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

shakun

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25 Apr 2017, 00:32

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Nikki&sunny

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

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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

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25 Apr 2017, 00:48

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shakun

Nikki&sunny

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

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?

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

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Updated on: 25 Apr 2017, 13:31

Originally posted by shakun on 25 Apr 2017, 12:08.
Last edited by shakun on 25 Apr 2017, 13:31, edited 1 time in total.

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attari92

shakun

Nikki&sunny

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

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?

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

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.
[Please note that number of factors of the surface-area doesn't play any role here as long as the above interpretation of statement-2 is correct]

attari92

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25 Apr 2017, 13:24

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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

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25 Apr 2017, 13:32

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attari92

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.

See my 'EDIT' section in my original response.

attari92

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25 Apr 2017, 13:46

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shakun

attari92

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.

See my 'EDIT' section in my original response.

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

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25 Apr 2017, 14:28

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attari92

shakun

attari92

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.

See my 'EDIT' section in my original response.

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.

attari92

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26 Apr 2017, 00:35

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

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

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26 Apr 2017, 00:42

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attari92

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

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

attari92

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.

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

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26 Apr 2017, 03:34

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(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.

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11 May 2017, 13:34

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ziyuen

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.

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

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11 May 2017, 13:39

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ziyuen

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.

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!

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

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