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A rectangular solid has a surface area of 94 square inches. What is its volume?

(1) The surface area of one side of the rectangular solid is 12.

(2) The surface area of one side of the rectangular solid is 20.

2(lb+BH+lh)=94 I.e. lb+BH+lh=47

Statement 1: lb=12 Not sufficient

Statement 2: bh=20 Not sufficient

Combining lh= 47-12-20=15

Only possibility of l,b,h are 3,4,5 Hence volume = 60

Sufficient

Answer Option C
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A rectangular solid has a surface area of 94 square inches. What is its volume?

(1) The surface area of one side of the rectangular solid is 12.

(2) The surface area of one side of the rectangular solid is 20.

Great (and tricky) question!

Target question:What is the volume of the rectangular solid?

This is a good candidate for rephrasing the target question.

Let x, y, and z be the dimensions (length, width and height) of the rectangular solid. So, xyz is its volume

REPHRASED target question:What is the value of xyz?

Given: The rectangular solid has a surface area of 94 square inches Each side of the rectangular solid is a RECTANGLE. So, 2 sides have the dimensions x by y, 2 sides have the dimensions x by z, and 2 sides have the dimensions y by z So, the total surface area = 2(xy + xz + yz) = 94 Divide both sides by 2 to get: xy + xz + yz = 47

Statement 1: The surface area of one side of the rectangular solid is 12. Let's say this is the side with dimensions x by y So, xy = 12 Is this enough information to determine the value of xyz? No. We know nothing about the value of z. Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The surface area of one side of the rectangular solid is 20 Let's say this is the side with dimensions x by z So, xz = 20 For the same reason as above, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 tells us that xy = 12 Statement 2 tells us that xz = 20 We also know that xy + xz + yz = 47

NOTE: since this is system of 3 equations with 3 variables, many people will conclude that we can solve it for x, y, and z. However, that rule only applies to linear equations. In this case, the equations are quadratic equations. So, let's see if we can solve this system and find the value of xyz

Take xy + xz + yz = 47 and replace xy with 12 and xz with 20 We get: 12 + 20 + yz = 47 So, yz = 15

We now have: xy = 12, xz = 20 and yz = 15 This means that (xy)(xz)(yz) = (12)(20)(15) Simplify: x²y²z² = 3600 Rewrite as: (xyz)² = 3600 So, xyz = 60....DONE!!! Since we can answer the target question with certainty, the combined statements are SUFFICIENT

ASIDE: Some people will say that, if (xyz)² = 3600, then EITHER xyz = 60 OR xyz = -60 However, we're dealing with a real world problem here, and in the real world, the volume cannot be negative. So, we can ignore the negative solution.

Re: A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

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24 Aug 2017, 06:24

I have a different answer to this. I find each of the information suffecient. Please hear me out

Let the sides be a, b and c.

2(ab+bc+ac) = 94 Therefore, ab+bc+ac = 47.

Now, statement 1 = lets assume ab, side is 12

therefore, bc+ac = 35 (b+a).c =35 Now either b+a = 7 and c = 5 or b+a = 5, c = 7 If b+a= 7, possible values of abc are (5,2,5) (4,3,5) or (6,1,5). However, only 1 combination gives 1 side area as 12 which is the (4,3,5)

If b+a=5 possible values of abc are (3,2,7) ,(4,1,7) . Ans none of them give 12 as the area. b+a will not be 5.

Therefore, the only possible value is (3,4,5)

Similarly, I found the same value by Statement 2 and I think both are sufficient on their own.

From B: Assuming l*b=20, we have w(l+b)=27, only combination that satisfies is l & b equals 5 & 4, hence w=3. Similarly answer can be derived from A as well.

From B: Assuming l*b=20, we have w(l+b)=27, only combination that satisfies is l & b equals 5 & 4, hence w=3. Similarly answer can be derived from A as well.

We are not told that the dimensions of the solid are necessarily integers.
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Re: A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

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05 Sep 2017, 11:49

1) insufficient LB =12 H=? 2) insufficient BH = 20 L=? combine 1&2 LB=12, BH=20 total area =94 2(LB+LB+LH) =94 LB+BH+LH=47 LB=12 BH=20 so LH=15 we dont require to calculate l,b,h JUST MULTIPLY ALL LBxBHxLH= (LBH)^2 = V^2 12x20x15 = V Definite Ans C _________________

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