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Question: If a pyramid has 5 vertices and 8 edges, how many faces does the pyramid have?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 12
Solution and Explanation
Approach Solution 1
Here we have a pyramid –
5 points and 8 sides.
Which is only possible in a pyramid with a square base and four triangles?
Hence Four sides of a triangle + one side of a square = five faces.
B is the correct answer.
Approach Solution 2
To find the number of faces in a pyramid with 5 vertices and 8 edges, we can use Euler's formula for polyhedra, which states that for any convex polyhedron (including pyramids):
Number of faces + Number of vertices - Number of edges = 2.
Let's plug in the values we have:
Number of vertices = 5
Number of edges = 8
Let's solve for the number of faces:
Number of faces + 5 - 8 = 2
Number of faces - 3 = 2
Number of faces = 2 + 3
Number of faces = 5
So, the pyramid has 5 faces.
So, the correct answer is B.
Approach Solution 3
Euler's formula for polyhedra can be used to figure out how many sides a pyramid with 5 vertices and 8 edges has. It says that for any convex polyhedron, including pyramids:
number of sides + number of vertices - Number of edges = 2.
Let's plug in what we know:
There are 5 vertices.
There are 8 edges.
Let's figure out how many faces there are:
Faces + 5 - 8 = 2
faces - 3 = 2
There are 5 faces.
So, there are 5 sides to the pyramid.
B is the right response.
“If a pyramid has 5 vertices and 8 edges, how many faces does the pyramid have?" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.
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