I’m a parent helping my daughter, I’ll post some math questions that she wasn’t able to solve. Here is the first question:
question 1- On a square gameboard that is divided into n rows of n squares each, k of these squares lie along the boundary of the gameboard. Which of the following is a possible value for k? The answer is 52 but I don’t know College Board got this.
The boundary comprises four corner squares and four stripes of n squares each:
k = 4 + 4n = 4 (1 + n),
k is a multiple of 4, and 52 is the only fitting snswer.
Aren’t you counting the corner squares twice? I think the formula should be 4(n-1) = k (which would be 52 for n = 14). Your reasoning (find the value divisible by 4) is accurate.
@AboutTheSame
You are right about k = 4(n-1), but my mistake wasn’t counting the corner squares twice: somehow I forgot this question and thought that a border was added to the gameboard.
The idea still works though:
Four corner squares plus the remaining (n-2) squares along each of the four edges of the gameboard totals
k = 4 + 4(n-2) = 4(n-1).
Another way to crack this question would be to start counting along the edge from the first corner square (including it) up to - but not including - the next corner square, then repeat this procedure around the gameboard. There’ll be four strips, each (n-1) squares long, so
k = 4(n-1).
And just for fun, one more approach:
we can cut out from the n x n gameboard the inner (n-2) x (n-2) square, leaving us with the boundary made of
n^2 - (n-2)^2 =
4(n-1) squares.
Not the prettiest but the most straight forward solution.
It also works well when we need to calculate the number of unit cubes in all six faces of, for example, 5x5x5 cube:
5^3 - 3^3 = 98.
Sorry for beating the dead gameboard - I just thought of applying a low tech but very useful technique to this question: looking for a pattern.
Draw several n x n grids for n from 2 to 4 or 5 and count a number of squares “k” along the boundaries.
n k
2 4
3 8
4 12
5 16.
The pattern is quite clear.
With that last post, I think @gcf101 has closed the book on this problem! As I followed this thread, every time I remembered another solution to this question, there was a new post from gcf101 laying it out plain to see 
For the record, the vast majority of my students who get this one right do it by that last method: draw a series of cases, look for a pattern. And if this is the kind of problem that would not make it on to the new SAT, that’s a step backwards.
Looking for a pattern is a really good strategy if you’re stuck. I highly recommend it.
@pckeller Can’t help it -seems this book will never be closed… 
@AboutTime gave me an idea (or maybe it was his solution to begin with): if we count the number of squares along each side of the game board and add them up, the total will be 4n, but because we counted each corner twice, we need to subtract 4 to get the number of squares along the boundary, so
k = 4n - 4,
k = 4(n - 1).