Plugging In Answers

In this episode we're going to talk about a strategy you're probably familiar with from other standardize tests and that's plugging in answers. A few things to know for the SAT, first off definitely consider plugging in answers if you're stuck on an SAT problem. It doesn't work for every question but it's good to remember you have it in your arsenal and sometimes you can solve really hard questions just by plugging in the choices. In addition some of it will be obvious way to start but if you don't know where to start, C is a good place to start and I'll show you why momentarily and lastly, it's pretty cool, you don't have to try all five answer choices in order to find the right answer. So let's look at those three principles in more detail.
The strategy is not too complicated so let's just launch into an example. As I mentioned, you could start with C, it's not a bad place to start and you're just going to plug it in for X. So let's see what that would look like, we have nine to the power of one point five plus one, that's nine to the power of two point five and if you put it into your calculator, it's a very ugly number, 243. Now looking back at the problem, you can see it's supposed to be 27 so, it's a little too high, and at this point you could try either A or B, let's just jump over to A and try it. Nine to the point five plus one, that equals nine to the one point five and if you were to plug that into your calculator, that would be 27. So sure enough these match and the answer is A. And one thing I like about this is, a lot of people will look at this problem and say, "Oh my God I have no memory of how to deal with exponents, I've always struggled with them..." it's actually perhaps even simpler to do the cheatty way, plugging in the answers than doing it the right way, not that I don't recommend doing it the right way if you know what you're doing. Let's look at a more example of plugging in. 'A clothing store sells short-sleeved shirts for 15 dollars and long-sleeved shirts for 20 dollars. Jamal buys seven shirts and spends a 110 dollars. How many short-sleeved shirts does he buy?' So again C, the middle number is a good place to start and I don't think I explained why, if you find that you need a large number, you just move down, if you need a smaller number, you move up. So it should be the case that the most you have to do is two or if you want to be safe three. Like if you need a smaller number, you only have to try these three, if you need a larger number these three, so you save a lot of time that way.
Let's start with the middle one, so let's see. He buys seven shirts total and if four of them are short-sleeved, he's going to do four times the cost of short-sleeved and those are 15, so four times 15. And if four of them are short-sleeved, that leaves three that are going to be long-sleeved and those are 20. So let's see what that comes out to, four times 15 is 60 and three times 20 is 60, so that's going to be 120 total. Now it said he only spent 110 so first of all, this is wrong and in addition we're going to need a cheaper option. So what's going to be cheaper is to get more short-sleeved shirts at 15 dollars and fewer long-sleeved shirts, so more short-sleeved shirts is going to be going down the list. We automatically know that these are going to be too expensive 'cause we're going to be buying a lot of long-sleeved shirts. So let's go ahead and try E, it doesn't matter either will work. So six short-sleeved shirts at 15 each and that leaves one long-sleeved shirt that cost 20, six times 15 is 90 and this is 20, so 90 plus 20 is 110 and sure enough that's what we were looking for. So our answer is 'E'. Pretty simple so let's just wrap that up.
So the bottom line on plugging in is that you should definitely do the real math if you're comfortable with it, but if you are and over your head or you think you're doing it right and it keeps on turning out wrong, keep this in mind as a great strategy to use when you're feeling stuck. It can get you points when nothing else can. When you do use plugging in, also consider starting with 'C' that way, as I mentioned earlier, if you need smaller values you can move up the list, large values you can move down the list and by taking that approach, you won't have to plug in all the choices, just two or three at most. So the pretty efficient way to go and that's plugging in.