Explain a General Math Strategy

Question

In the Math workbook for the SAT, one strategy is Plug in Numbers to Find a Pattern, they only give one example and it does not really help me understand the concept. I have to explain it to the rest of my class but I don't even understand it myself.  The example uses "When a positive integer k is divided by 5, the remainder is 3. What is the remainder when 3k is divided by 5?"

Answer 1

It is not necessary to plug in numbers and find a pattern.  When I teach this I tell my students that the simplest number satisfying the given condition is 3.  3 is just one number from the set of values that would satisfy the condition.  All of the values in the set that give you a remainder of 3 have to give you the same value when 3k is divided by 5 So just use 3.  3k = 9 and 9/5 gives a remainder of 4 which is the answer.  The proof is irrelevant since SAT only requires the correct answer.

Answer 2

I'm not sure if the book wants you to find a pattern. I think they just want you the guess and check the numbers. 

 

This would probably be an option if you're pressed for time and can't reason it out.