If the length of each edge of a certain rectangular solid is an

Question

If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?

(1) Two of the faces have areas of 32 square units and 16 square units.

(2) One of the edges is twice the length of another edge.

EMPOWERgmatRichC · Answer

Hi TARGET730,

This DS question has a number of interesting "restrictions" to it (and you have to pay careful attention to the restrictions to get the correct answer).

Here, we have a rectangular solid that has 4 faces with the same dimensions. In real basic terms, we have a box (NOT a cube), with the dimensions X, X and Y. We're also told that each dimension is an INTEGER. We're asked for the VOLUME of the solid.

Volume = (length)(width)(height)

Fact 1: Two of the faces have areas of 32 and 16

Since this rectangular solid has 4 faces with the same dimensions, the other 2 faces will have dimensions that match (but are different from the other 4 faces).

With the above values, we have just 2 possibilities:
The 4 sides are 32s and the 2 sides are 16s
The 4 sides are 16s and the 2 sides are 32s

While many Test Takers might dismiss this as insufficient, we need to do a bit more work to PROVE whether it's sufficient or insufficient.

If the 2 sides are 16s, then the two dimensions are 4 and 4
Since the others sides are 32s, those dimensions are 4 and 8
The volume of this solid is (4)(4)(8) = 126

If the 2 sides are 32s, then the two dimensions are (root32) and (root32). 
The prompt stated that the dimensions had to be INTEGERS though, so this set of dimensions does NOT MATCH the restrictions given. Thus, there is only one answer in Fact 1.
Fact 1 is SUFFICIENT

Fact 2: One of the edges is twice the length of another.

We could have (4)(4)(8) =126
We could have (1)(1)(2) = 2
Fact 2 is INSUFFICIENT.

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

TARGET730 · Answer

Hi Rich, 
I am not sure the OA is correct. i am trying to find the correct answer answer here. Can we consider the following possibilities with different volumes?

Area 32 
------ 
32 * 1 
16 * 2 
 8 * 4

Area 16
------ 
1 * 16 
2 * 8
4 * 4

Volume
-------
36 * 1 * 16 = 576
16 * 2 * 8 = 196
 8 * 4 * 4 = 128

EMPOWERgmatRichC · Answer

Hi TARGET730,

In the description of the rectangular solid, we're told that "4 of the faces have the same dimensions" - the ONLY way for that to occur is if the dimensions of the solid are X, X and Y (2 of the 3 dimensions MUST have the same length). We're also told that ALL the dimensions MUST be INTEGERS.

Using these restrictions, how many of your 'examples' actually match? You'll find that just one "fits" (the 4x4x8), so the final answer is  C

GAMT assassins aren't born, they're made,
Rich

sahilvijay · Answer

Ans is A
Length is integer, and 4 faces have equal areas
1) A1=32 and A2=16
from this LxB= 32 and  B^2 = 16 ,  => B= 4  and  L =8  and Volume= 8x4x4 = 128 cu.units

or BxL =32 and  L^2 = 16 ,  => L=4  and B = 8  and in this case Volume = 4x4x8 = 128 cu. units

Note B and L cant take any other value as L is an integer mentioned in question.

2)  L = 2B  or  B = 2L 
Clearly statement is insufficient to answer about volume which is  L^2  x B or  B^2  x L

GMATGuruNY · Answer

For the solid to have four faces with the same dimensions, two opposing faces must be SQUARES, as in the following figure: https://preview.ibb.co/koZpb8/rectangular_solid_with_square_base.png 
In the figure above:
The area of the square base and the area of the square top = L*L.
The areas of the other four faces = L*H.

Statement 1:
Since the dimensions must all be integers, the rectangular solid must look as follows:
 https://preview.ibb.co/gaFnw8/rectangular_solid_with_square_base_Statement_1.png 
Since the dimensions of the solid are known, the volume can be determined.
SUFFICIENT.

Statement 2:
Since the dimensions of the solid are unknown, the volume cannot be determined.
INSUFFICIENT.

A

Shishou · Answer

Statement 1 Since we are told that 4 faces have the same dimension and another 2 have a different dimension 
it means one group of faces has an area of 32 and the second groups an area of 16. What's also apparent is that these 2 areas share one dimension : a length, a width or a height.
Now 32 = 32×1/16×2/4×8
16=16×1/4×4

Only 4×8 and 4×4 allow us to have 4 faces with an equal area and another 2 faces with a different area.The volume is thus 4×4×8=128.Sufficient

Statement 2 : From statement 1 we know 4×4×8 would work but we also know 2×2×4 would also work. Either of them gives us a different volume 
Insufficient

Answer is A

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