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# M is a rectangular solid. Find the volume of M

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

Hi.
The info as per statement 1 is:
Bottom face of M has an area of 28, which can be expressed as 28 * 1 or 56*0.5 or 280*0.1 or 7*4 and so on.
Top face of M has an area of 35, which can expressed as 35*1 or 70*0.5 or 350*0.1 or 7*5 and so on.

So as per given info the three dimensions of rectangular solid can be 1*28*35 or 7*4*5 or 0.5*56*70 or 0.1*280*350
Both will have different volume. Hence option B is required to rule out everything except 7*4*5

Please give Kudos if you like the explanation.

Originally posted by ruchik on 02 Jan 2019, 21:07.
Last edited by ruchik on 02 Jan 2019, 21:59, edited 1 time in total.
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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]
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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]
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
Re: M is a rectangular solid. Find the volume of M [#permalink]
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