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

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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M is a rectangular solid. Find the volume of M  [#permalink]

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21 May 2013, 10:11
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Difficulty:

65% (hard)

Question Stats:

54% (01:28) correct 46% (01:25) wrong based on 205 sessions

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

The former has a full solution to this question.

Mike

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Mike McGarry
Magoosh Test Prep

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

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22 May 2013, 22:24
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In such questions i normally try to visualise. From st.1 I draw the solid and assign an area of 28 to one side and 35 to another. Since this is rectangular solid there should be one common side, so there should be one common number between 28 and 35. This number could be anything including integer and non-integer numbers, since there is no restriction according to statement 1 - not sufficient. From statement 2 we know that all the dimentions are integers greater than one, which is again gives us more than one answer - not sufficient.
Combining two answers we are can find out that the only common integer (greater than 1) between 28 and 35 is 7, so we can easily find out that the sides are 4, 5 and 7. The volume of the solid is 4*5*7=140
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Re: M is a rectangular solid. Find the volume of M  [#permalink]

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08 Oct 2018, 05:15
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:
http://magoosh.com/gmat/2012/gmat-math-3d-solids/
For more on factorization, see:
http://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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02 Jan 2019, 08:46
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:
http://magoosh.com/gmat/2012/gmat-math-3d-solids/
For more on factorization, see:
http://magoosh.com/gmat/2012/gmat-math-factors/

The former has a full solution to this question.

Mike
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Joined: 17 Apr 2017
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M is a rectangular solid. Find the volume of M  [#permalink]

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02 Jan 2019, 20:47
1
Can dimensions be a negative integer too ?
Manager
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M is a rectangular solid. Find the volume of M  [#permalink]

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Updated on: 02 Jan 2019, 21:59
1
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:
http://magoosh.com/gmat/2012/gmat-math-3d-solids/
For more on factorization, see:
http://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.
Manager
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Re: M is a rectangular solid. Find the volume of M  [#permalink]

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02 Jan 2019, 21:10
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]

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11 Feb 2019, 23:08
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?

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Posts: 56275
Re: M is a rectangular solid. Find the volume of M  [#permalink]

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11 Feb 2019, 23:37
1
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?

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] 11 Feb 2019, 23:37
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