT BE linear. To answer question 4) if you the relationship of the profit curve given the answer to question 3) you will be able to draw the profit curve on a plane. As quantity (# accounts opened) varies the profit will vary since it is not a constant. To answer question 5) the profit function should be a quadratic function and to take its derivative with respect to price and set it equal to zero, you should be able to find the maximum price. Once this is found you can plug it back to the quantity function and find the maximum quantity. If someone finds errors in my answer please post comments.

Case2: This is an interesting case. I would ask the interviewer on where to start. If the interviewer does not provide a starting point then I would apply a general framework. In order to answer the first question of the pros and cons (risk) of the particular situation I would ask the interviewer questions on why this situation occurred and whether find out whether this situation is firm specific or industry wide. In particular, who is the customer? I want to find the segment size, growth rates and market share for different types of customers. I also would ask information about the current year to historical numbers regarding customer segment size, growth rates and market share in order to identify demand trends. Other questions would be the needs of the each customer segments, price they are willing to pay etc. I would like at the company and its capabilities, cost structure and so forth. Hopefully by identifying key trends we are able to make a score card, then count the pros and cons and make a statement of whether there are advantages and what are the caveats. Calculating the profitability I would use the profitability framework where profit = total revenue - total cost and break down the segments there and ask information regarding to the each revenue/cost segments. Once those are known calculating profit is straight forward. For the next question, I would evaluate each options separately. Offering free months to increase quantity demand paribus ceteris will have effects to the profit function. Then find the maximum profit. I would also do the same analysis for option number 2. If maximum profit for option1 is greater than option2 then assuming the CEO is rational option1 would be better way to increase profit and vice versa. For the last question, I'm not sure what the original proposal is but assuming that we are conducting a break even point analysis regarding option1 and option2 we may look at this as a system of equations. Set option1 profit equation to nil and likewise to option2 profit function. Since both equations are equal to zero the equations are equal to each other. Then we can solve for the unknown variable, quantity, that would satisfy both equations. This is the point where both curves cross. If someone finds errors in my answer please post comments.

What topics are covered during the screening maths?Do you recall the 5 math questions?