Every student knows how to find his/her test average. If you’ve taken 5 tests, just add them up and divide by 5 to find the average, or mean. Such a straightforward problem simply won’t appear on an SAT. Instead, one of the best SAT strategies involves how to deal with the “backwards” situation.

Consider this problem: “Three numbers have an average of 50. Two of these numbers have an average of 40. What is the third number?” If three numbers have an average of 50, what must their sum have been? Of course, this sum must have been 3 times 50, or 150. You should train yourself to jot down 150 even before reading the second sentence. This is always the key to such a problem on averages. Use the same method with the second sentence. If two numbers have an average of 40, their sum must have been 2 times 40, or 80. Now, to find the missing third number, just subtract 150 minus 80, yielding 70.

This strategy can be used in a very common type of problem on averages. “On her first 5 math tests, a girl has had test scores of 88, 93, 84, 87 and 89. What must she score on the sixth test in order to pull herself up to a 90 average?” Employing this method, we ask ourselves how many total points must she have after 6 tests in order to have a 90 average. Simply multiply 6 times 90, or 540 points. Adding up her first 5 test scores we see that she had accumulated 441 points. Just subtract 540 minus 441 telling us that she better do some serious studying since she needs 99 points on this sixth test.

Approximately 30% of the SAT math questions concern arithmetic concepts – no algebra or geometry involved. One of the favorite arithmetic topics is averages and this method is often used once or twice on every SAT. I often tell SAT Prep Course students that if the first sentence of the first math problem of their SAT says “Five numbers have an average of 8,” they should immediately write 40 (5 times 8 ) on their paper and this will surely lead to an easy solution.

Tags: SAT Math, SAT Prep, SAT Preparation, Test Prep