Averages in SAT Word Problems

In math class, you probably learned a formula to find the average of a series of numbers. You still have to know that formula, but instead of applying it robotically to a bunch of similar questions, you have to first figure out how to crack the problem. That is, you are not going have all the numbers neatly arranged waiting for you to plug them into the equation that will cough up the answer. Below are several average problems. Note how they are all word problems – this is how almost all of the average problems will be on the SAT. And by the way, in some cases (though not in all!) you will need the formula: Average = Total/Number of Elements. 1.  Mike scored 78, 77, and 82 on his first three algebra tests. If he wants to average 80, what is the least he can score on his fourth test? (A)   80 (B)   83 (C)   84 (D) 89 (E)   90 Solution: This is the SAT! Don’t take the long road find the quick solution, and eliminate wrong answer choices when possible. So instead of plugging these numbers into the formula (yeah, you can tell by now that I’m not a fan of the formula!), let’s find a short cut. Notice that Mike has scored 78 (which is 2 less 80), 77 (which is 3 less than 80) and 82 (which is 2 more than 80). Let’s put this information together: . So we are 3 lower than 80. To balance things out – remember we are looking for an average of 80 – the next test score has to be three more than 80: 83. (B). Let’s not forget smart elimination: 80 – too low. 89, 90 too high. Even if you have no idea where to go from there you still have a 50/50 chance. 2. w, x, y, and z are distinct positive integers. If , what is the greatest possible value of w? (A)   13 (B)   25 (C)   26 (D) 94 (E)   97 Solution: If you follow the formula and reason that the average is 25 (100/4 = 25),   then you will fall for the SAT’s trap. 25 is not the answer. Ill be adding in a video explanation soon to explain why (as well as give you the answer!), so stay tuned!