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Magoosh GMAT Instructor
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Re: M is a rectangular solid. Find the volume of M [#permalink]
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mikemcgarry wrote:
M is a rectangular solid. Find the volume of M

Statement #1: The bottom face of M has an area of 28, and the front face, an area of 35.

Statement #2: All three dimensions of M are positive integers greater than one.


For more on 3D solids, see:
https://magoosh.com/gmat/2012/gmat-math-3d-solids/
For more on factorization, see:
https://magoosh.com/gmat/2012/gmat-math-factors/

The former has a full solution to this question.

Mike :-)


1) l*b = 28 & l*h = 35
not sufficient

2) (l,b,h) > 1 (+ integers)
not sufficient

1)+2)
l^2*b*h = 28*35 = 2^2*5*7^2
l^2 can be 1 or 2^2 or 7^2 or 2^2*7^2
only possible solution for (l,b,h) is (7,4,5)
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Re: M is a rectangular solid. Find the volume of M [#permalink]
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GmatAssasin24 wrote:
please explain , how can dimensions be assumed as negative value?

Solid tends to have positive value, then why option B mentions that it is greater than one/ positive?

can somebody elaborate this please?


Yes, dimensions must be positive but (2) says that "All three dimensions of M are positive integers greater than one". So, this statement excludes possibilities such as 1/2, 3/4, 5/2, 1, ... So, basically any non-integer values and 1.
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Re: M is a rectangular solid. Find the volume of M [#permalink]
Could someone provide further insight into this problem (and how to approach general problems like these)? Thank you!


mikemcgarry wrote:
M is a rectangular solid. Find the volume of M

Statement #1: The bottom face of M has an area of 28, and the front face, an area of 35.

Statement #2: All three dimensions of M are positive integers greater than one.


For more on 3D solids, see:
https://magoosh.com/gmat/2012/gmat-math-3d-solids/
For more on factorization, see:
https://magoosh.com/gmat/2012/gmat-math-factors/

The former has a full solution to this question.

Mike :-)
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M is a rectangular solid. Find the volume of M [#permalink]
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Can dimensions be a negative integer too ?
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Re: M is a rectangular solid. Find the volume of M [#permalink]
anmolsd1995 wrote:
Can dimensions be a negative integer too ?


I think you are referring to option B. Option B is required not for negative numbers but for greater than 1. Please look at the explanation in my earlier post.
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Re: M is a rectangular solid. Find the volume of M [#permalink]
please explain , how can dimensions be assumed as negative value?

Solid tends to have positive value, then why option B mentions that it is greater than one/ positive?

can somebody elaborate this please?
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Re: M is a rectangular solid. Find the volume of M [#permalink]
We cannot calculate volume since we don't know if they are integer or non integer values.

If area of bottom = 28,

From St 1: Dimensions of bottom can be=280*0.1 or 28*1 or 7*4

Hence v= 280*0.1*350 or 28*1*35 or 7*4*5

From St II, we can deduce that all sides are integers, and the two common factor between 28 and 35 is 7
Therefore, 7*4*5=only possible answer.

Option C
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Re: M is a rectangular solid. Find the volume of M [#permalink]
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