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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! 🙂

##### About Chris Lele

Chris Lele is the GRE and SAT Curriculum Manager (and vocabulary wizard) at Magoosh Online Test Prep. In his time at Magoosh, he has inspired countless students across the globe, turning what is otherwise a daunting experience into an opportunity for learning, growth, and fun. Some of his students have even gone on to get near perfect scores. Chris is also very popular on the internet. His GRE channel on YouTube has over 8 million views.

You can read Chris's awesome blog posts on the Magoosh GRE blog and High School blog!

You can follow him on Twitter and Facebook!

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