How do you approach problems that are seemingly ridiculous?

Test Preparation SAT Preparation
12

<p>Usually these sorts of ‘ridiculous’ problems involve patterns or sequences, but I recently encountered this geometry problem that fazed me because it didn’t seem to have all necessary information:</p>

<p><a href=“http://i44.■■■■■■■.com/27yqwoz.jpg[/url]”>http://i44.■■■■■■■.com/27yqwoz.jpg&lt;/a&gt;&lt;/p&gt;

<p>If triangle ABCD shown above has an area of 24, what is the probability that a randomly chosen point that lies in ABCD will be in the shaded region?
A. 1/3
B. 1/2
C. 2/3
D. 1
E. It cannot be determined from the information given.</p>

<p>I guessed 1/2, which is correct, according to my book. I chose it for two reasons:

  1. The answer is never “It cannot be determined from the information given.”
  2. I just imagined a string connected to points A and B, and thought that since it could cut the triangle in half if it touched point B or C, it would be able to do that no matter which point on BC it touched.</p>

<p>However, I don’t really trust my logic because I didn’t incorporate the area. Could anyone explain how to solve this the way College Board wants you to?</p>