What is the surface area of a certain rectangle solid?

Question

1) The volume of the solid is 96
2) The one face’s area of the solid is 12

* A solution will be posted in two days.

Pritishd · Answer

Hello Math Revolution,

Below is my reasoning. Please review the same, and tell me if I have made a mistake.

Surface area of a rectangular solid = 2 LW + 2 WH + 2 HL

1. Insufficient: Does not provide information on the length, width and height
Volume = L x W x H
96 = L x W x H

2. Insufficient: Does not provide information on the other two faces by itself.
Suppose, 12 = L x W

Combining Both;
96 = 12 x H => H = 8; Insufficient: Cannot deduce the L and W

Answer: E

GMATinsight · Answer

To know the Surface Area of rectangular solid we need the dimensions of the solid

Question  : Surface Area of Solid = ?

Statement 1:  The volume of the solid is 96 
i.e. L*B*H = 96
we nee to calculate 2(LB+BH+LH) but the individual products of two sides at a time are missing hence
NOT SUFFICIENT

Statement 2:  The one face’s area of the solid is 12 
Other sides are missing hence
NOT SUFFICIENT

Combining the two statements  
L*B*H = 96 and AREA of one face = 12 
let BH= 12
i.e. L = 96/12 = 8
but BH = 12 may give us either B=2 H= 6 or B=3 H=4 giving us different values and hence different values of Area. Hence
NOT SUFFICIENT

Answer: Option E

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the surface area of a certain rectangle solid?

1) The volume of the solid is 96
2) The one face’s area of the solid is 12

There are 3 variables(length, width, height) for a rectangular solid, which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which makes E the answer.

MathRevolution · Answer

You are also right. It is simper and better to solve this way: for a rectangular, there are 3 variables(width, length, height). In order to match with the number of equations. So you need 3 equation, which makes E the answer.

bumpbot · Answer

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What is the surface area of a certain rectangle solid?

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What is the surface area of a certain rectangle solid?

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