Question

What solid figure has eight edges and five vertices?
rectangular prism
square pyramid
pentagonal prism
triangular pyramid

Answer 1

Triangular Pyramid

Answer 2

Let's think our way through it. Option one is a rectangular prism, but that has six vertices, so that can't be right. Option three is a pentagonal prism which has even more vertices, so it's definitely not that. Option four, a triangular pyramid, has only four vertices, which isn't enough. So it has to be option two, a square pyramid. If we think about it we can see that there are four vertices on the bottom and one at the point, for five, and there are four edges on the bottom and four edges up to the point, for eight.

Answer 3

This is how I think of it, if it helps at all.
the first 2 options have a quadrilateral base, so there's 4 vertices just from that. The prism would mean that there are 2 bases, so from that we know there are (at least) 8 vertices -- too many. The pyramid means that there is an extra point so 4+1=5 -- just right.
So then you can check to see if the edges match: 4 edges from the base plus 4 from each vertex of the base connecting to that extra point -- 8 total edges