This question is a beast, and arguably one of the rare GMAT questions that it is nearly impossible to solve in under two minutes.
In the figure above, point O is the center of the circle and OC=AC=AB. What is the value of X?
Why is that the case?
There are a few reasons.
1) The problem relies on a little-used geometric theorem: in short, if we know that a certain line forms the diameter of the circle, any point tangent to the edge of the circle, if connected with straight lines, creates a Right Angle.
Just look at the picture and don’t read the words. It’ll be easier.
2) When the diagram is complete, you’ll find that there are three different variables required to solve. Cleverly—any by that I mean “annoyingly”—if you don’t head down exactly the right path when answering the question, you’ll go in circles forever, or at the very least, take five minutes to solve the question.
3) Given the answer choices, there’s no real way to backsolve or even eliminate ridiculous answer choices.
Basically, we’re screwed.
In a very un-GMAT way, it means we’re going to have to actually do the heavy lifting on this one.
Is there a simpler way to solve the question?
Look, buddy, if you got one, then show me because I haven’t seen one.
Check out the video for the process. And sign up for the mailing list if you like it. It’s up there. At the top. And the right.
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p.s. Are there any other difficult questions you’d like to see answered? Contact us and we’ll send ‘em out.
p.p.s. Seriously, if you know a better way than this, tell me!