SAT Video Friday – An Equilateral Nightmare

Oh, the dread ratio. Especially on geometry questions! How dare they not give us numbers!? Actually, sometimes ratios can make things easier. The same goes for percents. If you are only looking for the percent by which one thing is bigger than another, the actual numbers don’t matter. Just choose easy-to-work-with number(s).

The ratio of the radii of two circle is 4:5. How much percent less is the area of the smaller circle?

Technically, we don’t even need to find the area of the circle. Just square each radii, 4^2 = 16 and 5^2 = 25. How much percent less is 25 than 16? Viola! It’s 36% less.

You might be wondering how that is the case, but notice how the π would cancel out in both cases. Therefore, we just need to figure out on what makes the two circles different: the length of their radii.

Okay, maybe not too bad. So, here’s one that’s slightly rougher. Okay, a lot rougher. Do you got what it takes? (see video).

If you have any questions or comments about this, be sure to leave them below! 🙂



  • Chris Lele

    Chris Lele is the Principal Curriculum Manager (and vocabulary wizard) at Magoosh. Chris graduated from UCLA with a BA in Psychology and has 20 years of experience in the test prep industry. He's been quoted as a subject expert in many publications, including US News, GMAC, and Business Because. In his time at Magoosh, Chris has taught countless students how to tackle the GRE, GMAT, SAT, ACT, MCAT (CARS), and LSAT exams with confidence. Some of his students have even gone on to get near-perfect scores. You can find Chris on YouTube, LinkedIn, Twitter and Facebook!

By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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