Solve GRE Quant problems using no math

What is \(\pi\)? Yes, I know it’s \(3.14159 \ldots\). But what does it represent? What’s the concept behind the number and why is it so useful? If you know the answer to these questions, you may very well be able to abuse the concept of \(\pi\) and solve the following question in under 5 seconds:

Quantitative Comparison

A: The diameter of a circle A

B: An arch segment of circle A with a central angle of 120°

What’s bigger? Are they the same? Or is it simply impossible to tell?

I have simplified a GRE question in order to illustrate the power of understanding exactly what \(\pi\) is.

\(\pi\) simply represents how many times the diameter of a circle fits into its own circumference. That is, a circle can fit its diameter \(3.14159\) times into its circumference.

Now that you know the concept behind \(\pi\), you should be able to answer the question I presented above.

The answer is of course, B. The arch from option B can only fit in the circumference 3 times. Meanwhile, the diameter can fit \(\pi\) times. The arch can fit less times than the diameter, so it must be longer.

Now, you could probably solve this question picking a radius for the circle, calculating the length the circumference of the circle and then comparing both quantities, but by simply knowing what \(\pi\) represents, you can solve this problem in under 10 seconds. Now, granted, the original problem had some extra nuance, but it boiled down to exactly this same problem. Solve time for the original problem would only go up by a few seconds.

On the GRE, time is just precious, and having a good grasp of basic concepts can go a long way.

Now, if you think about it, you didn’t really do any math to solve this problem, if you just use the concepts approach. That’s the beauty of it. It’s way more efficient; you get to save time and energy. I really encourage people to try to tackle as many questions as possible using only concepts.