Easy PSAT/SAT Math strategy from your Austin tutor

There are several tips/strategies that everyone agrees help with the math section -- picking real numbers and using them to replace variables in abstract problems, for example.

One strategy that I haven't seen much talk about is using formulas.

It's so easy and basic -- and it's helped all of my students. Essentially, if you are stuck on a problem, you write down the formula and then just substitute information in.

Here's an example. (This is a very hard SAT math problem...)


The average of six numbers is 210. If all the numbers are distinct positive integers and one of the numbers is 24, what is the greatest possible value of one of the remaining five numbers?

This kind of question has freaked out a lot of students, but it's really, really easy to set up -- if you use the formula.

average = sum of terms divided by the number of terms

In this case, that would be

75 = [24+x+y+z+a+b]/6

Cross multiply and you get

450 = x+y+z+a+b+24




OK, this next part requires a little thinking:

In order to simplify, first we subtract 24 from both sides and get

426 =x+y+z+a+b

(This is a step that most students miss if they haven't used the formula).

In order to figure out what the GREATEST possible value of one of those variables is, we have to think for a second. For one number to be really big, the rest would have to be small. And if all the numbers are distinct, positive integers, then the smallest they could be is 1, 2, 3, and 4. (Remember each number has to be distinct -- otherwise, we could just use 1,1,1,1).

So if x =1, y=2, z=3, and a=4,

then

426 =1+2+3+4+b

and b = 416.

There's your answer -- that's the biggest possible number that could make the equation true...