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In the figure above, an edge, a face, and two vertices of a cube are i

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In the figure above, an edge, a face, and two vertices of a cube are i [#permalink]

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New post 15 May 2017, 04:53
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84% (01:27) correct 16% (00:14) wrong based on 19 sessions

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Cube-1.png
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In the figure above, an edge, a face, and two vertices of a cube are indicated. If e, f, and v denote the number of edges, faces, and vertices, respectively, of a cube, which of the following is true?

(A) e + f = v + 8
(B) e + f = v + 6
(C) e + f = 20 -v
(D) e - f = v - 2
(E) e – f = v/2




A kudo to dig into the old material to find a question that can contribute to someone's effort to achieve a dream would not hurt !! :wink:
[Reveal] Spoiler: OA

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In the figure above, an edge, a face, and two vertices of a cube are i [#permalink]

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New post 15 May 2017, 06:08
mihir0710 wrote:
Attachment:
Cube-1.png

In the figure above, an edge, a face, and two vertices of a cube are indicated. If e, f, and v denote the number of edges, faces, and vertices, respectively, of a cube, which of the following is true?

(A) e + f = v + 8
(B) e + f = v + 6
(C) e + f = 20 -v
(D) e - f = v - 2
(E) e – f = v/2

A kudo to dig into the old material to find a question that can contribute to someone's effort to achieve a dream would not hurt !! :wink:

I like this question. Thanks for digging it out. I think the question would be a little clearer if its first sentence said, "...an edge, a face, and a vertex are shown." Despite my being a professional editor in English, I got stumped for a few seconds by "two vertices" and "indicated." (I started thinking about discrete mathematics. Bad idea.)

Pretty sure this is a Euler formula (?), but you don't need to know or remember that to answer the question. You can just plug the number of faces, edges, and vertices into each answer:

A cube has 6 faces, 12 edges, and 8 vertices.

f=6

e=12

v=8

Only e-f = v-2 works:

12-6 = 8-2 [6=6]

Answer D

Hope it helps.
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Re: In the figure above, an edge, a face, and two vertices of a cube are i [#permalink]

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New post 17 May 2017, 22:53
E=12
F=6
V=8

Put values in each option and check for equality.

Only option D holds true.

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Re: In the figure above, an edge, a face, and two vertices of a cube are i   [#permalink] 17 May 2017, 22:53
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