SAT Question Of The Day – estimating for hard geometry

From the official SAT site, here’s the Question of the Day for 9/25/14:


The answer is C.  Choose it (on the site, using the link above), and you will see the explanation involving a 30-60-90 triangle.  This is definitely the way to go, if you ‘remember how’.

The problem is, so many students will look at this question and say ‘I don’t remember how to do this’ and then skip it.  DON’T SKIP IT!!!!

Just ‘measure’ it!  OK, it’s not really measuring.  But consider this:  The diagram does NOT say ‘not drawn to scale’.  Therefore, we can assume it IS reasonably drawn to scale.   Look at the diagram.  Triangle ABO does look equilateral, O does look like the center of the circle, and the circle does look like a circle.  So, take the given measurement – that the sides of triangle ABO are 6 – and run with it!  Look at segment AB below.  It is 6 units long.  Measure it with your fingers and then use the same distance to guess at the length of segment BC.  Below, I’ve shown that 6 units, placed twice end-to-end along segment BC, is just a little longer than segment BC.  So, segment BC is shorter than 12.  If you do it carefully, you’d probably guess segment BC is about 10-11 units long.


Look at the choices.  Calculate decimal approximations for A, B, and C by typing the answers into your calculator.  Which one is closest to our estimate? C! And it’s the right answer! 




You’d be surprised how often you can really do this and get the right answer.  Follow me, and you’ll see lots of these!

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