If cube X has an edge of length e and cube Y has an edge of length e +

Question

If cube X has an edge of length e and cube Y has an edge of length e + 1, how much greater is the total surface area of cube Y than that of cube X ?

A. 12e + 6
B. 6(e + 1)2
C. e + 1
D. e
E. 1

PS21177

ChigataCOUL · Answer

Aera of cube x = 6 e²

Aera of cube Y = 6 (e+1)² = 6e²+12e +6

Difference of two aera = 6+12e

Answer A

Abhishek009 · Answer

Surface Area of a cube is  6a^2

So, Difference in the total surface area of cube Y than that of cube X is -

= 6 { ( e + 1 )^2 - e^2 }

= 6 { ( e + 1 - e ) ( e + 1 + e ) }

= 6 { (1 ) ( 2e + 1) }

= 12e + 6 , Answer must be (A)

naveenban · Answer

Option A.
TSA Cube X = 6 e^2
TSA Cube Y = 6 ( e + 1 )^2 = 6e^2 + 12e + 6.
Difference = 6e^2 + 12e + 6 - 6e^2 
12e + 6

BrentGMATPrepNow · Answer

These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach. 
The posters above have solved the question algebraically, so let's use the INPUT-OUTPUT approach.

Let's say e =  3

Cube X  
Each edge has length  3 
Since each face of the cube is a SQUARE, the area of ONE face =  3 ² = 9
So, the area of all SIX faces = (6)(9) =  54

Cube Y  
Each edge has length  3  + 1. So, each edge has length 4
Since each face of the cube is a SQUARE, the area of ONE face = 4² = 16
So, the area of all SIX faces = (6)(16) =  96

How much greater is the total surface area of cube Y than that of cube X?  
Difference =  96  -  54  =   42

So, when we INPUT e =  3 , the answer to the question (i.e., the OUTPUT) is   42

Now we'll examine each answer choice, to see which one yields and output of   42   when we replace e with  3

We get: 
A. 12( 3 ) + 6 =   42   Great! Keep. 
B. 6( 3  + 1)² =   24  . We want an output of   42  . ELIMINATE B 
C.  3  + 1 =   4  . We want an output of   42  . ELIMINATE C
D.  3  =   3  . We want an output of   42  . ELIMINATE D
E. 1 =   1  . We want an output of   42  . ELIMINATE E

Answer: A

Cheers, 
Brent

NitishJain · Answer

SA for cube = 6 * (side)^2
SA for X = 6e^2
SQ for Y = 6(e+1)^2

SA for Y - SA for X = 6(e+1)^2 - 6e^2 = 6(e^2 + 2e + 1) -6e^2 = 12e + 6

Hence  A

ScottTargetTestPrep · Answer

Solution:

The total surface area of cube Y is 6(e + 1)^2 = 6(e^2 + 2e + 1) = 6e^2 + 12e + 6.

The total surface area of cube X is 6e^2.

Therefore, the total surface area of cube Y exceeds that of cube X by 12e + 6.

Answer: A

VerbalNote · Answer

could you please explain the difference between "how much greater" and "how many greater"?

If cube X has an edge of length e and cube Y has an edge of length e +

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If cube X has an edge of length e and cube Y has an edge of length e +

Prep Toolkit

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