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It’s Pi Day, March 14th (3.14)!

In celebration, I want to share a quick mindset about Pi that I think you’ll find really helpful. I had a student ask me recently how to “solve for pi” in GMAT geometry questions. We went back and forth and it turns out she was really confused about the concept of Pi.

You may be in the same boat.

What helped her was when I finally explained that Pi is just a number. You almost always see it written on the GMAT as the Greek letter that looks like this (∏), but it’s just a number. Pi can be approximated as 3.14, which you can just sort of mentally round down to 3. But it’s just a number.

(Note: If you’re curious about where Pi comes from, here’s a short video that breaks it down pretty well).

The reason I think this mindset is helpful is for challenging geometry questions on the GMAT, like this one:

At first this question can look intimidating. Even after learning foundational rules for circles, as taught in our “GMAT Geometry – Circles” course, it can still be a lot to handle.

Elsewhere in my Full GMAT Prep Course I teach a cool strategy for GMAT geometry questions called “eyeballing.” Let me introduce it to you here. The idea is pretty simple. Whenever you have a geometric figure that’s drawn to scale on a GMAT problem solving question, see if you can use anything given in the figure (the measure of an angle, the length of a side, etc.) to approximate the missing element and get a right answer without having to do the traditional geometry. It’s not always possible, but you’d be surprised at how often it is.

Applying the eyeball technique to this example, you have a reference point of 18, right? In other words, you’re told that the diameter of that circle is 18. So use that to your advantage! If you were forced to guess — that is, if you were to “eyeball” and approximate the length of PQ just by looking at it — you’d probably say that it’s about a third as long as the diameter 18, which would make it about 6. And you’d be right! Minor arc PQ does have a length of about 6.

But wait… none of the answer choices look like “about 6.” They all have a bunch of those weird ∏ symbols in them. So what to do?

This is where you need remember what I said earlier: Pi is just a number. It approximates to 3.14, so what if you swap out ∏ for 3.14 in all of those answer choices? Sure enough, answer choice A equals about 6 when you substitute 3.14 for ∏, and that is in fact the right answer. Pretty cool, eh?

There are a lot of ways to get to right answers on test day, and just remember that you don’t always have to take a traditional approach to get there. Hopefully this example — and a better understanding of Pi — has opened your eyes to that reality.

Questions? Please leave them below. Now get back to celebrating this most important holiday, Pi Day! Oh, and here’s one last Pi Day cartoon to leave a smile on your face: