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If the length of each edge of a rectangular solid is an integer, the
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Bunuel
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If the length of each edge of a rectangular solid is an integer, the [#permalink] New post  04 Feb 2021, 02:45
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If the length of each edge of a rectangular solid is an integer, the sum of the lengths of all the edges of the solid is necessarily divisible by which of the following?

A. 3
B. 4
C. 5
D. 6
E. 8
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If the length of each edge of a rectangular solid is an integer, the [#permalink] New post  04 Feb 2021, 03:03
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Bunuel wrote:
If the length of each edge of a rectangular solid is an integer, the sum of the lengths of all the edges of the solid is necessarily divisible by which of the following?

A. 3
B. 4
C. 5
D. 6
E. 8


There are 12 edges in a rectangular solid
4 lengths (l)
4 widths (b)
4 Heights (h)
Attachment:
1.png
1.png [ 9.24 KiB | Viewed 368 times ]

Sum of Length of each edge of a rectangular solid = 4*(l+b+h)

which is divisible by 4

Answer: Option B

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Re: If the length of each edge of a rectangular solid is an integer, the [#permalink] New post  19 Feb 2021, 03:54
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Bunuel wrote:
If the length of each edge of a rectangular solid is an integer, the sum of the lengths of all the edges of the solid is necessarily divisible by which of the following?

A. 3
B. 4
C. 5
D. 6
E. 8

Solution:

We can let the dimensions of the rectangular solid be x, y and z where x, y, and z are integers. Since each dimension appears as an edge 4 times, the sum of the lengths of all the edges will be 4x + 4y + 4z = 4(x + y + z). We see that the sum is always a multiple of 4, regardless of the values of x, y, and z.

Answer: B
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Re: If the length of each edge of a rectangular solid is an integer, the [#permalink]
19 Feb 2021, 03:54
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