Explanation for Question 7 From the Math (No Calc) Section on the 2017 May Sat
Let's consider a question. Seven question seven says if X plus 2 Y equals 13, an X minus Y equals two, 3 what is the value of X squared minus Y squared? 4 So they want the value of this right here. 5 And they only tell us what this and this equals. 6 We have to think about for this type of question. 7 They're never going to give us something that we can't solve. 8 So we want to figure out how they got two X squared minus Y 9 squared. If we look at the two things they did give us X plus 10 Y and X minus Y, we can see that 11 somehow we do something together to these two, 12 we'll get X squared minus Y squared. What that is is if you multiply 13 them together. So if you get X plus Y and multiply it times 14 X minus Y, before you got first 15 X squared, outer minus 16 X, Y inner plus X, 17 Y, and then minus Y squared for the last we 18 combine like terms, or we simplify these to cross out, 19 we get X squared minus Y squared. 20 So we see that to get to X squared minus Y squared. 21 All we had to do was take X plus Y times X 22 minus Y. Now we know that X plus Y is 23 equal to 13, and we know that X minus Y is equal to 24 two, so we can substitute those there. 25 We're still multiplying them. And that equals 26. 26 So our answer is B.