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What is the volume of a certain rectangular solid? (1) Two

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What is the volume of a certain rectangular solid? (1) Two [#permalink] New post 24 Aug 2008, 17:29
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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.


Please provide your answer explanations.
Lets also take it a step further. If you say it can be solved, could you please show how would you solve it.
I know you dont need to solve DS questions but this would be a great question for PS as well.
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Re: DS rectangular solid [#permalink] New post 24 Aug 2008, 18:19
this is one where you have to draw a diagram. It uses mostly math intuition instead of formulas and such. draw a rectangular solid in 3-D and write in the areas 15, 24, and 40 on the three faces. after staring for a few seconds, you can see that the only sides that make sense are 3,5, and 8. bc 3x5=15 8x3=24 and 5x8=40. and these can be set up to be adjacent as they are in the stimulus. so the answer is 3x5x8=120

PS Answer: 120

However, since 15 and 24 have two common factors, 3 and 1, just saying that they are adjacent does not do the trick (whereas two prime numbers would, like 7 and 5) so you cant predict the common side of the faces with just (1), so the third area must be known, where (2) gives you this information. And also these are the only sides that can be used to create the three areas in this manner.
Therefore,
DS Answer: C
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Re: DS rectangular solid [#permalink] New post 24 Aug 2008, 19:34
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elmagnifico 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.


Please provide your answer explanations.
Lets also take it a step further. If you say it can be solved, could you please show how would you solve it.
I know you dont need to solve DS questions but this would be a great question for PS as well.



Volume = wlh
1)
wh=15
hl =24

insufficient

2) wl= 40
insufficient

combine
wh=15
hl =24
wl =40
(wlh)^2 = 15*24*40
= 3*5*3*8*5*8
= (3*5*8)^2
wlh=120
suffcient
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Last edited by x2suresh on 25 Aug 2008, 06:02, edited 1 time in total.
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Re: DS rectangular solid [#permalink] New post 25 Aug 2008, 00:23
elmagnifico 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.


A.

1) two adjecent faces should have one side common.

15 = 5 * 3
24 = 3 * 8

3 is the side that is common, remaining sides are 5, 8

volume = 5 *3 * 8

suff.

2) insuff, we know just 2 sides.
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Re: DS rectangular solid [#permalink] New post 26 Aug 2008, 16:52
yeah you have to know all the area of all three faces or you cannot answer the question because the shared side could be any number that is a factor of the area of both sides. e.g. 1,3, or as x2 pointed out, any real number less than 15.
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Re: What is the volume of a certain rectangular solid? (1) Two [#permalink] New post 25 Feb 2012, 16:20
How does one which faces we are dealing with?

In (A), we could be talking about HW and HL or HL and WL.

Aren't WL and HL adjacent as well?
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Re: What is the volume of a certain rectangular solid? (1) Two [#permalink] New post 25 Feb 2012, 16:31
Lstadt wrote:
How does one which faces we are dealing with?

In (A), we could be talking about HW and HL or HL and WL.

Aren't WL and HL adjacent as well?


Good long discussion of this question: what-is-the-volume-of-a-certain-rectangular-solid-90748.html#p772095

Hope it helps.

In case of any question please post it there.
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Re: What is the volume of a certain rectangular solid? (1) Two   [#permalink] 25 Feb 2012, 16:31
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