## Fun with the PSAT

My students were recently making fun of some of the math problems on the **PSAT**. Apparently, one of the questions went something like this:

After having a bit of a laugh about it, we decided to try to help the PSAT exam writers make a more interesting question. Here is our revision:

Creating this new question was far more interesting than solving the original! And thanks to **Wolfram|Alpha**, we can easily check the answer.

Despite our complaints about the quality of the PSAT, we all know that it couldn’t be nearly as bad as a New York State Regents exam.

*Click here to see more in Appreciation.*

Could they generalize the problem by replacing 7 with n? What would the answer choices look like?

In a similar vein, consider the following metric: how do quantify how much a number LOOKS like it’s closest to another number, without actually computing it? I mean, obviously 7.01 looks closer to seven than any of the other solutions, but what’s interesting here is the second variable of it possibly not being the closest solution when considered with the other five. For example, nine is pretty close to seven. But maybe all the answers above are around eight. Most people would still argue, however, that nine appears to be closer, because it takes less time to confirm this than any of the above five answer choices. So, in a way, I’ve made a metric out of a simplified P vs. NP problem.