When the figure above is cut along the solid lines, folded a

Question

When the figure above is cut along the solid lines, folded along the dashed lines, and taped along the solid lines, the result is a model of a geometric solid. This geometric solid consists of 2 pyramids, each with a square base that they share. What is the sum of the number of edges and the number of faces of this geometric solid?
(A) 10
(B) 18
(C) 20
(D) 24
(E) 25

alanforde800Maximus · Answer

Hello Experts, Kindly explain this question.

Rich.C@EMPOWERgmat.com · Answer

Hi alanforde800Maximus,

We're told to cut along the solid lines, fold along the dashed lines, and tape along the solid lines to form a model of a geometric solid. This geometric solid consists of 2 pyramids, each with a square base that they share. We're asked for the sum of the number of edges and the number of faces of this geometric solid. This question has a number of built-in shortcuts that you can use to avoid doing lots of complex math.

To start, form the drawing, you can see that the shape will have 8 sides. When folded and taped together, each "edge" will be 'shared' by two of the sides. Thus, while there are 8 triangles in this shape (with 3 edges each), EVERY edge will be shared by 2 triangles, so we cannot count those edges twice. In simple terms, we have to divide the total number of edges by 2.... (8 triangles)(3 edges each)/(2... since each edge is counted twice) = 24/2 = 12 edges in the final shape.

12+8 = 20

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Last edited by [email protected] on Wed May 16, 2018 8:15 pm, edited 1 time in total.

Contact Rich at [email protected]

alanforde800Maximus · Answer

Rich.C@EMPOWERgmat.com wrote:Hi alanforde800Maximus, We're told to cut along the solid lines, fold along the dashed lines, and tape along the solid lines to form a model of a geometric solid. This geometric solid consists of 2 pyramids, each with a square base that they share. We're asked for the sum of the number of edges and the number of faces of this geometric solid. This question has a number of built-in shortcuts that you can use to avoid doing lots of complex math. To start, form the drawing, you can see that the shape will have 8 sides. When folded and taped together, each "edge" will be 'shared' by two of the sides. Thus, while there are 8 triangles in this shape (with 3 edges each), EVERY edge will be shared by 2 triangles, so we cannot count those edges twice. In simple terms, we have to divide the total number of edges by 2.... (8 triangles)(3 edges each)/(2... since each edge is counted twice) = 24/2 = 12 edges in the final shape. 12+2 = 20 Final Answer: C GMAT assassins aren't born, they're made, Rich Hello Rich, Thanks for your reply. Is there any diagrammatic approach that can be deployed on these questions?

Rich.C@EMPOWERgmat.com · Answer

Hi alanforde800Maximus,

If you're thinking about drawing this shape, then you could potentially do that - but if you focused too much on the drawing (and not on the description in the prompt) then you might find it a little tough to draw an appropriate sketch. For the sake of argument, could you draw one pyramid with triangle sides and a square base? How many sides and edges would that one pyramid have? Now, imagine/draw two of those pyramids, but in such as way that they share the SAME square base (the 2nd pyramid would be 'inverted', underneath the first pyramid).

With that drawing, you would see the 8 triangle sides and could count up the edges.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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