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Retired Moderator
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The figure above is cut along the solid lines, folded along the dashed
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21 Sep 2021, 08:01
21 Sep 2021, 08:01
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Question Stats:
40% (02:27) correct
60% (01:07) wrong based on 10 sessions
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Attachment:
This geometric solid consists of 2 pyramids.png [ 10.98 KiB | Viewed 1313 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
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
Re: The figure above is cut along the solid lines, folded along the dashed
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21 Sep 2021, 10:31
21 Sep 2021, 10:31
2
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
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.
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
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
The figure above is cut along the solid lines, folded along the dashed
[#permalink]
21 Sep 2021, 10:32
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.
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.
