Target question: What is the volume of a certain rectangular solid?ashish1354 wrote:What is the volume of a certain rectangular solid?
(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
(2) Each of two opposite faces of the solid has area 40.
Brent@GMATPrepNow wrote:We can see that (1) is not sufficient if we consider two sets of dimensions: 1x15x24 and 3x5x8ashish1354 wrote:What is the volume of a certain rectangular solid?
(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
(2) Each of two opposite faces of the solid has area 40.
(2) is definitely not sufficient.
To check statements(1) and (2) combined, let's let x be the length of one side of our box (see below).
As you can see, statements (1) and (2) combined lead us to conclude that x=3, from which the other 2 lengths can be calculated. So, the answer is C.
Hello Brent,Brent@GMATPrepNow wrote:Hi Sri,
I think statement 2 means that there are exactly 2 faces with area 40.
That said, it doesn't really matter for this question since statement 2 is insufficient, and statement 1 rules out the possibility of more than 2 faces having area 40.
Cheers,
Brent
Hi Brent,Brent@GMATPrepNow wrote:I think statement 2 means that there are exactly 2 faces with area 40.
That said, it doesn't really matter for this question since statement 2 is insufficient, and statement 1 rules out the possibility of more than 2 faces having area 40.
(2) Each of two opposite faces of the solid has area 40.Captchar wrote:Hi Brent,Brent@GMATPrepNow wrote:I think statement 2 means that there are exactly 2 faces with area 40.
That said, it doesn't really matter for this question since statement 2 is insufficient, and statement 1 rules out the possibility of more than 2 faces having area 40.
Stumbled upon this thread while searching for a discussion on this problem as I have some doubt on this.
Can you explain how statement 2 is individually insufficient? I understand that both statements together, it is not possible that more than a pair of opposite faces can have area 40. But statement 2 individually looks like trying to say 'each of two opposite faces of the solid has area 40' or each opposite faces have area 40 or all the faces of the solid has area 40. It never says exactly one pair of opposite faces have area 40.
Regards,
Charan
Thanks for your reply!Brent@GMATPrepNow wrote:It doesn't really matter whether it's possible for more than 2 faces to have an area of 40, since it doesn't change the fact that statement 2 is not sufficient.
Consider these two conflicting cases:
case a: the dimensions are 10x10x4 (four faces with area 40), in which case the volume is 400
case b: the dimensions are 10x4x3 (two faces with area 40), in which case the volume is 120
Ah, sorry for misinterpreting your question.Captchar wrote:Thanks for your reply!Brent@GMATPrepNow wrote:It doesn't really matter whether it's possible for more than 2 faces to have an area of 40, since it doesn't change the fact that statement 2 is not sufficient.
Consider these two conflicting cases:
case a: the dimensions are 10x10x4 (four faces with area 40), in which case the volume is 400
case b: the dimensions are 10x4x3 (two faces with area 40), in which case the volume is 120
But my question was different.
I was asking that doesn't statement individually means all the faces of the solid has area 40? I'm saying this because the statement says "each of two opposite faces..." not just simply "two opposite faces..." in which we could've interpreted that either 2 or 4 or 6 opposite faces are having area 40.
But by saying "each of two opposite faces..." don't we mean each pair of opposite faces or all the faces? In which case, only one such rectangular solid is possible and statement 2 by itself is sufficient to answer the question.
Regards,
Charan
