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

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New post 21 May 2013, 09:11
1
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:02) correct 42% (00:54) 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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Magoosh Test Prep


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

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New post 22 May 2013, 21:24
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1
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
Answer is C
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Re: M is a rectangular solid. Find the volume of M  [#permalink]

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New post 08 Oct 2018, 04:15
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 &nbs [#permalink] 08 Oct 2018, 04:15
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M is a rectangular solid. Find the volume of M

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