Deciding whether or not to guess when you have 5 answers left is a perfect example of one of the key principles of mastering SAT math – step back. Take a moment to process the problem and be sure your set-up is correct, because if it isn’t, everything else will go wrong.

     There are problems that look hard, but if you step back and process the concepts, you discover they are actually quite easy. And, of course, the other trickster – the problem that looks easier than it actually is. One example of this is the classic problem about traveling 30 mph going to a location and 50 mph on your way home – you are asked for your average speed and there’s a temptation to just say to yourself “Hey, the average of 30 and 50 is 40. It’s 40, I’m done!” But if you step back from the problem and think, you will realise that it must have taken longer to get there (since you were going more slowly) than it took to get home, and that the extra traveling time must have dragged your average speed down. Dangitall, there are going to be extra steps.

     So, let’s now look at guessing at 5. You might run across people who advocate this and their logic is as follows:  Since you gain 1 point for every right answer and lose 1/4 for each wrong answer, you will get 1 right and 4 wrong out of every 5 questions. 1 – 4(1/4) = 0 so they declare that there is in fact ‘no penalty for guessing’ and proceed to try to convince you this is a safe plan. And admittedly, it looks good at first and triggers an eye-widening omg effect as the reader thinks they have stumbled upon some revelation.

     Now there are a lot of potential problems with this approach, but we won’t be going into all of them right now. On its own terms, a crucial mistake has already been made. So what went wrong? The proponents did not step back. Stop and think – does it make any sense that you can be 100% sure of getting exactly 1 right and 4 wrong? Of course not. You might get 0, 2, 3, 4, or 5 right. To properly assess the probability, we need to put it in context. Like a weighted average, we need to factor in the likelihood of every possible outcome for those 5 questions.

     We now redo the math, correctly, and discover that getting 1 right and 4 wrong, far from being a guaranteed starting point, actually only occurs less than half of the time (about 41%). The next most likely scenario (at about 33%)? You guessed it – getting all 5 wrong. 😯 Your odds of getting all 5 wrong are much greater than your odds of getting 2, 3, 4 or 5 combined.
 

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