In advance, I called the ACT hotline and checked if discussing questions from a released test was okay. It is.
Here’s the question:
Suppose that equally spaced dots are marked on each side of a regular polygon, with a dot at each vertex, and that the distance between consecutive dots is the same for all sides. The figure below shows 4 equally spaced dots per side, including a dot at each vertex, for an equilateral triangle. Which of the following expressions represents the number of dots for a regular polygon with n equally spaced dots, including one at each vertex, marked on each of its s sides?
a. ns
b. ns-1
c. ns-s
d. ns+s
e. ns-n
i remember this quesion. i did not understand it as well. does anyone have any idea what it is asking? what are “the number of dots”? number of equally spaced dots or what?
I believe they are asking for the expression that gives the total number of dots on a polygon of ‘s’ sides with ‘n’ equally spaced dots per side (including verticies). In the example: filling in one side of the triangle gives a total of 4. Filling in the next side adds 3 more, and the final side adds 2–for a total of 9 dots. Since s=3 and n=4, answer C gives the total number of dots. You can quickly check it using a square with 4 dots per side: (4)(4)-4=12
Thanks Mathmeany, I knew the correct answer was c I just needed an explanation.