What is the volume of a certain rectangular solid? (1)The surface area

Question

What is the volume of a certain rectangular solid?

(1) The surface area of the solid is 148. 
(2) Each of two opposite faces of the solid has area 30.

0akshay0 · Answer

St I The surface area of the solid is 148 148 = 2*(lb+bh+lh); we cannot calculate the volume i.e. l*b*h with this information --------Insufficient St II Each of two opposite faces of the solid has area 30; no proper data is available to calculate l,b or h --------Insufficient St I and II 148 = 60 + 2(bh+lh) (I have considered 30 as the are calculated using lb) still we cannot calculate exact values of l, b or h --------Insufficient Hence Option E is correct. Hit Kudos if you lied it 8-)

Nikki&amp;amp;sunny · Answer

Each of two opposite faces of the solid has area 30.
I thought all the face have the area of 30 depending on the wordings "each of two opposite faces" and thus the figure under consideration is a cube with area of any face as 30
Please correct my thinking

Posted from my mobile device

shakun · Answer

Same thoughts here. But I thought sum of area of two opposite faces = 30. Hence each face has area = 15. Nevertheless, it turns out to be a cube.

So in my opinion it is 'B'. What am I missing here?

attari92 · Answer

However, 15 has four factors that could be expressed as a multiples of two dimensions in two ways and hence, the value not unique

shakun · Answer

Thanks for your feedback Attari.
 A genuine curiosity - What does the statement-2 mean? 
If it means that each face has 'same' area (be it 30 or 15) then the solid has to be a cube. Hence statement-2 is sufficient.
  EDIT: When each face has same area that means, xy=yz=zx. means x=y=z. Hence a cube.

attari92 · Answer

shakun 
but how come the same base area results in a solid to be a cube ? can't the base has sides measuring 3by5 ? there indeed exist an ambiguity in value. Just try out with some couple of multiples.

shakun · Answer

See my 'EDIT' section in my original response.

attari92 · Answer

were u also considering y=0 ? either x=z or y=0 and if 'y' happens to be zero then the capacity of the solid stands to nothing. Is it makes any sense ?

shakun · Answer

No Attari, obviously all of x,y,z > 0 as this is a solid rectangle. So I still argue the same.

attari92 · Answer

were u also considering y=0 ? either x=z or y=0 and if 'y' happens to be zero then the capacity of the solid stands to nothing. Is it makes any sense ? 
No Attari, obviously all of x,y,z > 0 as this is a solid rectangle. So I still argue the same.

If we were to consider each face has area =30 then isn't it contradicting statement 1st? and more importantly as per the GMAT each of the two statements are ought to be correct. I believe the real enigma lies in statement 2nd not being succinct.

shakun · Answer

Well, I do not know if two statements can contradict each other or not. But keeping that discussion aside, if we are given statement-2 alone, we can get the volume of the solid uniquely.

Alexey1989x · Answer

(1) Insuff by itself.
(2) ab=30; bc=30;ac=30
V=abc
Multiplying areas of all 3 sides we get a^2*b^2*c^2=30^3, extracting the root we get abc=30*30^1/2, hence  Sufficient .

Dear  ziyuen  please advise what point am I missing??? I absolutely agree with  shakun  's above reasoning

P.S. If question stem states that there is a rectangular solid thus we should deem only positive values of dimensions.

gmatexam439 · Answer

Bunuel  plzz correct me:

Shouldn't answer be B. Since we are told that EACH of the two opposite sides has area = 30,
Therefore we can say

lb=30
bh=30
lh=30

and if we multiply all eqautions:
(lbh)^2=30^3

Therefore we can calculate the value of lbh, hence sufficient.

Since my answer doesn't match with that of the OG, I am missing something here. Please help me out!

Bunuel · Answer

This is a copy of the following OG question: https://gmatclub.com/forum/what-is-the- ... fl=similar THIS POST from there will explain why the second statement is not sufficient.

What is the volume of a certain rectangular solid? (1)The surface area

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