<p>Getting a question right is +1, losing a point is -1/4, and there are 5 choices.</p>
<p>If you can eliminate one choice that you KNOW is wrong with 100% certainty, then the expected point gain from a completely random choice among the other four is the expected value of this event. The expected value here is the probability of a certain event times the value of that event:</p>
<p>Probability of gain * value of gain + Probability of loss * value of loss = expected gain or loss</p>
<p>Or</p>
<p>(1/4)<em>(1) + (3/4)</em>(-1/4) = 1/4 - 3/16 = 4/16 - 3/16 = 1/16 = 0.0625</p>
<p>In other words, if you can eliminate one answer, randomly guessing will, on average, result in a point gain (albeit a small one, it's still in your favor to guess. The idea is to maximize your score, so you have no reason not to use this strategy). The more you can do this, the better, obviously. However, this is assuming a RANDOM guess among the remaining four. Educated guesses are even better!</p>
<p>If you can't eliminate any answers, your average gain is: 0
If you can eliminate 1 answers, your average gain is: 0.0625
If you can eliminate 2 answers, your average gain is: 0.1666
If you can eliminate 3 answers, your average gain is: 0.375
If you can eliminate 4 answers, your average gain is: 1</p>
<p>This means that guessing at least won't, on average, result in a loss. However, there is a time constraint. You're better off leaving something blank and moving on so you can answer the other questions, and then coming back to the blank questions so you can spend more time on them. Some questions you'll get immediately, and others might take you many minutes. Spend time wisely and move on if you're wasting too much time on one question. It should feel obvious to you when this is happening... when you start to wonder "Crap there's so many more questions in this section" you should move on and come back to that question later.</p>
<p>I can speak from experience that this tactic is effective. My highest scores were achieved when I guessed on things I did not know. Leaving things blank is usually a bad idea, especially if you can eliminate a choice or two.</p>
<p>SUMMARY FOR PEOPLE WHO DON'T WANT TO READ:
-If you can eliminate at least one answer choice with 100% certainty, guess among the rest if you have to! It's in your favor!
-Leave things blank if you are wasting too much time on them and at least try to reach the last question. Use your remaining time by going back and answering the questions you left blank.</p>