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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 27 Jan 2008, 00:13
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What is the volume of a certain rectangular solid?

1) two adjacent faces of the solid have areas 20 and 40 respectively

2) two opposite faces of the solid has area 50.
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Re: DS - Volume of rectangular solid [#permalink] New post 27 Jan 2008, 01:42
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C

a,b,c - edges of rectangle.

ab,bc,ac - area of faces.

V=a*b*c

1. ab=20, bc=40

V=\frac{20}{b}*b*\frac{40}{b}=\frac{800}{b}

insuff.

2. ac=50. insuff.

1&2. ab*bc*ac=(abc)^2=V^2

V=\sqrt{20*40*50}=\sqrt{4*10^4}=200

suff
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Re: DS - Volume of rectangular solid [#permalink] New post 27 Jan 2008, 02:05
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sondenso wrote:
2. ac=50. insuff. "two opposite faces of the solid has area 50", does it means that 2 faces each have 50?


I confused by this statement too (as non-native speaker). But I think it does not matter here.

Area of opposites faces of rectangle are equal. Therefore, we have 50 or 25. Both values do not influence on answer.
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Re: DS - Volume of rectangular solid [#permalink] New post 27 Jan 2008, 22:55
Thank you Walker for your nice explanation.

OA is C.
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Re: DS - Volume of rectangular solid [#permalink] New post 28 Jan 2008, 12:17
+1 for this my friend..

my hunch was saying C, but I needed this scientific proof.


walker wrote:
C

a,b,c - edges of rectangle.

ab,bc,ac - area of faces.

V=a*b*c

1. ab=20, bc=40

V=\frac{20}{b}*b*\frac{40}{b}=\frac{800}{b}

insuff.

2. ac=50. insuff.

1&2. ab*bc*ac=(abc)^2=V^2

V=\sqrt{20*40*50}=\sqrt{4*10^4}=200

suff
Re: DS - Volume of rectangular solid   [#permalink] 28 Jan 2008, 12:17
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