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The figure above is cut along the solid lines, folded along the dashed

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KarunMendiratta
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The figure above is cut along the solid lines, folded along the dashed [#permalink] New post   21 Sep 2021, 08:01
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Attachment:
This geometric solid consists of 2 pyramids.png
This geometric solid consists of 2 pyramids.png [ 10.98 KiB | Viewed 1485 times ]


The figure above is cut along the solid lines, folded along the dashed lines, and taped along the solid lines. The result is a geometric solid consisting of 2 pyramids each with a square base that they share.

Quantity A
Quantity B
Sum of number of edges and number of faces of this geometric solid
18


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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A
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motion2020
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Re: The figure above is cut along the solid lines, folded along the dashed [#permalink] New post   21 Sep 2021, 10:31
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any square pyramid has 4 faces, 1 base and 8 edges

here, the base is shared and two pyramids have 8 faces and 12 edges (4 edges frame the shared base)

IMO answer is A, as Quantity A=20 > Quantity B=18

KarunMendiratta wrote:
Attachment:
This geometric solid consists of 2 pyramids.png


The figure above is cut along the solid lines, folded along the dashed lines, and taped along the solid lines. The result is a geometric solid consisting of 2 pyramids each with a square base that they share.

Quantity A
Quantity B
Sum of number of edges and number of faces of this geometric solid
18


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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grenico
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The figure above is cut along the solid lines, folded along the dashed [#permalink] New post   21 Sep 2021, 10:32
3
Trying to construct the figure from the picture is unnecessary - what is important is the statement:

The result is a geometric solid consisting of 2 pyramids each with a square base that they share.

This is essentially two pyramids that share a base: a 3D diamond for lack of a better word.

Each pyramid has 8 edges: the four that go upwards (or downwards) from the base, and the 4 at the base. Since the two pyramids share the base, we shouldn't overcount the edges at the base.

So we have (2)(4) + 4 = 12 edges.

Each pyramid has 5 faces, except that they share the base, so we shouldn't count the face of the base.

So we have 2(4) = 8 faces.

Putting these together we have 12+8 = 20.

Therefore the answer is A.
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The figure above is cut along the solid lines, folded along the dashed [#permalink]
21 Sep 2021, 10:32
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