M is a rectangular solid. Find the volume of M

Question

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

ziko · Answer

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

thefibonacci · Answer

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)

KHow · Answer

Could someone provide further insight into this problem (and how to approach general problems like these)? Thank you!

anmolsd1995 · Answer

Can dimensions be a negative integer too ?

ruchik · Answer

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.

ruchik · Answer

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.

GmatAssasin24 · Answer

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?

Bunuel · Answer

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.

gmatapprentice · Answer

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

M is a rectangular solid. Find the volume of M

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GMAT Data Sufficiency (DS) Questions

M is a rectangular solid. Find the volume of M

Prep Toolkit

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My Rewards