6.2 SAT Math - Weird Functions

You may have seen some questions on the SAT exam that look really bizarre, with weird symbols or diamond-shapes or stars, something like this:

15. For all integers w and z, let w and z be defined as follows:

If w = 4 and z = 3, what is the value of w?6?z ?

                     -SAT Math Hint: If you see weird symbols or definitions in a question, it's secretly a function.  Treat that symbol just as you would the parentheses in an f(x) equation.  Just follow the directions they gave you step by step, working left to right.

So in the above problem, start by putting in 4 and 3 for w and z in the requested equation.  You should then have 4?6?3.  Then follow the directions.  If you have ? between two numbers, you're supposed to multiply, so 4•6 = 24.  But what about the next symbol?  If you have ? between two numbers you're supposed to divide, but what are your two numbers?  Remember, you should be working left to right.  That means you should take the number you just found (24) and divide that by 3, NOT 6 divided by 3.  Dividing 6 by 3 would be violating the rules of PEMDAS because you'd be using that number twice, once to multiply and once to divide.  So your answer for this one should be 8.

Example Problem

Let's try another one:

Linked Function Problems

Sometimes you will get one function, or even a picture or graph, that is used for more than one SAT question.  If you get one like this, just be sure to read carefully.  Usually  the two questions will both use the same definition of a function or chart, but have nothing to do with each other; occasionaly the second question will ask you something for which whatever you found in the first question might be useable.  Take a look:

Questions 13 and 14 refer to the following information.

13. What was the average number of tickets sold per day listed on the chart?
(A) 13 (B) 20 (C) 21 (D) 22 (E) 24

14. If tickets cost $4 each, what was the average dollar amount of tickets sold per day for the entire week?
(A) $48 (B) $50 (C) $67 (D) $84 (E) $336

Though you can use information you discovered on the first equation for the second, be careful!  You can only use the sum you found on the first equation – since the first equation asks for the average per day listed, and the second asks for the average per day for the entire week, you need to divide by 7 to find the average per day in the second equation instead of dividing by 4.  [The answers are (C) 21 and (A) 48.]