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In the figure above, x, y and z are the dimensions of the rectangular

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Math Expert
Joined: 02 Sep 2009
Posts: 56300
In the figure above, x, y and z are the dimensions of the rectangular  [#permalink]

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08 Dec 2017, 03:43
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Difficulty:

25% (medium)

Question Stats:

74% (01:04) correct 26% (01:26) wrong based on 68 sessions

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In the figure above, x, y and z are the dimensions of the rectangular solid, and each of these dimensions is an integer greater than 1. Each of the following could be the volume of the rectangular solid except

(A) 8
(B) 12
(C) 24
(D) 27
(E) 69

Attachment:

2017-12-08_1440.png [ 11.78 KiB | Viewed 914 times ]

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Re: In the figure above, x, y and z are the dimensions of the rectangular  [#permalink]

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08 Dec 2017, 04:05
Bunuel wrote:

In the figure above, x, y and z are the dimensions of the rectangular solid, and each of these dimensions is an integer greater than 1. Each of the following could be the volume of the rectangular solid except

(A) 8
(B) 12
(C) 24
(D) 27
(E) 69

Attachment:
2017-12-08_1440.png

(A) 8 = 2*2*2
(B) 12 =2*2*3
(C) 24 = 2*4*3
(D) 27 = 3*3*3
(E) 69 = 3* 13 * 1..not possible

E
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Re: In the figure above, x, y and z are the dimensions of the rectangular  [#permalink]

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08 Dec 2017, 07:47
Bunuel wrote:

In the figure above, x, y and z are the dimensions of the rectangular solid, and each of these dimensions is an integer greater than 1. Each of the following could be the volume of the rectangular solid except

(A) 8
(B) 12
(C) 24
(D) 27
(E) 69

Attachment:
2017-12-08_1440.png

Among the choices only "69" can't be factored into three integers , each factor greater than One to fit the volume of rectangular solid (V = h * w * d)
So, Answer is E
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Joined: 11 Jan 2018
Posts: 19
Re: In the figure above, x, y and z are the dimensions of the rectangular  [#permalink]

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26 Feb 2018, 00:12
Sorry if this is a silly question, isn't a cube different from a rectangular solid?
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Joined: 02 Sep 2009
Posts: 56300
Re: In the figure above, x, y and z are the dimensions of the rectangular  [#permalink]

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26 Feb 2018, 00:16
minatminat wrote:
Sorry if this is a silly question, isn't a cube different from a rectangular solid?

All cubes are rectangular solids but not vise-versa.
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In the figure above, x, y and z are the dimensions of the rectangular  [#permalink]

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26 Feb 2018, 00:21
Split the answer options using the prime factorization method, but stop once you can split into 3 smaller factors to save time. The answer choice that is unable to give you 3 number of factors (excluding 1 & itself) is the answer.

A) 8 = 4*2 = 2*2*2 (ok)
B) 12 = 2*6 = 2*2*3 (ok)
C) 24 = 2*12 = 2*2*6 (ok)
D) 27 = 3*9 = 3*3*3 (ok)
E) 69 = 3*23

As 23 is a prime number and cannot be further split other than 1 and itself, E is the answer.
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Posts: 19
Re: In the figure above, x, y and z are the dimensions of the rectangular  [#permalink]

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26 Feb 2018, 00:36
Bunuel wrote:
minatminat wrote:
Sorry if this is a silly question, isn't a cube different from a rectangular solid?

All cubes are rectangular solids but not vise-versa.

Thanks so much for replying me!!
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Re: In the figure above, x, y and z are the dimensions of the rectangular  [#permalink]

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13 May 2019, 22:31
Bunuel wrote:

In the figure above, x, y and z are the dimensions of the rectangular solid, and each of these dimensions is an integer greater than 1. Each of the following could be the volume of the rectangular solid except

(A) 8
(B) 12
(C) 24
(D) 27
(E) 69

Attachment:
2017-12-08_1440.png

Volume= a*b*c, where a,b,c > 0 and a,b,c are INTEGERS

For 69 can be broken into= 3*23*1, not possible.
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Re: In the figure above, x, y and z are the dimensions of the rectangular   [#permalink] 13 May 2019, 22:31
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