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What is the volume of a certain rectangular solid? (1) Two [#permalink]

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24 Aug 2008, 17:29

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C

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E

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75% (01:02) correct
25% (01:12) wrong based on 179 sessions

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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.

Re: What is the volume of a certain rectangular solid? (1) Two [#permalink]

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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

Re: What is the volume of a certain rectangular solid? (1) Two [#permalink]

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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.

Re: What is the volume of a certain rectangular solid? (1) Two [#permalink]

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25 Aug 2008, 00:23

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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.

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: What is the volume of a certain rectangular solid? (1) Two [#permalink]

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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.

What is the volume of a rectangular solid? 1) Two adjacent [#permalink]

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05 Jul 2010, 09:25

What is the volume of a rectangular solid? 1) Two adjacent faces of the solid have areas of 15 and 24 repectively. 2) Each of two opposite faces of solid has area 40.
_________________

Consider me giving KUDOS, if you find my post helpful. If at first you don't succeed, you're running about average. ~Anonymous

Im nt clear about the statement 2. I thought each of the two opposite faces means: l*b= 40 b*h=40 l*h=40 it gives the value of l, b and h- which is Square root of 40. what does the statement 2 mean? OA is c.
_________________

Consider me giving KUDOS, if you find my post helpful. If at first you don't succeed, you're running about average. ~Anonymous

It means that out of the 6 faces of the solid rectangle, 2 opposite ones have an area of 40. This doesn't say anything about the 3rd dimension, so stmt2 is clearly insufficient to answer the question...

What is the volume of a rectangular solid? 1) Two adjacent faces of the solid have areas of 15 and 24 repectively. 2) Each of two opposite faces of solid has area 40.

I do not get this question. (2) says each of the two opposite faces. A rectangular solid has 6 faces and 3 pairs of 2 opposite faces. I read this as saying that basically all areas of the faces is 40. And thus the volume would be sqrt(40^3). Why is this wrong? On the other hand (1) is insufficient as it does not tell us about the entire solid. Bunuel?
_________________

This question is from Official Guide and Official Answer is C.

About rectangular solid:

In a rectangular solid, all angles are right angles, and opposite faces are equal, so rectangular solid can have maximum 3 different areas of its faces, on the diagram: yellow, green and red faces can have different areas. I say at max, as for example rectangular solid can be a cube and in this case it'll have all faces equal, also it's possible to have only 2 different areas of the faces, for example when the base is square and the height does not equals to the side of this square.

Volume of rectangular solid is Volume=Length*Height*Depth.

BACK TO THE ORIGINAL QUESTION:

What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively --> let the two adjacent faces be blue and yellow faces on the diagram --> \(blue=d*h=15\) and \(yellow=l*h=24\) --> we have 2 equations with 3 unknowns, not sufficient to calculate the value of each or the product of the unknowns (\(V=l*h*d\)).

To elaborate more: If \(blue=d*h=15*1=15\) and \(yellow=l*h=24*1=24\) then \(V=l*h*d=24*1*15=360\); If \(blue=d*h=5*3=15\) and \(yellow=l*h=8*3=24\) then \(V=l*h*d=8*3*5=90\).

Two different answer, hence not sufficient.

(2) Each of two opposite faces of the solid has area 40 --> just gives the areas of two opposite faces, so clearly insufficient.

(1)+(2) From (1): \(blue=d*h=15\), \(yellow=l*h=24\) and from (2) each of two opposite faces of the solid has area 40, so it must be the red one: \(red=d*l=40\) --> here we have 3 distinct linear equations with 3 unknowns hence we can find the values of each and thus can calculate \(V=l*h*d\). Sufficient.

To show how it can be done: multiply these 3 equations --> \(l^2*h^2*d^2=(l*h*d)^2=15*24*40=24^2*5^2\) --> \(V=l*h*d=24*5=120\).