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Chris Lele

SAT Video Friday: Math Challenge Question – Number of Numbers

Don’t take the long way

The SAT is testing how you think, not how fast you can write. Yet students often do a question the long way, writing out as many numbers as possible. Instead, rely on logic and formulas, when applicable.

Let’s take a look at the following question:

How many numbers less than 100 are not divisible by 3?

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Instead of writing out all the numbers and then crossing out the ones that are not divisible by 3, find a way to identify the numbers that are divisible by 3. The best way to do this is by finding the highest number less than 100 that is divisible by 3. 99 should jump out at you.

Since every third number up to 99 is divisible by 3, we can divide 99 by 3 (giving us 33) to find the number of numbers less than 100 that ARE divisible by 3. To answer the question subtract 33 from 99 (99 – 33 = 66). Remember: do not include 100, since the question asks for how many numbers less than 100.

Now, let try a harder question, the SAT Challenge Question.

The Challenge Question

How many digits less than 1,000 are divisible by 3 and 5, but not by 7?


After you’ve watched the video for the explanation, leave me any comments or questions you have 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 10 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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