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What is the volume of a certain rectangular solid? (1) Two [#permalink]
24 Aug 2008, 16:29

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Difficulty:

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Question Stats:

69% (01:28) correct
31% (02:29) wrong based on 35 sessions

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.

Re: DS rectangular solid [#permalink]
24 Aug 2008, 18:34

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This post received KUDOS

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.

Re: DS rectangular solid [#permalink]
24 Aug 2008, 17:19

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

Re: DS rectangular solid [#permalink]
24 Aug 2008, 23:23

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

Re: DS rectangular solid [#permalink]
26 Aug 2008, 15:52

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.