The profit and loss problem form or P&L problem form that this problem fits into
is one that has very strong DSM’s into mathematics. Here we are tempted to do the math in part because that’s so easy, it’s so available to us and this is characteristic of a mid-level arithmetic problem where there’s some shifts and shimmies but overall it’s a fairly straightforward problem that utilizes no more than the four basic operations. So on the one hand this is pre-algebra or even sort of grade school math, on the other this makes the solution path much
So of course we can follow the math. We can add up all the costs, five thousand plus two dollars, times twenty thousand and then contrast that with the revenue that comes in which is
twelve times twenty thousand. But thenwe’re left with the ugly division
problem that brings us to the profit per t-shirt, and this is where the GMAT
So instead of handling this in aggregate it’s strongly preferable to handle it with a higher level solution path. Let’s take a look at a few:
One way to do this is to distribute the fixed cost over the cost per t-shirt and this is actually a lot easier than it seems, twenty thousand t-shirts, five thousand dollars, five over twenty is one-quarter, therefore it costs one-quarter per t-shirt in addition to the two dollars in variable cost, and so twelve minus two is equal to ten dollars, minus one quarter is equal to nine dollars and
seventy-fivecents. It’s sitting right there for us in literally a moment.
We can also use a graphic equalization method in order to get to the same conclusion. If the numbers were more complicated, understanding that that shift is one-quarter down, that is the fixed cost is one-quarter down then we know we’re looking for something that ends in a seventy-five cents. That allows us to eliminate all the answer choices or at least all the answer choices that don’t end in 0.75 and then we can use scale to determine that 9.75 is the correct answer.
There are more complicated versions of this problem form, in particular I’d encourage you to explore being told that the t-shirt company is breaking even and then determining the amount of variable costs or fixed cost that’s there or even the production run. Similarly, you can be given a target profit or loss, the break-even just being the zero, so it’s a bit easier and have to reverse engineer the relationships.
Once again, this doesn’t have to be done algebraically as you begin to appreciate the subtlety of the ratio between costs production run and total P&L all of these problems should be simplified and should be very straightforward.
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